Saxon Math Course 1 © 2012 Common Core State Standards for

Saxon Math Course 1 © 2012 correlated to the Common Core State Standards for Mathematics, Grade 6

Dom

ain

Stan

dard

Text of Objective

Saxon Math Course 1 Citations

Description

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

1. Make sense of problems and persevere in solving them.

This standard is covered throughout the program; the following are examples.

INSTRUCTION:

New Concept: Lesson 11, pp. 58-61, Example 1-2; Lesson 13, pp. 68-70, Examples 1-3; Lesson 15, pp. 78-79; Lesson 22, pp. 117-119, Examples 1-4; Lesson 36, pp. 187-189; Lesson 50, pp. 259-261; Lesson 66, pp. 342-344; Lesson 68, pp. 349-351; Lesson 77, pp. 399-401; Lesson 105, pp. 548-550; Lesson 111, pp. 582-584

Investigation(s): Investigation 9, pp. 470-473; Investigation 10, pp. 524-527

MAINTENANCE:

Power Up: Lesson 18, p. 93; Lesson 27, p. 141; Lesson 37, p. 191; Lesson 44, p. 231; Lesson 54, p. 280; Lesson 70, p. 358; Lesson 87, p, 452; Lesson 92, p. 479; Lesson 110, p. 573

Problem Solving : Lesson 3, p. 18; Lesson 36, p. 187; Lesson 44, p. 231; Lesson 49, p. 254; Lesson 55, p. 285; Lesson 62, p. 324; Lesson 74, pp. 385; Lesson 83, p. 431; Lesson 105, p. 548

Written Practice: Lesson 11 (#1, #4), Lesson 24 (#1, #2, #3), Lesson 38 (#2, #3, #28), Lesson 50 (#3, #5), Lesson 69 (#4, #7, #24), Lesson 78 (#4, #16), Lesson 94 (#18), Lesson 110 (#13)

Performance Activity: 2

Problem solving is integrated into the Saxon Math program every day. Focusing on a four-step problem solving process, which guides students to understand, plan, solve and check, Saxon Math teaches students a consistent process for evaluating different problem solving situations and persevering in solving them. The four steps closely mirror the different aspects of this Standard for Mathematical Practice, encouraging students to understand the problem and make a plan before solving. Students also end by checking their solutions, providing opportunities to ask, “Does this make sense?” and re-direct if necessary.

In Course 1, students begin the year by focusing on problem solving in the Problem-Solving Overview on page 1 of the Student Edition. They use the four-step problem solving process outlined in the overview on daily problem solving opportunities in the Power Up. These build in complexity throughout the year. There is also a problem solving discussion guide for the teacher to guide students to make sense of the problems and use efficient strategies to persevere in solving them. Additional problem solving opportunities occur in the cumulative written practice every day. There are additional Investigations and Performance Tasks for focused activities and applications of complex problems. Many of these are hands-on and explorative in nature. The Teacher’s Manual provides support with questioning prompts, math conversations, and checks for understanding. On page 117B in the Teacher's Manual Volume 1, you will find one example of a modeled dialogue that highlights the understand, plan, solve and check process. These types of modeled dialogues are provided throughout the program to ensure teachers can support students as they become successful problem solvers.

Common Core State Standards for Mathematics© Copyright 2010, National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. 1


D

omai

n

Stan

dard

Text of Objective


Description

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

2. Reason abstractly and quantitatively.


INSTRUCTION:

New Concept: Lesson 3, pp. 18-21, Examples 1-4; Lesson 4, pp. 24-26, Examples 1-4; Lesson 16, pp. 82-84, Examples 1-5; Lesson 18, pp. 93-96, Examples 1-4; Lesson 59, pp. 306-307, Examples 1-2; Lesson 77, pp. 399-401, Examples 1-2; Lesson 95, pp. 493-494, Examples 1-2; Lesson 103, pp. 538-540; Lesson 118, pp. 617-618

Investigation: Investigation 10, pp. 524-527

MAINTENANCE:

Problem Solving: Lesson 13, p. 68; Lesson 36, p.187; Lesson 44, p. 231; Lesson 49, p. 254; Lesson 54, p. 280; Lesson 70, p. 358; Lesson 92, p. 479; Lesson 107, p. 557

Written Practice: Lesson 3 (#17, #18, #21, #24), Lesson 5 (#5, #22, #24), Lesson 16 (#7, #8, #9), Lesson 25 (#2, #23), Lesson 36 (#18, #21, #22, #23, #24), Lesson 43 (#18), Lesson 77 (#4), Lesson 78 (#4), Lesson 118 (#30)

The goal of Saxon Math is to produce mathematically proficient students – including fluency with computational and conceptual understanding. The distributed nature of Saxon Math lends itself naturally to developing abstract and quantitative reasoning. Because students are exposed to different concepts at the same time through incremental instruction and mixed practice, review, and assessment, they learn the importance of making sense of quantities and their relationships and of carefully considering the units involved. Problems do not focus simply on one concept, but rather may involve multiple concepts just as they would in real-world situations. Therefore, it is essential that students are able to make connections, think about what the quantities actually mean in a specific context, and solve appropriately.

For example, in the New Concepts portion of Lesson 4, students consider multiplication facts and how they could still be solved if one of the factors were unknown. This requires students to pause to consider how each number is being used and what it means in that particular context.



D

omai

n

Stan

dard

Text of Objective


Description

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

3. Construct viable arguments and critique the reasoning of others.


INSTRUCTION:

New Concept: Lesson 16, pp. 82-84, Examples 1-5; Lesson 51, pp. 268-270, Examples 1-3; Lesson 64, pp. 333-334; Lesson 89, pp. 460-462, Examples 1-4; Lesson 93, pp. 484-485; Lesson 97, pp. 503-505; Lesson 109, pp. 566-569, Examples 1-3

MAINTENANCE:

Problem Solving: Lesson 3, p. 18; Lesson 5, p. 28; Lesson 7, p. 36; Lesson 15, p. 78; Lesson 18, p. 93; Lesson 26, p. 136; Lesson 28, p. 145; Lesson 34, p. 178; Lesson 43, p. 225; Lesson 56, p. 289; Lesson 64, p. 333; Lesson 72, p. 375; Lesson 83, p. 431; Lesson 99, p. 513; Lesson 103, p. 538; Lesson 110, p. 573; Lesson 117, p. 612

Written Practice: Lesson 17 (#3, #4, #12, #13), Lesson 22 (#3, #8, #13, #22), Lesson 53 (#5, #12, #13), Lesson 59 (#6, #7, #24, #25), Lesson 62 (#7, #8, #9, #10, #11), Lesson 91 (#9), Lesson 93 (#15, #25)

Performance Activity: 2, 8, 14

Saxon Math is based on the belief that people learn by doing. Students learn mathematics not only by watching or listening to others, but by communicating and solving the problems themselves and with their classmates. Saxon Math’s incremental and distributed structure enables students to view the big picture of mathematics and therefore make viable arguments between and among all of the math strands. Additionally, Math Conversations in the Teacher's Manuals provide discussion questions that help students construct viable arguments and critique the reasoning of others in a constructive environment. For example, on page 11 of the Teacher's Manual Volume 1, several Math Conversations are provided. Teachers ask students questions like "Why was addition used to find the answer?" This gives students the opportunity to express their reasoning and respond to the reasoning of others.



D

omai

n

Stan

dard

Text of Objective


Description

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

4. Model with mathematics. This standard is covered throughout the program; the following are examples.

INSTRUCTION:

New Concept: Lesson 1, pp. 8-10, Examples 1-6; Lesson 26, pp. 136-139, Examples 1-5; Lesson 83, pp. 431-433, Examples 1-3; Lesson 98, pp. 508-510; Examples 1-2; Lesson 117, pp. 612-614, Examples 1-2

Investigation(s) Investigation 2, pp.109-111; Investigation 6, pp. 314-319; Investigation 11, pp. 578-581

MAINTENANCE:

Problem Solving: Lesson 10, p. 50; Lesson 17, p. 87; Lesson 24, p. 127; Lesson 30, p. 156; Lesson 34, p. 178; Lesson 39, p. 200; Lesson 70, p. 358; Lesson 78, p. 404; Lesson 98, p. 508; Lesson 117, p. 612

Written Practice Lesson 28 (#9, #10, #16, #22, #24, #25, #27), Lesson 31 (#4, #5, #8, #17, #28, #29), Lesson 43 (#27, #29, #30), Lesson 52 (#19, #20, #25, #27, #30), Lesson 69 (#1, #17, #26, #30), Lesson 77 (#4, #5, #19, #20), Lesson 81 (#7, #8, #21, #22, #30), Lesson 90 (#4, #9, #10, #23, #30), Lesson 110 (#3, #4, #8, #23, #24, #30)

Performance Activity: 6, 10

Students use many different types of models throughout Saxon Math to analyze mathematical relationships and solve problems. Models serve as visual aids to help make sense of situations so students truly understand the problem at hand and both how and why their solutions work.

For example, in Lesson 26, students use fraction manipulatives to model fractions. This allows them to concretely see and experience the fractions and gain a better understanding of what they mean.



D

omai

n

Stan

dard

Text of Objective


Description

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

5. Use appropriate tools strategically. This standard is covered throughout the program; the following are examples.

INSTRUCTION:

New Concept: Lesson 7, pp. 37-39, Examples 1-3; Lesson 10, pp. 50-52, Examples 2-3; Lesson 17, pp. 88-90, Examples 1-2; Lesson 27, pp. 141-143; Lesson 48, pp. 250-252; Lesson 61, pp. 320-321; Lesson 62, pp. 324-326


MAINTENANCE:

Problem Solving: Lesson 10, p. 50

Written Practice: Lesson 7 (#24, #25, #30), Lesson 10 (#4, #30), Lesson 13 (#22), Lesson 17 (#11, #30), Lesson 19 (#8, #29), Lesson 22 (#25), Lesson 31 (#24), Lesson 46 (#28), Lesson 57 (#24, #25), Lesson 71 (#23, #24), Lesson 81 (#25), Lesson 107 (#29), Lesson 110 (#26)


Saxon Math provides and supports grade level appropriate tools for instruction and problem solving. This begins with concrete models at the primary levels and moves to more sophisticated tools like geometry software at the secondary levels. Saxon offers instruction and guidance for appropriate usage throughout the program.

For example, in Lesson 7, students learn about lines, segments and rays and practice measuring with an inch ruler and a centimeter ruler, strategically selecting tools with appropriate units to measure different lengths.



Dom

ain

Stan

dard

Text of Objective


Description

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

6. Attend to precision. This standard is covered throughout the program; the following are examples.

INSTRUCTION:

New Concept: Lesson 7, pp. 37-39, Examples 1-3; Lesson 8, pp. 42-44, Examples 1-2; Lesson 10, pp. 50-52, Examples 1-3; Lesson 28, pp. 145-148, Examples 1-2; Lesson 31, pp. 164-166, Examples 1-3; Lesson 32, pp. 169-171, Examples 1-4; Lesson 60, pp. 310-312, Examples 1-3; Lesson 69, pp. 353-355, Examples 1-2; Lesson 78, pp. 404-405, Examples 1-2; Lesson 81, pp. 421-423, Examples 1-4; Lesson 90, pp. 465-467, Examples 1-3; Lesson 102, pp. 533-535, Examples 1-2; Lesson 113, pp. 592-594, Examples 1-4; Lesson 120, pp. 626-627

Investigation(s): Investigation 3, pp.161-163; Investigation 11, pp. 578-581; Investigation 12, pp. 630-636

MAINTENANCE:

Written Practice: Lesson 8 (#4, #16, #25), Lesson 10 (#1, #3, #4), Lesson 11 (#1, #4, #5), Lesson 12 (#1, #2, #3, #5), Lesson 13 (#12, #18, #22), Lesson 15 (#8, #9, #22), Lesson 31 (#4, #5, #6), Lesson 36 (#8, #10), Lesson 45 (#23), Lesson 71 (#24, #30)

Saxon students are encouraged to attend to precision throughout the program, both directly in their student materials and indirectly through teacher tips in the Teacher’s Manual. Additionally, because practice, review and assessment are mixed, it is especially important that students precisely identify units and symbols to accurately assess how to solve the problem correctly. Not all questions will cover the same concept, so students learn to look carefully at each situation and attend to precision in their answers.

For example, in Lesson 7, students measure with both inches and centimeters and must attend to precision to apply the appropriate units to their solutions. Example 3 explicitly addresses this concept, pointing out how different units can be used to measure the same things but certain units are more appropriate than others.



D

omai

n

Stan

dard

Text of Objective


Description

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

7. Look for and make use of structure. This standard is covered throughout the program; the following are examples.

INSTRUCTION:

New Concept: Lesson 5, pp. 29-30, Examples 1-3; Lesson 12, pp. 64-66, Examples 1-5; Lesson 21, pp. 112-114, Examples 1-3; Lesson 24, pp. 127-129, Examples 1-5; Lesson 25, pp. 132-134, Examples 1-5; Lesson 32, pp. 169-171, Examples 1-4; Lesson 34, pp. 178-180, Examples 1-2; Lesson 43, pp. 225-228, Examples 1-4; Lesson 44, pp. 231-233, Examples 1-3; Lesson 46, pp. 239-242, Examples 1-5; Lesson 52, pp. 272-273, Examples 1-2; Lesson 65, pp. 337-340, Examples 1-2; Lesson 67, pp. 346-347; Lesson 72, pp. 375-376; Lesson 84, pp. 437-438; Lesson 92, pp. 479-481, Examples 1-3; Lesson 113, pp. 592-594, Examples 1-4

MAINTENANCE:

Written Practice: Lesson 5 (#9, #10, #11, #12), Lesson 15 (#23), Lesson 46 (#4, #10, #12), Lesson 48 (#4, #5, #13), Lesson 52 (#4), Lesson 85 (#23), Lesson 90 (#27), Lesson 93 (#10, #26), Lesson 94 (#8, #14)

Saxon Math emphasizes structure throughout the program, explicitly teaching number properties as well as how concepts connect. A strong focus on number properties also prepares students to utilize structure in problem-solving situations. Because the fundamentals of numbers and operations are highlighted in every lesson through mixed review, students develop a strong sense of mental math and comfort composing and decomposing numbers.

