images.pcmac.orgimages.pcmac.org/Uploads/DesotoCSD/DesotoCSD... · Web viewThe teacher notes state that these two lessons could be combined into one day. This is a foundational strategy

6th Grade Core Connections 1 Chapter 3

Lesson MS-CCRS Taught Focus for Lesson

MS-CCRS Specific

Problem(s)

Optional Supplements

and Adjustments

Pre-requisite standards and skills

3.1.1

Preparation for 6.RP.3cFind a percent quantity.

Day 1Focus of lesson is to introduce the strategy the “Giant One” for equivalent ratios.(3-4 and 3-5)

3-13 (6.RP.3d)

The teacher notes state that these two lessons could be combined into one day. This is a foundational strategy for the year, so if two days are available, it may be best to keep it as two days.

No pre-requisite standards taught in prior grades.

Day 2Focus of today is simplifying fractions using factoring to understand their equivalence.(3-8)

3.1.2

6.RP.3cFind 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.

You are defining a percent and introducing the percent ruler as a strategy to represent equivalent portions in different forms.(3-27 and 3-28)

3-35 (6.NS.3)

It would be great if teachers could use 3-29 as an exit ticket or closure.

No pre-requisite standards taught in prior grades.

3.1.3

Preparation for 6.NS.3Operations with decimals.

Day 1Focus is to see how portions can be written in multiple ways, (fraction, decimal, percent, words, etc.).(3-39)

None 5.NBT.B.5Fluently multiply multi-digit numbers5.NBT.B.6Find whole number quotients (4-digit by 2-digit)5.NBT.B.7Operations with decimals

Day 2Focus is still to show relationships between forms of numbers.(4-41 and 4-42)

None

College Preparatory Mathematics Desoto County Schools



MS-CCRS Specific

Problem(s)


and Adjustments


3.1.4

6.NS.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

The Portions Web is introduced in this lesson. However, the focus of the lesson is understanding place value and the importance of the decimal location when adding and subtracting decimals.(3-58)

None 5.NBT.B.5Fluently multiply multi-digit numbers5.NBT.B.6Find whole number quotients (4-digit by 2-digit)5.NBT.B.7Operations with decimals

3.1.5Preparation for 6.RP.3cFind a percent quantity.

Finding patterns in converting between number forms.(3-69)

None No pre-requisite standards taught in prior grades.

3.1.6

6.RP.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

The focus is understanding ratio language, (what numbers represent and how they are related).A bonus of the lesson is problem 3-82 as it relates to 6.RP.3 as well.

(3-81 and 3-82)

3-84 (6.RP.1 and 6.RP.3c)3-86 (6.SP.4)3-87 (6.NS.5)

5.NF.B.5Interpreting multiplication as scaling5.OA.B.3Generating patterns given rules4.OA.A.2Multiply or divide to solve word problems




MS-CCRS Specific