For example, in the problem solving section of Lesson 12, students are asked to consider ways to calculate the sum of the first ten natural numbers. Going through the four-step problem solving process, they identify the need to make the problem simpler. Students then discover that adding certain pairs of numbers together uncovers a pattern that helps solve the problem. For example, 1 plus 10, 2 plus 9, 3 plus 8, and so on all equal 11. This allows students to see that adding the first ten natural numbers is the same thing as multiplying 11 times five, uncovering how structure can be used to make problem solving easier.



D

omai

n

Stan

dard

Text of Objective


Description

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

8. Look for and express regularity in repeated reasoning.


INSTRUCTION:

New Concept: Lesson 10, pp. 50-52, Examples 1-3; Lesson 22, pp. 117-119, Examples 1-5; Lesson 25, pp. 132-134, Examples 1-5; Lesson 29, pp. 150-154, Examples 1-7; Lesson 33, pp. 174-175, Examples 1-2; Lesson 35, pp. 182-185, Examples 1-6; Lesson 42, pp. 222-223, Examples 1-2; Lesson 46, pp. 240-242, Examples 1-5; Lesson 55, pp. 285-287; Lesson 56, pp. 289-292, Examples 1-4; Lesson 57, pp. 295-296, Examples 1-2; Lesson 63, pp. 329-330; Lesson 74, pp. 385-387, Examples 1-4; Lesson 75, pp. 390-392, Examples 1-6; Lesson 76, pp. 395-396, Examples 1-2; Lesson 85, pp. 441-443, Examples 1-4; Lesson 94, pp. 488-490, Examples 1-4; Lesson 99, pp. 513-514; Lesson 112, pp. 587-589; Lesson 115, pp. 602-603; Lesson 116, pp. 606-608; Lesson 117, pp. 612-614, Examples 1-2

MAINTENANCE:

Problem Solving: Lesson 1, p.7; Lesson 4, p. 23; Lesson 11, p. 58; Lesson 12, p. 63; Lesson 16, p. 82; Lesson 80, p. 413; Lesson 94, p. 488; Lesson 102, p. 533; Lesson 109, p. 566

Written Practice: Lesson 10 (#1, #3, #4), Lesson 22 (#4, #5, #6), Lesson 23 (#2, #5, #6, #13), Lesson 31 (#1, #3, #8), Lesson 43 (#4, #5, #17), Lesson 48 (#2, #13, #14), Lesson 117 (#21, #25), Lesson 118 (#3, #11, #26)

Regularity and repeated reasoning are supported throughout Saxon Math program to ensure students understand their importance and how they can be used to solve problems. Repeated reasoning scenarios allow students to make better sense of number and operations.

In Course 1, the daily Power Up provides practice and support with mental math, problem solving, and number sense. Students build strong generalization, problem solving strategies, and reasoning skills with this daily reinforcement. They are able to see patterns and connections between number concepts through an algebraic perspective, particularly with ratios, algebraic expressions, and proportions. Concepts are introduced through examples and explanation, connecting back to previous mastered concepts. This aids in students’ ability to look for repeated reasoning and maintain an oversight of processes. This guides student’s conceptual understanding and facilitates deep connections between all math strands. There are further Investigations and Performance Tasks giving students additional opportunities for seeing and communicating reasonableness of solutions.

An example of expressing regularity in repeated reasoning can be found in Lesson 46. Students explore the idea that whenever they multiply by a power of ten, it corresponds to a shift in the decimal point. This repeated reasoning can be simplified into a rule that aids in problem solving.



D

omai

n

Stan

dard

Text of Objective

Saxon Math Course 1 Citations/Examples References in italics indicate foundational.

6.R

P R

atio

s and

Pro

port

iona

l Rel

atio

nshi

ps

Understand ratio concepts and use ratio reasoning to solve problems.

In Course 1, students learn how to solve to a wide variety of ratio and rate problems. In the beginning of the book in Lesson 23 the students are introduced to the basics of a ratio or rate problem so that by Lesson 80 they are able to solve real world mathematical problems and can describe the relationship between the two quantities. As the year progresses students are able to find the missing values in tables, (Lesson 88) they can plot pairs of values on a coordinate plane, (Lesson 96) are able to work with Unit Multipliers (Lesson 114) and can solve problems to find the percent of a quantity as a rate (Lesson 119). Students are able to practice solving rate or ratio problems in the mental math portion of the power-up, the problem solving problems, the frequent practice sets, and are given cumulative assessments throughout the year to ensure mastery.

6.R

P.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

INSTRUCTION:

New Concept: Lesson 23, pp. 122-123, Examples 1-2

MAINTENANCE:

Problem Solving: Lessons 36, 57, 87, 91, 118

Written Practice: Lesson 23 (#26, #30); Lesson 24 (#9); Lesson 25 (#17); Lesson 28 (#28); Lesson 30 (#6); Lesson 31 (#22); Lesson 32 (#23); Lesson 35 (#30); Lesson 39 (#30); Lesson 44 (#23); Lesson 54 (#19, #23); Lesson 57 (#18); Lesson 61 (#19); Lesson 82 (#21); Lesson 84 (#1, #30)); Lesson 90 (#26); Lesson 98 (#29); Lesson 103 (#5); Lesson 104 (#3); Lesson 109 (#3); 118 (#6)

6.R

P.2

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 1 1Expectations for unit rates in this grade are limited to non-complex fractions.

INSTRUCTION:


MAINTENANCE:

Problem Solving: Lessons 78, 91

Written Practice: Lesson 23 (#4); Lesson 24 (#18); Lesson 26 (#23); Lesson 28 (#13); Lesson 30 (#3); Lesson 32 (#3, #30); Lesson 98 (#29); Lesson 107 (#3)



D

omai

n

Stan

dard

Text of Objective


6.R

P R

atio

s and

Pro

port

iona

l Rel

atio

nshi

ps

6.R

P.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,

double number line diagrams, or equations.

6.R

P.3a

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

INSTRUCTION:

New Concept: Lesson 80, p. 423, Example 4; Lesson 88, pp. 456-458, Examples 1-2; Lesson 96, pp. 497-501, Examples 1-3; Lesson 101, pp. 528-530, Example 1

Standards Success Activity: Activity 8

MAINTENANCE:

Written Practice: Lesson 88 (#5); Lesson 89 (#4); Lesson 91 (#3); Lesson 93 (#1); Lesson 101 (#1); Lesson 103 (#6); Lesson 117 (#28)

6.R

P.3b

Solve unit rate problems including those involving unit pricing and constant speed.

INSTRUCTION:


MAINTENANCE:

Problem Solving: Lessons 57, 78, 91, 118

Written Practice: Lessons 23 (#4); Lesson 24 (#18); Lesson 26 (#23); Lesson 28 (#13); Lesson 30 #3); Lesson 32 (#3, #30)

6.R

P.3c

Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

INSTRUCTION:

New Concept: Lesson 41, pp. 216-219, Examples 1-5; Lesson 119, pp. 621-623, Examples 1-2

MAINTENANCE:

Written Practice: Lesson 41 (#1, #2, #4, #18, #19, #30); Lesson 43 (#1); Lesson 44 (#10); Lesson 71 (#14); Lesson 77 (#22, #23); Lesson 119 #10)



D

omai

n

Stan

dard

Text of Objective


6.R

P R

atio

s and

Pro

port

iona

l Rel

atio

nshi

ps

6.R

P.3d

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

INSTRUCTION:


MAINTENANCE:

Power Up: Lessons 2, 8, 12, 16, 23, 41, 55, 63, 79, 97, 105

Written Practice: Lesson 114 (#6, #26); Lesson 116 (#15); Lesson 118 (#17); Lesson 120 (#17)



D

omai

n

Stan

dard

Text of Objective


6.N

S T

he N

umbe

r Sy

stem

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

The groundwork that Saxon Math laid in earlier grade levels in multiplication, division, and working with fractions creates a straightforward transition for the students to be able to divide fractions by fractions. In Course 1, students are shown, using visual fraction models, how to divide using fractions and are able to interpret and compute quotients of fractions (Lesson 54). Throughout the school year, the students are able to practice word problems about dividing fractions by fractions in the written practice problems and the teacher can ensure mastery by the results of the cumulative assessments.

6.N

S.1

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

INSTRUCTION:


MAINTENANCE:

Written Practice: Lesson 54 (#22), Lesson 55 (#24), Lesson 56 (#28), Lesson 57 (#57), Lesson 58 (#19), Lesson 59 (#10), Lesson 60 (#8), Lesson 62 (#1), Lesson 69 (#2), Lesson 72 (#27)

Compute fluently with multi-digit numbers and find common factors and multiples.

Learning how to find the Greatest Common Factor and Least Common Multiple is a tool that students will need for Algebra. Lesson 20 teaches the students how to find the greatest common factor of any two numbers and how to use the distributive property to express the sum of two whole numbers with a common factor with a sum of two whole numbers without a common factor. In Lesson 30, students are taught how to find the least common multiple of any two numbers. Saxon Math uses the standard algorithms to teach students addition, subtraction, multiplication, and division. In Course 1, students are immersed in working with multi-digit decimal problems for each operation and are giving ample practice problems in both power-up and written practice to ensure mastery. This standard is repeatedly practiced in the practice set and assessed in the cumulative assessment throughout the year to ensure a deep level of mathematical understanding.



D

omai

n

Stan

dard

Text of Objective


6.N

S T

he N

umbe

r Sy

stem

6.N

S.2

Fluently divide multi-digit numbers using the standard algorithm.

INSTRUCTION:


MAINTENANCE:

Power Up: Lesson 31, p. 164; Lesson 32, p.169; Lesson 33, p. 174; Lesson 35, p. 182; Lesson 36, p. 187; Lesson 37, p. 191; Lesson 39, p. 200; Lesson 40, p. 205; Lesson 41, p. 216; Lesson 42, p. 221; Lesson 46, p. 239; Lesson 49, p. 254; Lesson 50, p. 259; Lesson 53, p. 276; Lesson 55, p. 285

Written Practice: Lesson 2 (#1, #8, #30), Lesson 3 (#1, #4, #5, #7), Lesson 4 (#1, #2, #6, #17), Lesson 9 (#1, #3, #13), Lesson 12 (#21, #22, #24), Lesson 16 (#12, #13, #17), Lesson 18 (#8, #9, #10), Lesson 20 (#10, #13, #14), Lesson 22 (11, #12), Lesson 30 (#20), Lesson 31 (#15, #16, #17), Lesson 33 (#12, #13), Lesson 37 (#13, #14)

6.N

S.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

INSTRUCTION:

New Concept: Lesson 37, p. 192, Examples 1-2; Lesson 38, pp. 195-198, Examples 1-2; Lesson 39, pp. 200-202, Examples 1-3; Lesson 40, p. 205-208, Examples 1-3; Lesson 45, pp. 235-236, Examples 1-3; Lesson 46, pp. 240-242, Examples 2-5; Lesson 49, pp. 254-256, Examples 1-2; Lesson 53, pp. 276-277

MAINTENANCE:

Power Up: Lesson 15, p. 78; Lesson 19, p. 99; Lesson 23, p. 122; Lesson 26, p. 136; Lesson 32, p. 169; Lesson 36, p. 187; Lesson 40, p. 205; Lesson 44, p. 231; Lesson 47, p. 244; Lesson 52, p. 272; Lesson 61, p. 320; Lesson 71, p. 368; Lesson 72, p. 375; Lesson 75, p. 390; Lesson 82, p. 426; Lesson 98, p. 508; Lesson 99, p. 513; Lesson 100, p. 517; Lesson 101, p. 528; Lesson 102, p. 533; Lesson 103, p. 538; Lesson 105, p. 548

Written Practice: Lesson 37 (#4, #5), Lesson 39 (#4, #5, #6, #7, #8, #9), Lesson 42 (#7), Lesson 45 (#4, #5, #6, #15, #17), Lesson 47 (#9, #10, #22, #23, #30), Lesson 49 (#1, #3, #6, #7, #8, #9, #10, #11), Lesson 51 (#2, #7, #9, #10, #15, #46), Lesson 53 (#8, #9, #10), Lesson 55 (#7, #8, #9, #10), Lesson 57 (#10, #15), Lesson 76 (#16, #17), Lesson 88 (#15, #16), Lesson 103 (#13), Lesson 115 (#15)



D

omai

n

Stan

dard

Text of Objective


6.N

S T

he N

umbe

r Sy

stem

6.N

S.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

INSTRUCTION:



MAINTENANCE:

Written Practice: Lesson 20 (#8), Lesson 21 (#13), Lesson 23 (#21), Lesson 24 (#21), Lesson 26 (#10, #15), Lesson 28 (#19), Lesson 30 (#5), Lesson 32 (#24), Lesson 36 (#20), Lesson 38 (#1, #14), Lesson 39 (#15), Lesson 42 (#12), Lesson 43 (#24)

Apply and extend previous understandings of numbers to the system of rational numbers.

Students in Course 1 extend their previous knowledge of the number line to include all rational numbers in particular negative integers. Additionally, Lesson 14 allows the students to rationalize and evaluate absolute values. In Investigation 7, students are able to locate points in all four quadrants of the coordinate plane and are able to analyze the placing of the coordinates. In Investigation 14, students are able to work with real-world mathematical problems to be able understand the value of learning how to solve problems using coordinate planes. Throughout the year, the series incorporates numerous times for the students to practice these standards in the power up and in the written practice. Furthermore, cumulative assessments are given to observe mastery.



D

omai

n

Stan

dard

Text of Objective


6.N

S T

he N

umbe

r Sy

stem

6.N

S.5

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

INSTRUCTION:

New Concept: Lesson 14, pp. 73-75, Example 2; Lesson 100, pp. 517-21, Examples 3-5; Lesson 104, pp. 543-545

MAINTENANCE:

Written Practice: Lesson 14 (#29), Lesson 15 (#7, #9, #30), Lesson 19 (#3), Lesson 22 (#22), Lesson 29 (#15, #23), Lesson 43 (#16), Lesson 48 (#21), Lesson 57 (#25), Lesson 62 (#22), Lesson 63 (#2), Lesson 71 (#2), Lesson 72 (#3), Lesson 85 (#2), Lesson 87 (#24), Lesson 94 (#25), Lesson 101 (#7, #8, #58), Lesson 105 (#5, #25)

6.N

S.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to

represent points on the line and in the plane with negative number coordinates.

6.N

S.6a

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., – (–3) = 3, and that 0 is its own opposite.

INSTRUCTION:


MAINTENANCE:

Written Practice: Lesson 14 (#29), Lesson 15 (#7, #9, #30), Lesson 100 (#4, #5, #6), Lesson 101 (#7, #8, #58), Lesson 105 (#5, #25), Lesson 114 (#20)



D

omai

n

Stan

dard

Text of Objective


6.N

S T

he N

umbe

r Sy

stem

6.N

S.6b

Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

INSTRUCTION:



MAINTENANCE:

Written Practice: Lesson 71 (#15, #16), Lesson 73 (#26, #27), Lesson 77 (#27), Lesson 84 (#29), Lesson 88 (#25), Lesson 91 (#28, #29), Lesson 110 (#27), Lesson 114 (#27)

6.N

S.6c

Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

INSTRUCTION:



MAINTENANCE:

Written Practice: Lesson 14 (#4, #5, #6, #12, #29), Lesson 15 (#6), Lesson 34 (#23), Lesson 35 (#25), Lesson 43 (#16), Lesson 46 (#23), Lesson 62 (#22), Lesson 71 (#15, #16), Lesson 73 (#26, #27), Lesson 77 (#27), Lesson 78 (#27), Lesson 87 (#24, #30), Lesson 90 (#30), Lesson 98 (#21), Lesson 100 (#4), Lesson 102 (#29), Lesson 118 (#28)

6.N

S.7 Understand ordering and absolute value of rational numbers.



D

omai

n

Stan

dard

Text of Objective


6.N

S T

he N

umbe

r Sy

stem

6.N

S.7a

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

INSTRUCTION:

New Concept: Lesson 9, pp. 46-48, Examples 1-3; Lesson 14, pp. 73-75, Examples 1-3, 4-5

MAINTENANCE:

Written Practice: Lesson 9 (#8, #9, #10, #26, #28), Lesson 10 (#7), Lesson 12 (#8), Lesson 14 (#4, #5, #8, #12, #25), Lesson 19 (#3, #20), Lesson 21 (#10), Lesson 23 (#20)

6.N

S.7b

Write, interpret, and explain statements of order for rational numbers in real-world contexts.

INSTRUCTION:

New Concept: Lesson 9, pp. 46-48; Lesson 14, pp. 73-75

MAINTENANCE:

Written Practice: Lesson 9 (#26, #30), Lesson 15 (#6, #9), Lesson 20 (#5), Lesson 22 (#7)

6.N

S.7c

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

INSTRUCTION:


6.N

S.7d

Distinguish comparisons of absolute value from statements about order.

INSTRUCTION:




D

omai

n

Stan

dard

Text of Objective


6.N

S T

he N

umbe

r Sy

stem

6.N

S.8

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

INSTRUCTION:





D

omai

n

Stan

dard

Text of Objective


6.E

E E

xpre

ssio

ns a

nd E

quat

ions

Apply and extend previous understandings of arithmetic to algebraic expressions.

Students in Course 1 are able to write and evaluate numerical expressions involving exponents. In Lesson explains how to work with exponents greater than 2 and in Lesson 92 the students are able to use exponents in expanded notation and are able to fully understand the order of operations by having problems with exponents in them. Throughout Saxon Math, students are able to practice working with exponents in mental math and in written practice. The teacher can ensure mastery of the concept in the cumulative assessments offered throughout the series.

6.E

E.1

Write and evaluate numerical expressions involving whole-number exponents.

INSTRUCTION:


MAINTENANCE:

Written Practice: Lesson 73 (#8, #13, #24, #28), Lesson 74 (#8), Lesson 75 (#26), Lesson 79 (#8, #23), Lesson 82 (#24), Lesson 84 (#19), Lesson 92 (#6), Lesson 93 (#8, #9, #10, #20), Lesson 94 (#8, #28), Lesson 104 (#17, #20), Lesson 113 (#16)

6.E

E.2

Write, read, and evaluate expressions in which letters stand for numbers.

6.E

E.2

a

Write expressions that record operations with numbers and with letters standing for numbers.

INSTRUCTION:

New Concept: Lesson 3, pp. 18-21, Examples 1-4; Lesson 4, pp. 24-26, Examples 1-4; Lesson 11, pp. 58-61, Examples 1-2; Lesson 15, pp. 78-79

MAINTENANCE:

Written Practice: Lesson 3 (#17, #18, #19, #20, #21), Lesson 4 (#7, #8, #9, #10, #11), Lesson 5 (#5, #22, #23, #24, #25), Lesson 8 (#18, #21, #22, #23, #24), Lesson 9 (#20, #21, #22, #23, #29), Lesson 11 (#7, #8, #9, #10, #14), Lesson 12 (#6, #11, #12, #22, #23), Lesson 13 (#20, #27, #28, #29, #30), Lesson 14 (#17, #19), Lesson 15 (#4, #17, #18, #19, #20), Lesson 19 (#16, #17, #), Lesson 21 (#18, #19), Lesson 27 (#3, #7), Lesson 28 (#3, #3)



D

omai

n

Stan

dard

Text of Objective


6.E

E E

xpre

ssio

ns a

nd E

quat

ions

6.E

E.2

b

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

INSTRUCTION:

New Concept: Lesson 2, pp. 12-16, Example 2; Lesson 3, pp. 18-20, Example 2; Lesson 12, pp. 12-13, Example 5; Lesson 19, pp. 99-102, Examples 1-2; Lesson 87, pp. 452-453, Examples 1-3

Standards Success Activity: Activity 10A

MAINTENANCE:

Written Practice: Lesson 2 (#1, #3, #5, #24), Lesson 3 (#1, #27, #30), Lesson 11 (#2, #21), Lesson 14 (#1), Lesson 17 (#1), Lesson 19 (#9, #10, #18), Lesson 37 (#28), Lesson 42 (#28)

6.E

E.2

c

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

INSTRUCTION:

New Concept: Lesson 13, pp. 68-70, Examples 1-3; Lesson 47, pp. 246-247; Lesson 82, pp. 426-429, Examples 1-3; Lesson 91, pp. 474-476

Standards Success Activity: Activity 9, Activity 10B

MAINTENANCE:

Written Practice: Lesson 84 (#26); Lesson 86 (#29), Lesson 87 (#19); Lesson 88 (#6); Lesson 99 (#5)




D

omai

n

Stan

dard

Text of Objective


6.E

E E

xpre

ssio

ns a

nd E

quat

ions

6.E

E.3

Apply the properties of operations to generate equivalent expressions.

INSTRUCTION:

New Concept: Lesson 1, pp. 7-10, Example 5; Lesson 2, pp. 12-16, Example 4; Lesson 5, pp. 29-30

Standards Success Activity : Activity 10A

MAINTENANCE:

Problem Solving: Lesson 114, p. 597; Lesson 116, p. 606

Written Practice: Lesson 2 (#21, #22, #23, #26), Lesson 3 (#25, #26, #28), Lesson 6 (#27, #28, #29), Lesson 7 (#23, #26), Lesson 8 (#14, #15), Lesson 11 (#26, #29), Lesson 13 (#23, #26), Lesson 19 (#18)

6.E

E.4

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

INSTRUCTION:


Reason about and solve one-variable equations and inequalities.

Throughout Course 1, students are able to work with solving equations using the order of operations. Students are able to name all parts of an equation using mathematical terms, (sum, difference, product, and quotient) and are able to evaluate variables in mathematical expressions. Starting in Lesson 3, students are able to solve simple one step equations with one variable in the question. In Lesson 9 students are able to write, solve and graph inequalities and in Lesson 15 the student can solve real world mathematical problems that have one variable in the problem. With Saxon’s cumulative review each day the students are able to practice past concepts learned throughout the year and teachers can easily monitor student progress with Power Up, cumulative review and cumulative tests included in the program, again ensuring that students develop a high level of mathematical understanding.



Dom

ain

Stan

dard

Text of Objective


6.E

E E

xpre

ssio

ns a

nd E

quat

ions

6.E

E.5

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

INSTRUCTION:

New Concept: Lesson 3, pp. 18-21, Examples 1-4; Lesson 4, pp. 24-26, Examples 1-4; Lesson 106, p. , Examples


MAINTENANCE:

Power Up: Lesson 87, p. 452; Lesson 92, p. 479; Lesson 93, p. 484; Lesson 94, p. 488; Lesson 95, p. 493

Problem Solving : Lesson 114, p. 597; Lesson 116, p. 606; Lesson 118, p. 617; Lesson 119, p. 621

Written Practice Lesson 3 (#17, #18, #19, #20, #21), Lesson 4 (#7, #8, #9, #10, #11), Lesson 5 (#5, #17, #22, #23, #24), Lesson 6 (#18, #19, #20, #21, #22), Lesson 7 (#14, #20, #21, #22, #27), Lesson 9 (#20, #21, #22, #24, #29), Lesson 11 (#7, #8, #9, #10, #14), Lesson 12 (#6, #11, #12, #22, #23), Lesson 13 (#20, #27, #28, #29, #30), Lesson 14 (#17, #19), Lesson 16 (#57, #28, #29), Lesson 17 (#12, #13, #14, #15), Lesson 18 (#15, #16, #17), Lesson 20 (#16, #17, #18, #19, #20), Lesson 21 (#18, #19), Lesson 24 (#24, #25, #26, #27), Lesson 29 (#16, #17, #18), Lesson 33 (#20), Lesson 41 (#21, #22, #24), Lesson 97 (#22)



D

omai

n

Stan

dard

Text of Objective


6.E

E E

xpre

ssio

ns a

nd E

quat

ions

6.E

E.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

INSTRUCTION:

New Concept: Lesson 3, pp. 18-21, Examples 1-4; Lesson 4, pp. 24-26, Examples 1-4; Lesson 11, pp. 58-61, Examples 1-2; Lesson 15, pp. 78-79; Lesson 88, p. 456-458, Examples 1-2

MAINTENANCE:


Problem Solving: Lesson 114, p. 597; Lesson 116, p. 606; Lesson 118, p. 617; Lesson 119, p. 621

Written Practice: Lesson 3 (#17, #18, #19, #20, #21), Lesson 5 (#5, #4, #22, #23, #24), Lesson 9 (#20, #21, #22, #23, #29), Lesson 12 (#6, #11, #12, #22, #26), Lesson 16 (#21, #27, #28, #29), Lesson 18 (#15, #16, #17), Lesson 22 (#8, #9), Lesson 29 (#16, #17, #18), Lesson 37 (#3, #7), Lesson 41 (#5, #6, #21, #22, #24), Lesson 74 (#20), Lesson 87 (#1)

6.E

E.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

INSTRUCTION:

New Concept: Lesson 3, pp. 18-21, Example 2; Lesson 4, pp. 24-26, Examples1-2; Lesson 15, pp. 78-79; Lesson 87, pp. 452-453, Examples 1-3; Lesson 106, pp. 553-554, Examples 1-2

MAINTENANCE:

Problem Solving: Lesson 114, p. 597; Lesson 116, p. 606; Lesson 118, p. 617; Lesson 119, p. 621

Written Practice: Lesson 87 (#4, #5, #7), Lesson 88 (#3, #7, #8), Lesson 89 (#87, #21), Lesson 90 (#8), Lesson 91 (#20), Lesson 96 (#22, #23), Lesson 98 (#11)



D

omai

n

Stan

dard

Text of Objective


6.E

E E

xpre

ssio

ns a

nd E

quat

ions

6.E

E.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

INSTRUCTION:


ASSESSMENT:

Standards Success Extension Test: Extension Test 1

Represent and analyze quantitative relationships between dependent and independent variables.

Students in Course 1 are able write and examine an equation with two variables to represent a relationship between the dependent and independent variables (Lesson 96). They are able to create tables such as function boxes and are able to describe the relationship between the quantities. Throughout the cumulative practice, review, and tests the students are able to master this concept to be ready to move on to seventh grade.

6.E

E.9

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

INSTRUCTION:



MAINTENANCE:

Written Practice: Lesson 96 (#12), Lesson 97 (#3), Lesson 99 (#30), Lesson 102 (#25), Lesson 105 (#28), Lesson 109 (#16), Lesson 114 (#30), Lesson 118 (#23), Lesson 119 (#22)

Performance Activity 20



D

omai

n

Stan

dard

Text of Objective


6.G

Geo

met

ry

Solve real-world and mathematical problems involving area, surface area, and volume.

In Course 1 students are able to apply the techniques taught on area, surface area, and volume to solve real world mathematical problems. In Investigation 6, students learn how to break apart polygons and three dimensional shapes to be able to find the area and surface area. In Investigation 7, students are able to plot polygons on coordinate planes and work towards construction of scale drawings for seventh grade. Throughout the school year the students are able to discuss, develop and justify formulas used to find the area and volume of shapes by completing the written practices, extension activities, and investigations. The teacher can ensure mastery by having the students complete the cumulative and benchmark assessments

6.G

.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

INSTRUCTION:



MAINTENANCE:

Power Up: Lesson 32, p. 169; Lesson 33, p. 174; Lesson 45 p. 235


Written Practice Lesson 79 (#7), Lesson 80 (#4, #5), Lesson 81 (#7), Lesson 83 (#23), Lesson 84 (#5, #6, #9), Lesson 89 (#9, #10), Lesson 90 (#9), Lesson 94 (#23), Lesson 100 (#22), Lesson 106 (#27), Lesson 113 (#17, #24), Lesson 115 (#18, #27), Lesson 116 (#1, #18), Lesson 118 (#18), Lesson 119 (#17)



D

omai

n

Stan

dard

Text of Objective


6.G

Geo

met

ry

6.G

.2

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

INSTRUCTION:



MAINTENANCE:

Written Practice: Lesson 82 (#27), Lesson 84 (#26), Lesson 85 (#26), Lesson 86 (#5), Lesson 87 (#18), Lesson 88 (#6), Lesson 91 (#23), Lesson 93 (#4), Lesson 98 (#14)

6.G

.3

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

INSTRUCTION:


MAINTENANCE:

Written Practice: Lesson 75 (#27), Lesson 76 (#27), Lesson 77 (#27), Lesson 82 (#26), Lesson 88

6.G

.4

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

INSTRUCTION:


MAINTENANCE:

Problem Solving: Lesson 70, p. 358

Written Practice: Lesson 64 (#21, #22), Lesson 74 (#15, #27, #28)



D

omai

n

Stan

dard

Text of Objective


6.SP

Sta

tistic

s and

Pro

babi

lity

Develop understanding of statistical variability.

In Investigation 1 of Course 1, students study the process of data collection. Through this investigation students are able to answer a statistical question and are able to describe the distribution by its center, spread and overall shape. In Investigation 5, students are able to recognize the difference between the measure of center and measure of variability. Statistical variation questions are continuously practiced and reviewed throughout the year and appear both on the practice sets and cumulative tests to ensure deep and long-lasting understanding.

6.SP

.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

INSTRUCTION:



MAINTENANCE:

Written Practice: Lesson 89 (#23, #24, #25)

6.SP

.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

INSTRUCTION:

Investigation(s): Investigation 1, pp. 54-57; Investigation 4, pp. 211-215; Investigation 5, pp. 264-267

Standards Success Activity: Activity 5B

MAINTENANCE:

Written Practice: Lesson 16 (#30), Lesson 24 (#30), Lesson 56 (#17, #23, #24)



D

omai

n

Stan

dard

Text of Objective


6.SP

Sta

tistic

s and

Pro

babi

lity

6.SP

.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

INSTRUCTION:



MAINTENANCE:

Power Up: Lesson 26, p. 136; Lesson 30, p. 156; Lesson 39, p. 200; Lesson 50, p. 259; Lesson 72, p. 375; Lesson 73, p. 380; Lesson 74, p. 385; Lesson 75, p. 390; Lesson 77, p. 399; Lesson 78, p. 404; Lesson 116, p. 606; Lesson 117, p. 612; Lesson 118, p. 617; Lesson 119, p. 621; Lesson 120, p. 626

Written Practice: Lesson 51 (#30), Lesson 53 (#4), Lesson 59 (#23), Lesson 76 (#18), Lesson 90 (#1), Lesson 99 (#18), Lesson 106 (#28), Lesson 113 (#27, #28), Lesson 115 (#21), Lesson 118 (#7), Lesson 120 (#7)

Summarize and describe distributions. Students in Course 1 are able to collect, organize, display and interpret numerical data sets (Investigation 4). Furthermore, throughout the cumulative practice in the investigations, extension activities, and written practices the students are able to identify clusters, peeks, gaps and symmetry in the data sets while considering the context in which the data was collected. Teachers can easily monitor student progress by using the cumulative and extension tests included in the program to ensure that students develop a high level of mathematical understanding.

6.SP

.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

INSTRUCTION:

Investigation(s): Investigation 1, pp. 54-57; Investigation 4, pp. 211-215; Investigation 5, pp. 264-267




D

omai

n

Stan

dard

Text of Objective


6.SP

Sta

tistic

s and

Pro

babi

lity

6.SP

.5 Summarize numerical data sets in relation to their context, such as by:

6.SP

.5a

Reporting the number of observations.

INSTRUCTION:


MAINTENANCE:

Written Practice: Lesson 16 (#30), Lesson 24 (#30), Lesson 56 (#24)

6.SP

.5b

Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

INSTRUCTION:




MAINTENANCE:



Written Practice: Lesson 58 (#22), Lesson 60 (#25), Lesson 65 (#7), Lesson 74 (#4), Lesson 82 (#21), Lesson 92 (#1), Lesson 95 (#30), Lesson 97 (#30), Lesson 100 (#9), Lesson 103 (#8, #24), Lesson 109 (#6. #12), Lesson 119 (#27)




Dom

ain

Stan

dard

Text of Objective


6.SP

Sta

tistic

s and

Pro

babi

lity

6.SP

.5c

Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

INSTRUCTION:


Standards Success Activity: Activity 4A, Activity 5A, Activity 5B

MAINTENANCE:

Power Up: Lesson 73, p. 380; Lesson 74, p. 385; Lesson 75, p. 390; Lesson 77, p. 399; Lesson 78, p. 404; Lesson 116, p. 606; Lesson 117, p. 612; Lesson 118, p. 617; Lesson 119, p. 621; Lesson 120, p. 626

Written Practice: Lesson 51 (#30), Lesson 53 (#4), Lesson 59 (#23), Lesson 80 (#1, #24, #25), Lesson 99 (#18), Lesson 106 (#28), Lesson 113 (#27, #28), Lesson 120 (#7)

6.SP

.5d

Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

INSTRUCTION:


Standards Success Activity: Activity 5A, Activity 5B

MAINTENANCE:

Power Up: Lesson 73, p. 380; Lesson 74, p. 385; Lesson 75, p. 390; Lesson 77, p. 399; Lesson 78, p. 404; Lesson 116, p. 606; Lesson 117, p. 612; Lesson 118, p. 617; Lesson 119, p. 621; Lesson 120, p. 626

Written Practice: Lesson 56 (#23), Lesson 62 (#30), Lesson 80 (#1, #24, #25), Lesson 89 (#23, #24, #25), Lesson 94 (#27), Lesson 102 (#1), Lesson 107 (#26, #27), Lesson 114 (#28), Lesson 117 (#24), Lesson 119 (#30)

Saxon Math Course 2 ©2007 correlated to the

Common Core State Standards for Mathematics Grade 7

1

Standard Descriptor Saxon Math Course 2 Citations

References in italics indicate foundational. Ratios and Proportional Relationships 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 1 Compute unit rates associated with ratios of fractions, including ratios

of lengths, areas and other quantities measured in like or different units.

INSTRUCTION: New Concept 329-333, 375-376 Investigation 773-777 MAINTENANCE: Problem Solving 400, 472, 710 Written Practice 333, 344, 345, 349, 356, 366,

372, 390, 404, 437, 444, 462, 482, 493, 520, 526, 531, 547, 595, 633, 639, 645, 683, 721, 742, 788, 796, 801

2 Recognize and represent proportional relationships between

quantities.

2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

INSTRUCTION: New Concept 677-682 Investigation 624-630 MAINTENANCE: Written Practice 634, 763



2

Standard Descriptor Saxon Math Course 2 Citations References in italics indicate foundational.

2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

INSTRUCTION: New Concept 329-333 Investigation 624-630 MAINTENANCE: Problem Solving 400, 472, 710 Written Practice 333, 344, 345, 349, 356, 366,

372, 390, 404, 437, 444, 462, 482, 493, 520, 526, 531, 547, 595, 633, 639, 645

2c Represent proportional relationships by equations.

INSTRUCTION: New Concept 194-197, 280-282, 329-333,

386-389, 507-509 MAINTENANCE: Problem Solving 710 Written Practice 284, 292, 301, 307, 315, 322,

328, 333, 344, 366, 372, 390, 404, 437, 444, 462, 482, 493, 520

2d Explain what a point (x, y) on the graph of a proportional relationship

means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

INSTRUCTION: New Concept 677-682 Investigation 624-630 MAINTENANCE: Written Practice 729



3


3 Use proportional relationships to solve multistep ratio and percent problems.

INSTRUCTION: New Concept 420-423, 636-639, 765-770 MAINTENANCE: Problem Solving 704 Written Practice 424, 520, 532, 543, 548, 557,

567, 584, 590, 633, 639, 646, 650, 657, 674, 675, 683, 690, 727

The Number System 7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 1 Apply and extend previous understandings of addition and

subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

1a Describe situations in which opposite quantities combine to make 0.

INSTRUCTION: New Concept 413-416, 480-482

1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

INSTRUCTION: New Concept 413-416, 480-482 MAINTENANCE: Written Practice 417, 418, 424, 425, 439, 445,

446, 450, 483, 506, 517, 522

1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

INSTRUCTION: New Concept 413-416, 453-456, 480-482 MAINTENANCE: Written Practice 457, 463, 469, 483, 506, 517,

522



4


1d Apply properties of operations as strategies to add and subtract rational numbers.


517, 522, 533, 544

2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

INSTRUCTION: New Concept 513-515 MAINTENANCE: Power Up 562, 586, 604, 642, 668, 704,

739, 745, 759 Written Practice 515, 516, 522, 527, 532, 538,

543, 548, 556, 568, 574, 579, 585

2b Understand that integers can be divided, provided that the divisor is

not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

INSTRUCTION: New Concept 6-10, 513-515, 592-595, 825-

828 MAINTENANCE: Written Practice 19, 25, 33, 39, 44, 59, 65, 80,

92, 99, 112, 126, 198, 515, 522, 527, 532, 538, 548, 556, 574, 585



5


2c Apply properties of operations as strategies to multiply and divide rational numbers.


179, 182-185, 247-251, 323-326, 513-515, 592-595

MAINTENANCE: Power Up 13, 34, 75, 100, 120, 169, 194,

296, 329, 363, 386, 406, 459, 529, 686

Problem Solving 149, 175, 200, 247, 255, 296,

329, 386, 440, 523, 545, 636 Written Practice 90, 105, 118, 131, 154, 185,

198, 233, 240, 272, 279, 328, 334, 351, 392, 405, 439, 446, 450, 468, 489, 495, 515, 522, 527, 579, 585, 762

2d Convert a rational number to a decimal using long division; know that

the decimal form of a rational number terminates in 0s or eventually repeats.


528, 532, 557, 646, 698



6


3 Solve real-world and mathematical problems involving the four

operations with rational numbers.1


185, 194-197, 317-320, 323-326

MAINTENANCE: Power Up 13, 40, 60, 107, 128, 188, 296,

329, 347, 386, 480, 518, 545, 598, 717, 778, 832

Problem Solving 75, 157, 163, 188, 228, 255,

296, 323, 363, 386, 440, 507, 592, 653

Written Practice 90, 91, 105, 111, 118, 124, 131,

140, 154, 172, 185, 450, 456, 468

Expressions and Equations 7.EE Use properties of operations to generate equivalent expressions. 1 Apply properties of operations as strategies to add, subtract, factor, and

expand linear expressions with rational coefficients.


621, 647, 667, 676, 692, 697, 707, 709, 764, 816, 823, 824, 831, 835, 836, 841

1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions.



7


2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

INSTRUCTION: New Concept 704-706 MAINTENANCE: Problem Solving 393, 562 Written Practice 708, 709, 714, 722, 736, 744,

751, 756, 762, 781, 814, 822, 829

Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 3 Solve multi-step real-life and mathematical problems posed with

positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

INSTRUCTION: New Concept 75-79 MAINTENANCE: Problem Solving 336, 557, 598 Written Practice 79, 85, 86, 92, 98, 118, 131,

140, 160, 185, 191, 239, 244 4 Use variables to represent quantities in a real-world or

mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

INSTRUCTION: New Concept 20-23, 75-78, 82-85, 88-90, 93-

94, 636-639, 704-707 MAINTENANCE: Problem Solving 413 Written Practice 24, 32, 39, 43, 51, 59, 64-65,

79, 86, 90-91, 98, 111, 708, 709, 714, 722, 736, 744, 751, 756, 762, 781, 814, 722, 829, 841



8


4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.


589, 622, 647, 658, 684, 716, 834

Geometry 7.G Draw, construct, and describe geometrical figures and describe the relationships between them. 1 Solve problems involving scale drawings of geometric figures,

including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.


756, 757, 771, 798, 808, 829

2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

INSTRUCTION: New Concept 264-270, 441-444, 817-820 Investigation 429 MAINTENANCE: Written Practice 133, 271, 446, 452, 463, 470,

483, 487, 506, 834

3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

INSTRUCTION: New Concept 472-476 MAINTENANCE: Problem Solving 618, 693



9


Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 4 Know the formulas for the area and circumference of a circle and use

them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

INSTRUCTION: New Concept 459-462, 569-571 MAINTENANCE: Power Up 459, 466, 480 Problem Solving 610 Written Practice 462, 469, 478, 487, 493, 505,

510, 511, 516, 521, 527, 532, 539, 542, 549, 572, 578, 584, 601, 615, 622, 634, 651, 666, 696, 715, 728

5 Use facts about supplementary, complementary, vertical, and adjacent

angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.


756, 814, 829 6 Solve real-world and mathematical problems involving area, volume

and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

INSTRUCTION: New Concept 136-140, 264-270, 432-437,

490-493, 523-526, 653-656, 731-735, 791-795, 799-801

Investigation 218, 773-777 MAINTENANCE: Problem Solving 347, 352, 485, 545, 570, 686 Written Practice 162, 186, 181, 197, 270, 425,

445, 452, 590, 601, 622, 651, 658, 715, 803, 808, 821



10


Statistics and Probability 7.SP Use random sampling to draw inferences about a population. 1 Understand that statistics can be used to gain information about a

population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences

INSTRUCTION: Investigation 293-295, 359-362 MAINTENANCE: Written Practice 300, 314, 358, 384, 404, 438,

464, 483, 486, 506, 583, 595, 621, 656, 674, 707, 720, 801

This standard is further addressed in Course 3; opportunities to review can be found on pages 606-609

2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

INSTRUCTION: Investigation 359-362 This standard is further addressed in Course 3; opportunities to review can be found on pages 606-609

Draw informal comparative inferences about two populations. 3 Informally assess the degree of visual overlap of two numerical data

distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

INSTRUCTION: Investigation 359-362 MAINTENANCE: Written Practice 404, 801

4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

INSTRUCTION: Investigation 293-295 MAINTENANCE: Written Practice 300, 314, 358, 384, 438, 483,

486, 506, 566, 583, 595, 656, 674, 707, 720, 788



11


Investigate chance processes and develop, use, and evaluate probability models. 5 Understand that the probability of a chance event is a number between

0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

INSTRUCTION: New Concept 95-98, 257-258, 648-650 Investigation 550-561 MAINTENANCE: Written Practice 278, 284, 306, 321, 426, 577,

590, 697, 801

6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

INSTRUCTION: New Concept 95-98, 257-258 Investigation 550-561 MAINTENANCE: Written Practice 278, 284, 306, 321, 426, 577,

590, 697, 801

7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

INSTRUCTION: New Concept 255-260 Investigation 559-561 MAINTENANCE: Written Practice 278, 284, 306, 321, 426, 577,

590, 697, 801



12


7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.


801, 813, 822, 829

8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.


801, 813, 822, 829

8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.


801, 813, 822, 829

8c Design and use a simulation to generate frequencies for compound events.


801, 813, 822, 829

Common Core State Standards for Mathematics, Grade 8 correlated to Saxon Math Course 3 © 2012

Common Core State Standards for Mathematics© Copyright 2010, National Governor’s Association Center for Best Practices and Council of Chief State School Officers. All rights

Dom

ain

Stan

dard

Text of Objective


Narrative

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

1. Make sense of problems and persevere in solving them.

INSTRUCTION: New Concept: Lesson 3, pp. 19-22; Lesson 4, pp. 27-28; Lesson 34, pp. 223-226; Lesson 87, pp. 580-582; Lesson 89, pp. 593-596; Lesson 105, pp. 697-699 Investigation: Investigation 2, pp. 132-138;, Investigation 7, pp. 476-478; Lesson 10, pp. 670-674; Lesson 12, pp. 782-784 MAINTENANCE: Power Up: Lesson 2, pp. 11-12; Lesson 8, pp. 47-48; Lesson 13, p. 85; Lesson 23, pp. 153-154; Lesson 40, p. 264; Lesson 56, p. 382; Lesson 73, p. 491; Lesson 85,p. 568; Lesson 98, p. 651 Problem Solving: Lesson 1, p. 6; Lesson 12, p. 78; Lesson 23, p. 153; Lesson 35, p. 229; Lesson 45, p. 308; Lesson 53, p. 360; Lesson 64, p. 435; Lesson 76, p. 507; Lesson 83, p. 557; Lesson 92, p. 617; Lesson 102, p. 681; Lesson 115, p. 754 Written Practice: Lesson 3, pp. 23-24(#1, #2, #3, #4, #5, #6, #7); Lesson 4, pp. 28-30(#1, #2, #3, #4, #5, #25); Lesson 5, pp. 33-35(# 1, #2, #3, #4, #6,#9, #17); Lesson 6, pp. 38-40 (#1,#2,#3,#11; Lesson 7, pp. 45-46 (#4,#5,#7); Lesson 18, pp. 117-119 (#26,#27); Lesson 26, pp. 174-175; Lesson 37,pp. 248-249 (#11); Lesson 38, pp. 254-256 (#5-#8); Lesson 39, pp. 261-263 (#28); Lesson 40, pp. 268-270 (#4, #5, #27); Lesson 87, pp. 582-583 (#2, #7); Lesson 90, p. 603 (#1); Lesson 91, pp. 603-604 (#1, #16); Lesson 94, p. 631 (#3); Lesson 105, pp. 699-700 (#4, #12); Lesson 106, pp. 704-705 (#2, #5, #9); Lesson 108, pp. 715-716 (#7, #12, #13, #14) Standards Success Activity: Activity 16, pp. 31-32

Developing enthusiastic and proficient problem solvers is the focus of the Saxon Math series. To reinforce this commitment from day one, Course 1 opens with a “Problem-Solving Overview” on pages 1 - 5. Working from Polya’s classic four-step problem solving process, and beginning with ten general strategies, students are reminded to understand the information that has been provided and the question being asked, to plan accordingly before beginning, to solve the problem while remaining open to re-direction, and to check their solution for reasonableness and possible extensions. Additional emphasis is placed at this level of problem solving on solving most efficiently, and the ability to effectively communicate in writing a process and results.

The process and strategies outlined in the overview are discussed daily in the Problem Solving portion of the daily Power Up, and practiced daily in the integrated Written Practice, where students are not only expected to solve, but to also formulate problems. All problems build in complexity throughout the year, and to support good questioning, teacher materials include a “Problem Solving Discussion Guide” for each Power-Up, and “Math Conversation” prompts for each Lesson and Written Practice.

Saxon’s pedagogy of daily integrating and gently evolving domains simultaneously naturally promotes perseverance. Students are provided both the time to master and the material to maintain skill sets. This avoids the current phenomenon of students learning enough to get by on the next test but forgetting those skills shortly thereafter, forcing them to be reviewed again the following year

reserved.



Dom

ain

Stan

dard

Text of Objective


Narrative

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

2. Reason abstractly and quantitatively.

INSTRUCTION: New Concept: Lesson 3, pp. 19-23; Lesson 17, pp. 108-111; Lesson 59, pp. 401-403; Lesson 89, pp. 593-596 Investigation: Investigation 7, pp. 476-478; Investigation 9, pp. 606-609 MAINTENANCE: Power Up: Lesson 20, p. 126; Lesson 21, p. 139; Lesson 25, p. 163; Lesson 29, p. 186; Lesson 33, p. 218; Lesson 44, p. 300; Lesson 61, p. 415; Lesson 66, p. 446; Lesson 75, p. 502; Lesson 90, p. 599 Problem Solving: Lesson 12, p.78; Lesson 15, pp. 97-97; Lesson 17, p. 108; Lesson 25, p. 163; Lesson 37, p. 245; Lesson 45, p. 308; Lesson 54, p. 367; Lesson 61, p. 415; Lesson 72, p. 486; Lesson 79, p. 525; Lesson 94, p. 629; Lesson 99, p. 658; Lesson 109, p. 717; Lesson 118, p. 768 Written Practice: Lesson 17, pp. 111-113 (#27, #28); Lesson 18, pp. 117-119 (#26, #27); Lesson 21, pp. 144-145 (#6, #8, #11, #12, #20); Lesson 24, pp. 161-162 (# 4, #5, ); Lesson 26, pp. 174-175; Lesson 59, Lesson 89, p. 597 (#19); Lesson 93, p. 628 (#17) Standards Success Activity: Activity 6, pp. 11-12; Activity 14, pp. 27-28; Activity 20, pp. 39-40

The foundation of the Saxon Math series is mathematically proficient students, as measured by both computational fluency and in modeling conceptual understanding with numbers and variables in expressions, equations, and inequalities. Daily Written Practice does not focus simplistically on one standard at a time, but rather involves multiple domains just as real-world situations require. Examples and Practice Problems in the student text are marked with blue icons signifying to students the need to coherently “Generalize,” “Represent,” “Formulate,” and “Model” their work. Students develop habits of fluency and flexibility in both contextualizing (generating models of their understanding) and decontextualizing (simplifying a problem into symbolic form).

reserved.



D

omai

n

Stan

dard

Text of Objective


Narrative

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

3. Construct viable arguments and critique the reasoning of others.

INSTRUCTION: New Concept: Lesson 3, pp. 19-23; Lesson 17, pp. 108-111 MAINTENANCE: Problem Solving: Lesson 1, pp. 6-7; Lesson 15, pp. 97-98; Lesson 25, p. 163; Lesson 36, p. 237; Lesson 49, p. 330; Lesson 68, p. 457; Lesson 79, p. 525; Lesson 96, p. 640; Lesson 109, p. 717 Written Practice: Lesson 18, p. 119 (#26); Lesson 19, pp. 151 (#19); Lesson 21, p. 144 (#19); Lesson 22, p. 235 (#11); Lesson 26, p. 189 (#15); Lesson 29, p. 221 (#26); Lesson 35, p. 285 (#6) Standards Success Activity: Activity 5, pp. 9-10

Mathematically proficient students are able to communicate their personal thinking, to ask useful questions, and to clarify or improve upon the arguments of others. The opening “Power Up” activities of each lesson provided throughout the Saxon Math series are designed to foster discussion within the classroom and amongst classmates as to individual perspectives and preferences, strategies, and techniques of problem solving.

Examples, Practice Problems, and “Thinking Skill” prompts in the margins of the student text are marked with blue icons signifying to students the need to “Discuss,” “Explain,” “Justify,” and “Verify” their solutions.

Teacher Manuals provide daily “Error Alert” and “Error Analysis” prompts to emphasize opportunities for evaluative discussion of student thinking.

reserved.



D

omai

n

Stan

dard

Text of Objective


Narrative

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

4. Model with mathematics INSTRUCTION: New Concept: Lesson 9, pp. 55-57; Lesson 10, pp. 60-65; Lesson 22, pp. 147-150; Lesson 26, pp. 169-174; Lesson 31, pp. 203-207; Lesson 33, pp. 218-220; Lesson 55, pp. 375-378; Lesson 68, pp. 457-458 (Ex.1); Lesson 75, pp. 502-504; Lesson 78, pp. 520-521 (Ex. 1, 2) Investigation: Investigation 1, pp. 68-71; Investigation 4, pp. 271-276; Investigation 5, pp. 342-345; Investigation 8, pp. 538-544 MAINTENANCE: Problem Solving: Lesson 6, p. 36; Lesson 9, pp. 4-44; Lesson 11, pp. 72-72; Lesson 22, pp. 146-147; Lesson 26, p. 169; Lesson 34, p. 223; Lesson 59, p. 400; Lesson 74, p. 496; Lesson 84, p.563; Lesson 92, p. 617; Lesson 113, p. 742 Written Practice: Lesson 6, pp. 38-40 (#1-3, ); Lesson 10, pp. 66-67 (#5-9, #22); Lesson 27, pp. 178-180 (# 7, #9); Lesson 34, pp. 227-228 (#3, #26, #27); Lesson 36, pp. 242-244 (#9, #11, #12, #15); Lesson 41, pp. 284-286 (#4, #30); Lesson 43, pp. 297-299 (#5, #30); Lesson 45, pp. 310-312 (#1, #3, #4); Lesson 64, p. 438 (#6); Lesson 66, p. 451 (#21); Lesson 108, p. 714 (#3) Standards Success Activity: Activity 15, pp. 29-30; Activity 19, pp. 37-38; Activity 23, pp. 45-46; Activity 28, pp. 55-56

Saxon Math is based on the belief that people learn by doing, and the ultimate “doing” is applying mathematical concepts to everyday life situations. The Saxon Math series seeks to produce mathematically proficient students who can then use the quantitative skills they have honed to create solutions, and apply quantitative methods to practical challenges. Examples and Practice Problems in the student text are marked with blue icons signifying to students the need to “Represent,” “Formulate,” and “Model” their work. Activities in the Student Edition and active learning prompts in the margin of the Teacher’s Edition highlight opportunities for students to apply their mathematical understanding as they model real-world situations.

reserved.



D

omai

n

Stan

dard

Text of Objective


Narrative

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

5. Use appropriate tools strategically.

INSTRUCTION: New Concept: Lesson 16, pp. 103-105; Lesson 18, pp. 114-117; Lesson 28, pp. 181-183; Lesson 30, pp. 192-194; Lesson 38, pp. 251-254; Lesson 73, pp. 491-494, Lesson 87, pp. 580-582 Investigation: Investigation 2, pp. 132-138 MAINTENANCE: Written Practice: Lesson 39, pp. 261-263 (#28); Lesson 43, pp. 297-299 (#5, #30); Lesson 76, pp. 512-513 (#10, #13, #24) Standards Success Activity: Activity 10, pp. 19-20

Saxon Math requests and requires the use of grade level appropriate tools for instruction and problem solving. This begins with concrete models at the primary level, regularly includes representational tools such as diagrams, graphs and tables, and moves to more sophisticated tools like geometry software at the secondary level. Saxon offers instruction and guidance for appropriate use of tools throughout the program, and has compiled a complete manipulative set for the middle school. Icons in the margins of the textbook indicate to students appropriate places for use of calculators, and formal instruction in the use of graphing calculators is part of Course 3. Graphing calculator icons in the textbook indicate additional related/extension activities available on-line.

Alongside the standard use of tools, “Alternate Approach with Manipulatives” notes in the Teacher Manual and the “Adaptation Teaching Guide” provide additional techniques for working with at-risk students via standard manipulatives, reference guides, and adaptation prompts.

reserved.



D

omai

n

Stan

dard

Text of Objective


Narrative

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

6. Attend to precision. INSTRUCTION: New Concept: Lesson 8, pp. 48 – 51; Lesson 18, pp. 114 – 117; Lesson 42, pp. 287-290; Lesson 43, pp. 294-297; Lesson 76, pp. 507-511, Lesson 86, pp. 574-578; Lesson 87, pp. 580-582; Lesson 91, pp. 610-613; Lesson 117, pp. 763-766 MAINTENANCE: Power Up: Lesson 1, pp. 6-7; Lesson 4, pp. 26-27; Lesson 6, p. 36; Lesson 8, p. 47; Lesson 10, p. 60; Lesson 18, p. 114; Lesson 32, p. 210; Lesson 38, pp. 250-251; Lesson 42, p287; Lesson 49, p. 330; Lesson 61, p. 415; Lesson 79, p. 525; Lesson 95, p. 634 Problem Solving: Lesson 32, p. 210 Written Practice: Lesson 8, pp. 51-53 (#1-4); Lesson 10, pp. 66-67 (#5-9, #19, #22); Lesson 12, pp. 83-84 (#6-8, #21, #23); Lesson 13, pp. 90-91 (#4, #6-14,); Lesson 22, pp. 150-152 (#8-11, #13); Lesson 26, pp. 174-175; Lesson 42, pp. 290-293 (#3); Lesson 43, pp. 297-299 (#5, #30); Lesson 45, pp. 310-312 (#1, #3, #4); Lesson 47, pp. 324-325; Lesson 77, p. 518 (#22); Lesson 78, p. 523 (#19, #20); Lesson 86, pp. 578-579 (#4, #25); Lesson 87, pp. 582-583 (#1, #2, #5, #7); Lesson 91, pp. 614 (#4, #6, #9, #15); Lesson 94, pp. 631, 633 (#3, #22) Standards Success Activity: Activity 8, pp. 15-16; Activity 9, pp. 17-18; Activity 13, pp. 25-26

To ensure students use appropriate terminology correctly, communicate precisely, calculate accurately and efficiently, and then maintain that proficiency, 30 fully integrated and evolving Written Practice problems have been designed to daily guarantee students’ minds do not go on autopilot, which is the brain’s natural tendency when presented with too many of the same thing in a single seating. Conscientious effort has been made by author Stephen Hake to guarantee that if, for example, a function is to be posed daily, that it be presented from different perspectives so as to very naturally require and instill the practice of attention to detail. Students may simply define a function on one day, evaluate or compare functions the next day, and/or use a function to model a relationship between quantities the following day. Each practice and assessment question is referenced to its lesson of initial instruction to encourage students to reference rather than guess when in doubt.

Automaticity of basic skill sets is promoted with a 2-3 minute timed practice set that opens the Power-Up portion of each lesson.

Parallel to the student textbook, the “Student Adaptation Workbook” provides additional starting points, hints/tips for progressing, and reminders to label to encourage and reinforce precision with special needs and at-risk students.

reserved.



D

omai

n

Stan

dard

Text of Objective


Narrative

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

7. Look for and make use of structure.

INSTRUCTION: New Concept: Lesson 2, pp. 13-16; Lesson 3, pp. 19-23; Lesson 21, pp. 140-143; Lesson 73, pp. 491-494 Investigation: Investigation 2, pp. 132-138 MAINTENANCE: Written Practice: Lesson 4, pp. 28-30 (#1-5, #25, #27); Lesson 5, pp. 33-35 (#1-4, #6, #9, 17); Lesson 7, pp. 45-46 (#4, $5, #7); Lesson 9, pp. 57-59 (#7, #26-29); Lesson 21, pp. 144-145 (#6, #8, #11,#12, #20); Lesson 23, pp. 156-158 (#12, #13, #20); Lesson 26, pp. 174-175Lesson 73, p. 495 (#11, #24); Lesson 74, p. 501 (#13, #15) Standards Success Activity: Activity 11, pp. 21-22; Activity 24, pp. 47-48; Activity 27, pp. 53-54

Saxon Math builds solid structure throughout the program first by explicitly teaching number properties and how concepts connect, and then by encouraging students to use both problem solving strategies and their skill fluency to notice possible patterns and apply basic structures to new or unique challenges.

Author Stephen Hake is careful to phrase examples and practice problems of a single concept in a variety of ways to assure flexibility of student thinking exists within the fluency. “What is NOT?” is a frequent form of questioning, and blue icons identify “Connect,” “Classify,” and “Analyze” questions within the Written Practice that require students to step back, get an overview of the problem at hand, and shift their perspective if necessary.

reserved.



D

omai

n

Stan

dard

Text of Objective


Narrative

Stan

dard

s for

Mat

hem

atic

al P

ract

ice

8. Look for and express regularity in repeated reasoning.

INSTRUCTION: New Concept: Lesson 15, pp. 98-101; Lesson 21, pp. 140-143Lesson 61, pp. 415-418; Lesson 73, pp. 491-494; Lesson 97, pp. 646-648; Lesson 102, pp. 681-683 Investigation: Investigation 10, pp. 670-674 MAINTENANCE: Problem Solving: Lesson 26, p. 169; Lesson 37, p. 245; Lesson 40, p. 264; Lesson 42, p. 287; Lesson 44, p. 300; Lesson 48, p. 326; Lesson 51, p. 346; Lesson 59, p. 400; Lesson 103, p. 686; Lesson 107, p. 707; Lesson 111, p. 731; Lesson 116, p. 758 Written Practice: Lesson 22, pp. 150-152 (#8-11); Lesson 23, pp. 156-158 (#12, #13, #20); Lesson 26, pp. 174-175; Lesson 29, pp. 189-191; Lesson 73, p. 495 (#11); Lesson 74, pp. 500-501 (#7, #13, #15); Lesson 76, p. 513 (#13, #14); Lesson 97, p. 650 (#12, #23); Lesson 98, p. 655 (#6, #18); Lesson 102, pp.683-684 (#4, #15, #16, #19); Lesson 108, p. 715 (#10) Standards Success Activity: Activity 2, pp. 3-4

Distributing the instruction of concepts over the course of the year allows Saxon curriculum to visit the ever-increasing “big picture” on a daily basis while attending to finer and finer detail. Multiple opportunities are provided over the course of the school year for students to solve and model like problems to ensure they are developing connections, cohesiveness, and flexibility in their work within the grade level standard. “Shortcuts” are not introduced or utilized in Saxon until students exemplify proficiency with all subtasks of the skill set. For instance, in Investigation 1 of Course 3 students revisit graphing points on the coordinate plane, and in Lesson 41 define functions, describe their rules, and identify their graphs. In Lesson 44 they define the slope of a line, and in Lesson 47 graph functions, but not until Lesson 56 is the “aha” – the shortcut - of using the slope-intercept method of graphing linear equations utilized. Frequently in Saxon, the shortcut has already been discovered and utilized by students themselves by the time it is formally introduced.

reserved.



Dom

ain

Stan

dard

Text of Objective


8.N

S T

he N

umbe

r Sy

stem

Know that there are numbers that are not rational, and approximate them by rational numbers.

Rational and Irrational numbers are defined early in Course 3, and are then able to be utilized daily throughout the course. Knowledge and use of rational and irrational numbers for 8th graders is expanded upon in Course 3 at the following points: Lesson 10 Rational Numbers Lesson 12 Decimal Numbers Lesson 16 Irrational Numbers (Approximating Values and Position on a Number Line) Investigation 2 The Pythagorean Theorem Lesson 30 Repeating Decimal Numbers Lesson 63 Rational Numbers; Non-terminating Decimals Lesson 66 Special Right Triangles Lesson 84 Selecting Appropriate Rational Numbers

8.N

S.1

Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.

INSTRUCTION: New Concept: Lesson 12, pp. 78-82; Lesson 16, pp. 103-105, Lesson 30, pp. 192-194, Lesson 63, pp. 429-432 Investigation: Investigation 2, pp. 132-138 MAINTENANCE: Problem Solving: Lesson 89, p. 593 Written Practice: Lesson 12, pp. 83-84 (#5-8, #21, #23) ; Lesson 16, pp. 105-107 (#28-30); Lesson 18, pp. 117-119 (#26, #27); Lesson 19, pp. 124-125; Lesson 20, pp. 139-131 (#14) ; Lesson 30, pp. 195-196 (#13) ; Lesson 31, pp. 209-209 (#14, #15, #18) ; Lesson 32, pp. 214-217 (#4, #5,#23, #24) ; Lesson 35, pp. 234-236 (#17, #28, #29) ; Lesson 39, pp. 261-263 (#28) ; Lesson 43, pp. 297-299 (#5, 30) ; Lesson 47, pp. 324-325; Lesson 50, pp. 338-341 (#4-9, #27) ; Lesson 56, pp. 386-388 (#5); Lesson 63, pp. 433 (#7, #8), Lesson 81, p. 548 (#16) Graphing Calculator Activities: Activity 3 (Lesson 13) Standards Success Activity: Activity 4, pp. 7-8

reserved.



D

omai

n

Stan

dard

Text of Objective


8.N

S T

he N

umbe

r Sy

stem

8.N

S.2

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2).

INSTRUCTION: New Concept: Lesson 16, pp. 103-105Lesson 66, pp. 446-449 MAINTENANCE: Power Up: Lesson 31, p. 202 Problem Solving: Lesson 18, p. 118 Written Practice Lesson 18 pp. 117-119 (#26, #27); Lesson 19, pp. 124-125; Lesson 20, pp. 129-131 (#14); Lesson 78, p, 523 (#15); Lesson 81, p. 548 Standards Success Activity: Activity 2, pp. 3-4

reserved.



Dom

ain

Stan

dard

Text of Objective


8.E

E E

xpre

ssio

ns a

nd E

quat

ions

Work with radicals and integer exponents. Students revisit and begin utilizing powers and roots to the nth degree in Lesson 15 of Course 3. Work with radicals and exponents for 8th graders is expanded upon in Course 3 at the following points: Lesson 15 Powers and Roots Lesson 16 Irrational Numbers Lesson 27 Laws of Exponents Lesson 28 Scientific Notation for Large Numbers (w/ notation for Graphing Calculator use) Lesson 36 Multiplying and Dividing Integers Lesson 46 Problems Using Scientific Notation Lesson 51 Negative Exponents; Scientific Notation for Small Numbers Lesson 57 Operations with Small Numbers in Scientific Notation Lesson 66 Special Right Triangles Lesson 74 Simplifying Square Roots Lesson 93 Equations with Exponents Lesson 96 Geometric Measures with Radicals

8.E

E.1

Know and apply the properties of integer exponents to generate equivalent numerical expressions.

INSTRUCTION: New Concept: Lesson 15, pp. 97-101; Lesson 27, pp. 176-178; Lesson 51, pp. 346-351; Lesson 57, pp. 389-391 Investigation: Investigation 2, pp. 132-138 MAINTENANCE: Power Up: Lesson 16, p. 103; Lesson 17, p. 108; Lesson 19, p. 120; Lesson 31, p. 202; Lesson 62, p. 422; Lesson 64, p. 435; Lesson 66, p. 446; Lesson 72, p. 486; Lesson 86, p. 574; Lesson 96, p. 640; Lesson 100, p. 664 Problem Solving: Lesson 62, p. 422 Written Practice: Lesson 16, p. 102; Lesson 25, p. 167; Lesson 28, p. 184; Lesson 29, p. 189; Lesson 30, p. 195; Lesson 31, p. 209; Lesson 32, p. 216; Lesson 33, p. 221; Lesson 34, p. 227; Lesson 41, p. 285 Standards Success Activity: Activity 1, pp. 1-2

reserved.



Dom

ain

Stan

dard

Text of Objective


8.E

E E

xpre

ssio

ns a

nd E

quat

ions

8.E

E.2

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

INSTRUCTION: New Concept: Lesson 15, pp. 97-101; Lesson 16, pp. 103-105Lesson 66, pp. 446-449, Lesson 93, pp. 624-626 Investigation: Investigation 2, pp. 132-138 Appendix Lesson: Lesson A84-A87, pp. 805-807 MAINTENANCE: Written Practice: Lesson 16, pp. 105-107 (#28-#30); Lesson 17, pp. 111-113 (#28, #29); Lesson 85, p. 571 (#7); Lesson 93, p. 627 (#5, #9); Lesson 96, p. 643 (#15); Lesson 98, p. 656 (#17); Lesson 102, p. 684 (#18); Lesson 105, p. 700 (#15, #19); Lesson 107, p. 711 (#15); Lesson 111, p. 735 (#10, #13); Lesson 112, p.740 (#15); Lesson 115, p. 757 (#9, #10, #16, #20) Graphing Calculator Activities: Activity 16 (Investigation 8), pp. 538-544 Standards Success Activity: Activity 19, pp. 37-38

reserved.



Dom

ain

Stan

dard

Text of Objective


8.E

E E

xpre

ssio

ns a

nd E

quat

ions

8.E

E.3

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

INSTRUCTION: New Concept: Lesson 28, pp. 181-183; Lesson 46, pp. 313-316; Lesson 51, pp.346-351; Lesson 57, pp. 389-391 MAINTENANCE: Written Practice: Lesson 30, pp. 195-196 (#13); Lesson 31, pp. 208-209 (#14 , #15 #18, #27); Lesson 34, pp. 227 -228(#3, #26, #27); Lesson 39, pp. 261-263 (#28); Lesson 47, pp. 324-325; Lesson 52, pp. 357-359 (#5, #6); Lesson 53, pp. 364-366 (#6); Lesson 55, 378-381; Lesson 56, pp. 386-388 (#5); Lesson 58 , pp. 397- 399 (# 2); Lesson 59, pp. 403- 405 (#4); Lesson 405, Lesson 99, p. 663 (#23) Graphing Calculator Activities: Activity 6 (Lesson 28); Activity 11 (Lesson 51) Standards Success Activity: Activity 12, pp. 23-24

8.E

E.4

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

INSTRUCTION: New Concept: Lesson 28, pp. 181-183; Lesson 46, pp. 313-316; Lesson 51, pp. 346-351; Lesson 57, pp. 389-391; MAINTENANCE: Written Practice: Lesson 28, pp. 181-183; Lesson 46, pp. 313-316; Lesson 51, pp. 346-351; Lesson 57, pp. 389-391;Lesson 99, p. 663 (#23) Graphing Calculator Activities: Activity 6 (Lesson 28); Activity 11 (Lesson 51) Standards Success Activity: Activity 10, pp. 19-20

reserved.



Dom

ain

Stan

dard

Text of Objective


8.E

E E

xpre

ssio

ns a

nd E

quat

ions

Understand the connections between proportional relationships, lines, and linear equations.

Beginning at Lesson 7 in Course 3, and addressed daily throughout, is the expectation that students will apply to their own experiences their understanding and interpretation of proportional reasoning. Daily work with proportional relationships for 8th graders is expanded upon in Course 3 at the following points: Lesson 7 Rates Investigation 1 The Coordinate Plane Lesson 29 Ratio Lesson 34 Proportions and Ratio Word Problems Lesson 35 Similar Polygons Lesson 41 Functions Lesson 44 Solving Proportions with Cross Products; Slope of a Line Lesson 45 Ratio Problems Involving Totals Lesson 47 Graphing Functions Lesson 49 Solving Rate Problems with Proportions and Equations Lesson 52 Using Unit Multipliers to Convert Measurement Lesson 56 Slope-Intercept Equation of a Line Lesson 64 Using Unit Multipliers to Convert a Rate Lesson 66 Applications Involving Similar Triangles Lesson 69 Direct Variation Extension Activity 15 “How can I find and interpret a rate of change?” Lesson 72 Multiple Unit Multipliers Lesson 88 Review of Proportional and Non-proportional Relationships Extension Activity 17 “Describe and Sketch Functions” Lesson 98 Relations and Functions Lesson 99 Inverse Variation Lesson 102 Exponential Growth and Decay Lesson 105 Compound Average Rate Problems

reserved.



Dom

ain

Stan

dard

Text of Objective


8.E

E E

xpre

ssio

ns a

nd E

quat

ions

8.E

E.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

INSTRUCTION: New Concept: Lesson 41, pp. 277-284; Lesson 44, pp. 301-304; Lesson 69, pp. 463-467; Lesson 88, pp. 585-589 MAINTENANCE: Written Practice: Lesson 47, pp. 324-325; Lesson 48, pp. 328-329(#4); Lesson 49, pp. 333-335(#1, #2); Lesson 77, p. 517 (#4, #5); Lesson 88, p. 592 (#25) Standards Success Activity: Activity 15, pp. 29-30

8.E

E.6

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

INSTRUCTION: New Concept: Lesson 56, pp. 382-386 Standards Success Activity: Activity 28, pp. 55-56

reserved.



D

omai

n

Stan

dard

Text of Objective


8.E

E E

xpre

ssio

ns a

nd E

quat

ions

Analyze and solve linear equations and pairs of simultaneous linear equations.

Students revisit and begin daily solving equations in one variable in Lesson 14 of Course 3. Depth and complexity of work with linear equations for 8th graders are further developed and expanded upon in Course 3 at the following points: Lesson 14 Solving Equations by Inspection Lesson 21 Distributive Property; Order of Operation Lesson 31 Collect Like Terms Lesson 38 Property of Equality to Solve Equations Lesson 50 Solving Multi-step Equations Lesson 56 Slope-Intercept Algebra Lesson 61 Equations with Decimals Algebra Lesson 63 Equations with Fractions (Lesson 82 Graphing Equations Using Intercepts) Algebra Lesson 87 Solve Equations with Two Variables Using Substitution Lesson 89 Solving Problems with Two Unknowns by Graphing Extension Activity 18 “Systems of equations with one, none, or infinitely many solutions” Lesson 92 Solving Systems of Equations by Substitution, Part 1 Lesson 93 Equations with Exponents Lesson 99 Solving Systems of Equations by Elimination, Part 1 Lesson 102 Solving Systems of Equations by Substitution, Part 2 Lesson 104 Solving Systems of Equations by Elimination, Part 2 Algebra Lesson 112 Solving Systems of Inequalities Algebra Lesson 114 Solving Systems of Inequalities from Word Problems

reserved.



D

omai

n

Stan

dard

Text of Objective


8.E

E E

xpre

ssio

ns a

nd E

quat

ions

8.E

E.7

Solve linear equations in one variable.

8.E

E.7

.a

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

INSTRUCTION: New Concept: Lesson 14, pp. 92-94 MAINTENANCE: Written Practice: Lesson 14, pp. 94-95(#5-#10, #15-#18); Lesson 16, pp. 105-107(#28, #29, #30); Lesson 17, pp. 111-113(#27, #28); Lesson 18, pp. 117-119(#26, #27); Lesson 19, pp. 124-125; Lesson 20, pp. 129-131(#14); Lesson 21, pp. 144-145(#6, #8, #11, #12, #20); Lesson 23, pp. 156-157 (#12, #13); Lesson 46, pp. 316-318 (#4, #5); Lesson 57, pp. 391-393 Standards Success Activity: Activity 7, pp. 13-14

8.E

E.7

.b

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

INSTRUCTION: New Concept: Lesson 38, pp. 250-254; Lesson 50, pp. 336-338; Lesson 56, pp. 382-386; Lesson A61, pp. 787-790 MAINTENANCE: Written Practice: Lesson 50, pp. 338-340(#4-#9); Lesson 51, pp. 351-353(#16); Lesson 52, pp. 357-359(#5, #6); Lesson 54, pp. 371-374(#5, #6); Lesson 55, pp. 378-381; Lesson 56, pp. 386-388(#5); Lesson 57, pp. 391-393; Lesson 58, pp. 397-399(#2); Lesson 61, p. 419 (#10, #11, #12, #13, #14, #15); Lesson 62, p. 428 (#18, #19, #20, #21, #22); Lesson 64, p. 439 (#20, #21, #22); Lesson 66, p. 451 (#22, #223); Lesson 69, p. 469 (#19, #20, #21) Standards Success Activity: Activity 25, pp. 49-50

reserved.



Dom

ain

Stan

dard

Text of Objective


8.E

E E

xpre

ssio

ns a

nd E

quat

ions

8.E

E.8

Analyze and solve pairs of simultaneous linear equations.

8.E

E.8

.a

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

INSTRUCTION: New Concept: Lesson 89, pp. 593-596 Appendix Lesson: Lesson A92-A95, pp. 809-811; Lesson A97, pp. 814-815; Lesson A99-A100, pp. 818-821; Lesson A102, pp. 824-826; Lesson A104, pp. 827-829 MAINTENANCE: Written Practice: Lesson A92, p. 811; Lesson A97, p. 816; Lesson A99-A100, p. 821; Lesson A104, p. 829 Standards Success Activity: Activity 18, pp. 35-36

8.E

E.8

.b

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

INSTRUCTION: Appendix Lesson: Lesson A92-A94, pp. 809-811; Lesson A99-A100, pp. 818-821; Lesson A102-A104, pp. 824-827; Lesson A104, pp. 827-829 MAINTENANCE: Written Practice: Lesson A92-A94, p. 811; Lesson A99-A100, p. 821; Lesson A102, p. 826; Lesson A204, p. 829 Standards Success Activity: Activity 18, pp. 35-36

8.E

E.8

.c Solve real-world and mathematical problems

leading to two linear equations in two variables.

INSTRUCTION: Appendix Lesson: Lesson A92-A94, pp. 809-811; Lesson A97, pp. 814-815

reserved.



D

omai

n

Stan

dard

Text of Objective


8.F

Func

tions

8.F

Define, evaluate, and compare functions. Course 3 has students revisit basic concepts of “input, output” tables in Lesson 41 in preparation for applying their understanding of functions as they model contextual situations. Work with functions for 8th graders is expanded upon in Course 3 at the following points: Lesson 41 Functions Lesson 44 Solving Proportions; Slope of a Line Lesson 47 Graphing Functions Lesson 56 Slope-Intercept Equation of a Line Lesson 61 Sequences Extension Activity 26 Comparing Linear Functions Lesson 69 Direct Variation Lesson 70 Solve Direct Variation Problems Extension Activity 28 Deriving the Equation of a Line Lesson 73 Formulas for Sequences Lesson 82 Graphing Equations Using Intercepts Lesson 88 Review of Proportional and Non-proportional Relationships Lesson 97 Recursive Rules for Sequences Lesson 98 Relations and Functions Lesson 99 Inverse Variation Investigation 11 Nonlinear Functions Extension Activity 21 Applying Nonlinear Functions Extension Activity 22 Linear, Quadratic and Exponential Functions

reserved.



D

omai

n

Stan

dard

Text of Objective


8.F

Func

tions

8.F.

1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1

INSTRUCTION: New Concept: Lesson 41, pp. 277-284; Lesson 47, pp. 319-323; Lesson 98, pp. 651-655 Investigation: Investigation 11, pp. 727-730 Appendix Lesson: Lesson A98, pp. 816-818 MAINTENANCE: Problem Solving: Lesson 18, p. 114; Lesson 40, p. 264; Lesson 48, p. 326 Written Practice: Lesson 42, pp. 290-293(#3, #18); Lesson 34, pp. 297-299(#5); Lesson 44, pp. 305-307; Lesson 45, pp. 310-312(#1, #3, #4); Lesson 46, pp. 316-318 (#4); Lesson 47, 324- 325; Lesson 48, pp. 328- 329(#4); Lesson 49, pp. 333- 335(#1, #2); Lesson 50, pp. 338- 341(#4-9); Lesson 51, pp. 351-353 (#16); Lesson 53, pp, 364 -366 (#6); Lesson 98, p.655 (#4, #5); Lesson 103, p. 688 (#4, #5); Lesson A98, p. 818 Graphing Calculator Activities: Activity 9 (Lesson 47), pp. ; Activity 22 (Lesson 11) Standards Success Activity: Activity 21, pp. 41-42

8.F.

2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

INSTRUCTION: New Concept: Lesson 41, pp. 277-284, Lesson 88, pp. 585-589 Investigation: Investigation 11, pp. 727-730 MAINTENANCE: Written Practice Lesson 41, pp. 284-286(#4, #30); Lesson 42, pp. 290-293(#3 #18); Lesson 44, pp. 305- 307; Lesson 45, pp. 310-312 (#1,#3, #4); Lesson 46, pp. 316-318 (#4); Lesson 47, pp. 324- 325; Lesson 48, pp. 328-329(# 4); Lesson 49, pp. 333- 335(#1, #2); Lesson 50, pp. 338 – 341 (#4-9, #27), Lesson 98, p. 655 (#7) Standards Success Activity: Activity 26, pp. 51-52

1 Function notation is not required in Grade 8.

reserved.



Dom

ain

Stan

dard

Text of Objective


8.F

Func

tions

8.F.

3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

INSTRUCTION: New Concept: Lesson 56, 382-38; Lesson 69, pp. 463-467, Lesson 82, pp. 550-553 Investigation: Investigation 11, pp. 727-730 MAINTENANCE: Written Practice: Lesson 56, pp. 387(#5); Lesson 57, p. 391; Lesson 58, p. 397(#2); Lesson 61, p. 420 (#20); Lesson 62, p. 428 (#22); Lesson 71, p. 483 (#6); Lesson 72, p. 489 (#4); Lesson 75, p. 506 (#25); Lesson 77, p. 517 (#4, #5); Lesson 88, p. 592 (#25) Graphing Calculator Activities: Activity 13 (Investigation 69); Activity 17 (Lesson 82), pp. 550-556 Standards Success Activity: Activity 22, pp. 43-44

Use functions to model relationships between quantities.

In Course 3, students build a foundation of functions as a relationship of quantities first through an input-output table before moving into abstract representations of sequences and patterns expressed algebraically. Functions are used as quantitative models in the following Course 3 lessons: Lesson 41 Functions Lesson 44 Solving Proportions; Slope of a Line Lesson 47 Graphing Functions Lesson 61 Sequences Lesson 69 Direct Variation Lesson 70 Solve Direct Variation Problems Lesson 73 Formulas for Sequences Lesson 88 Review of Proportional and Non-proportional Relationships Lesson 97 Recursive Rules for Sequences Lesson 98 Relations and Functions Lesson 99 Inverse Variation Investigation 11 Nonlinear Functions Extension Activity 21 Applying Nonlinear Functions Extension Activity 22 Linear, Quadratic and Exponential Functions

reserved.



Dom

ain

Stan

dard

Text of Objective


8.F

Func

tions

8.F.

4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

INSTRUCTION: New Concept: Lesson 41, p. 277-284, Lesson 44, p. 300-304, Lesson 47, p. 319-323, Lesson 69, pp. 463-467 Appendix Lesson: A68, pp. 793-794; Lesson A98, pp. 816-818 MAINTENANCE: Problem Solving: Lesson 18, p. 114; Lesson 40, p. 264; Lesson 48, p. 326 Written Practice: Lesson 44, p. 307(#29); Lesson 50, p. 340(#27); Lesson 69, p. 468 (#14); Lesson 70, p. 475 (#25); Lesson 77, p. 517 (#5); Lesson 95, p. 639 (#25); Lesson 100, p. 669 (325); Lesson A98, p. 818 Graphing Calculator Activities: Activity 9 (Lesson 47); Activity 13 (Lesson 69), pp. 463-469 Standards Success Activity: Activity 27, pp. 53-54

8.F.

5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

INSTRUCTION: New Concept: Lesson 41, p. 277-284Lesson 69, pp. 463-467; Lesson 88, pp. 585-589 Investigation: Investigation 11, pp. 727-730 Appendix Lesson: Lesson A98, pp. 816-818 MAINTENANCE: Written Practice: Lesson 42, p. 286; Lesson 42, p. 292(#18); Lesson 43, p. 297(#5); Lesson 44, p. 307(#29); Lesson 47, p. 325; Lesson 48, p. 329; Lesson 49, p. 335; Lesson 50, p. 341; Lesson 71, p. 483 (#4, #6); Lesson 72, p. 489 (#4, #8) Graphing Calculator Activities: Activity 13 (Lesson 69), pp. 463-469 Standards Success Activity: Activity 17, pp. 33-34

reserved.



D

omai

n

Stan

dard

Text of Objective


8.G

Geo

met

ry

Understand congruence and similarity using physical models, transparencies, or geometry software.

Students begin working with two-dimensional figures in Investigation 1 in Course 3 so as to allow for opportunities to practice on a daily basis throughout the course. Geometric concepts for 8th grade are built upon at the following points within Course 3: Investigation 1 Coordinate Plane Lesson 19 Polygons Lesson 20 Triangles Lesson 26 Transformations Lesson 35 Similar Polygons Lesson 37 Combined Polygons Investigation 5 Graphing Transformations Lesson 54 Angles Relationships Lesson 65 Applications Using Similar Triangles Lesson 71 Percent Change in Dimensions Lesson 88 Review of Proportional Relationships Lesson 95 Slant Heights of Pyramids and Cones Lesson 96 Geometric Measures with Radicals Lesson 112 Ratios of Side Lengths of Right Triangles Lesson 115 Relative Sizes of Sides and Angles of a Triangle

reserved.



D

omai

n

Stan

dard

Text of Objective


8.G

Geo

met

ry

8.G

.1

Verify experimentally the properties of rotations, reflections, and translations:

8.G

.1.a

Lines are taken to lines, and line segments to line segments of the same length.

INSTRUCTION: New Concept: Lesson 25, pp. 169-174 Investigation: Investigation 5, pp. 342-345 MAINTENANCE: Problem Solving: Lesson 22, p. 146, Lesson 84, p.563 Written Practice: Lesson 27, p.179 (#7, #9); Lesson 29, p. 189; Lesson 51, p. 353; Lesson 58, p. 399; Lesson 59, p. 405; Lesson 68, p. 462 (#25); Lesson 71, p. 484 (#15); Lesson 76, p. 513 (#25); Lesson 79, p. 530 (#25); Lesson 81, p. 548 (#3, #4); Lesson 83, p. 561 (#12); Lesson 85, p. 573 (#25) Graphing Calculator Activities: Activity 10 (Investigation 5), pp. 342-345

8.G

.1.b

Angles are taken to angles of the same measure.

INSTRUCTION: New Concept: Lesson 26, pp. 169-174 Investigation: Investigation 5, pp. 342-345 MAINTENANCE: Problem Solving : Lesson 22, p. 146, Lesson 84, p. 563 Written Practice Lesson 27, p. 179(#7, #9); Lesson 51, p. 353; Lesson 58, p. 399; Lesson 59, p. 405; Lesson 68, p. 462 (#25); Lesson 71, p. 484 (#15); Lesson 76, p. 513 (#25); Lesson 79, p. 530 (#25); Lesson 81, p. 548 (#3, #4); Lesson 83, p. 561 (#12); Lesson 85, p. 573 (#25) Standards Success Activity: Activity 3, pp. 5-6

reserved.



D

omai

n

Stan

dard

Text of Objective


8.G

Geo

met

ry

8.G

.1.c

Parallel lines are taken to parallel lines.

INSTRUCTION: New Concept: Lesson 26, pp.169-174 MAINTENANCE: Problem Solving: Lesson 42, p. 146, Lesson 84, p.563 Written Practice: Lesson 29, p. 189; Lesson 51, p. 353; Lesson 58, p. 399; Lesson 59, p 405; Lesson 76, p.513 (#25); Lesson 81, p. 548 (#3) Graphing Calculator Activities: Activity 10 (Investigation 5), pp. 342-345 Standards Success Activity: Activity 3, pp. 5-6

8.G

.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

INSTRUCTION: New Concept: Lesson 19, pp. 120-123, Lesson 26, pp. 169-174 Investigation: Investigation 5, pp. 342-345 MAINTENANCE: Written Practice Lesson 51, p.353; Lesson 58, p. 399; Lesson 59, p. 405; Lesson 68, p. 462 (#25); Lesson 76, p. 513 (#25); Lesson 79, p. 530 (#25); Lesson 83, p. 561 (#12); Lesson 85, p. 573 (#25) Standards Success Activity: Activity 8, pp. 15-16

8.G

.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

INSTRUCTION: New Concept: Lesson 26, pp. 169-174, Lesson 71, pp. 479-483 Investigation: Investigation 5, pp. 342-345 MAINTENANCE: Written Practice: Lesson 51, p. 352; Lesson 56, p. 387; Lesson 58, p. 399; Lesson 68, p. 462 (#25); Lesson 76, p. 513 (#25); Lesson 79, p. 530 (#25); Lesson 81, p. 548 (#3); Lesson 93, p. 627 (#4); Lesson 114, p. 753 (#16) Graphing Calculator Activities: Activity 10 (Investigation 5), pp. 342-345

reserved.



Dom

ain

Stan

dard

Text of Objective


8.G

Geo

met

ry

8.G

.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

INSTRUCTION: New Concept: Lesson 19, pp. 120-123, Lesson 26, pp. 169-174, Lesson 71, pp. 479-483 Investigation: Investigation 5, pp. 342-345 MAINTENANCE: Written Practice Lesson 27, p.179; Lesson 34, p. 228; Lesson 36, p.242, Lesson 39, p. 256, Lesson 40, p. 268, Lesson 57, p. 387, Lesson 60, p. 410, Lesson 71, p. 484 (#10, #16); Lesson 81, p. 548 (#3, #4); Lesson 93, p. 627 (#4); Lesson 643 Standards Success Activity: Activity 9, pp. 17-18

8.G

.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

INSTRUCTION: New Concept: Lesson 54, pp. 367-371, Lesson 65, pp. 440-443, Lesson 115, pp. 754-756 MAINTENANCE: Power Up: Lesson 11, p. 72, Lesson 14, p. 92, Lesson 16, p.103, Lesson 19, p.120, Lesson 19, p. 120, Lesson 64, p. 435, Lesson 66, p. 446 Problem Solving : Lesson 92, p. 617, Lesson 65, p. 443 Written Practice: Lesson 27, p.179; Lesson 34, p. 228; Lesson 36, p.242, Lesson 39, p. 256, Lesson 40, p. 268, Lesson 57, p. 387, Lesson 60, p. 410, Lesson 61, p. 419 (#5); Lesson 62, p. 426 (#5); Lesson 63, p. 433 (#5); Lesson 64, p. 437 (#5); Lesson 66, p. 450 (#5, #6); Lesson 68, p. 461 (#5, #12) Standards Success Activity: Activity 11, pp. 21-22; Activity 14, pp. 27-28; Activity 24, pp. 47-48

reserved.



Dom

ain

Stan

dard

Text of Objective


8.G

Geo

met

ry

Understand and apply the Pythagorean Theorem.

Students begin using the Pythagorean Theorem early in Course 3 and practice and apply its principals meaningfully throughout the course in order to be able to utilize it in problem-solving situations and eventually prove its origins. These applications occur at the following points in Course 3: Investigation 2 Pythagorean Theorem Extension Activity 5 The Pythagorean Theorem and Its Converse Extension Activity 6 The Pythagorean Theorem and Distance Lesson 95 Slant Heights of Pyramids and Cones Lesson 96 Geometric Measures with Radicals Extension Activity 20 Using the Pythagorean Theorem in 2-D and 3-D Figures Investigation 12 Proof of the Pythagorean Theorem

8.G

.6

Explain a proof of the Pythagorean Theorem and its converse.

INSTRUCTION: Investigation: Investigation 12, pp. 782-784 Standards Success Activity: Activity 5, pp. 9-10

8.G

.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

INSTRUCTION: New Concept: Lesson 37, pp. 245-247, Lesson 95, pp. 634-636 Investigation: Investigation 2, pp. 132-138 MAINTENANCE: Written Practice: Lesson 21, p.145, Lesson 28, p. 185, Lesson 32, p. 215, Lesson 39, p.263, Lesson 46, p.318, Lesson 55, p. 379, Lesson 59, p. 404, Lesson 62, p. 427 (#8, #13); Lesson 65, p. 444 (#10); Lesson 68, p. 46 (#10); Lesson 70, p. 475; Lesson 72, p. 489 (#9); Lesson 75, p. 505 (#7); Lesson 82, p. 553 (#5); Lesson 88, p. 591 (#10); Lesson 91, p. 614 (#8); Lesson 92, p. 622 (#15); Lesson 93, p. 628 (#25); Lesson 94, p. 632 (#6); Lesson 97, p. 649 (#10); Lesson 99, p. 662 (#4); Lesson 103, p. 689 (#11); Lesson 108, p. 716 (#14); Lesson 110, p. 726 (#12); Lesson 111, p. 735 (#10); Lesson 112, p. 741 (#22); Lesson 115, p. 757 (#6, #16) Standards Success Activity: Activity 20, pp. 39-40

reserved.



Dom

ain

Stan

dard

Text of Objective


8.G

Geo

met

ry

8.G

.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

INSTRUCTION: New Concept: Lesson 96, pp. 640-642 MAINTENANCE: Written Practice: Lesson 96, pp. 644 (#19); Lesson 104, p. 695; Lesson 111, p. 736 (#22); Lesson 114, p. 753 (#15); Lesson 115, p. 757 (#13); Lesson 119, p. 777 (#23) Standards Success Activity: Activity 6, pp. 11-12

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Students revisit and begin utilizing volume in context in Lesson 76 of Course 3. Applications of volume for 8th graders are expanded upon in Course 3 at the following points: Lesson 76 Volume of Prisms and Cylinders Lesson 86 Volume of Pyramids and Cones Lesson 106 Review of the Effect of Scale on Volume Lesson 107 Volume and Surface Area of Compound Solids Lesson 111 Volume and Surface Area of the Sphere

8.G

.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

INSTRUCTION: New Concept: Lesson 76, pp. 507-511, Lesson 86, pp. 574-578, Lesson 106, pp. 702-704, Lesson 107, pp. 707-709, Lesson 111, pp. 731-734 MAINTENANCE: Written Practice: Lesson 76, p. 512 (#5, #6); Lesson 78, p. 523 (#19); Lesson 79, p. 529 (#20, #22); Lesson 80, p. 536 (#6); Lesson 87, p. 583 (#5); Lesson 96, p. 643; Lesson 111, p. 735 (#1); Lesson 112, p. 740 (#8); Lesson 113, p.746

reserved.



D

omai

n

Stan

dard

Text of Objective


8.SP

Sta

tistic

s and

Pro

babi

lity

Investigate patterns of association in bivariate data.

Students in Course 3 will build upon basic plotting of data points (Investigation 1) to begin determining relationships between two sets of data points: is the association negative or positive, and to what degree? Were “outlier” data points valid or a measurement error? Students begin working with two sets of data points in Investigation 6 of Course 3 and provide opportunities to practice on a daily basis throughout the remainder of the course. Concepts regarding bivariate data for 8th grade are built upon at the following points within Course 3: Investigation 1 Graphing on a Coordinate Plane Investigation 6 Collect, Display, Interpret Data Extension Activity 13 Two-way Tables Investigation 8 Scatter Plots Extension Activity 16 Scatter Plots and Model Fit Lesson 113 Using Scatter Plots to Make Predictions Extension Activity 23 Patterns in Scatter Plots

8.SP

.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

INSTRUCTION: New Concept: Lesson 113, pp. 742-745 Investigation: Investigation 8, pp. 538-544 MAINTENANCE: Written Practice: Lesson 97, p. 650 (#25); Lesson 101, p. 680 (#24) Graphing Calculator Activities: Activity 16 (Investigation 8), pp. 538-544 Standards Success Activity: Activity 23, pp. 45-46

8.SP

.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

INSTRUCTION: New Concept: Lesson 113, pp. 742-745 Investigation: Investigation 8, pp. 538-544 MAINTENANCE: Written Practice: Lesson 97, p. 650 (#25); Lesson 101, p. 680 (#24) Graphing Calculator Activities: Activity 16 (Investigation 8), pp. 538-544 Standards Success Activity: Activity 16, pp. 31-32

reserved.


Common Core State Standards for Mathematics© Copyright 2010, National Governor’s Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

D

omai

n

Stan

dard

Text of Objective


8.SP

Sta

tistic

s and

Pro

babi

lity

8.SP

.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

INSTRUCTION: New Concept: Lesson 96, p. 642; Lesson 113, pp. 742-745 Investigation: Investigation 8, pp. 538-544 MAINTENANCE: Problem Solving : 382 Written Practice: Lesson 66, p. 451; Lesson 90, p. 604; Lesson 101, p. 680 (#24)

8.SP

.4

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

INSTRUCTION: Investigation: Investigation 8, pp. 538-544 Investigation: Investigation 6, pp. 412-414 MAINTENANCE: Written Practice: Lesson 66, p. 451 Standards Success Activity: Activity 13, pp. 25-26

Documents

Saxon Math Course 1 © 2012 Common Core State Standards for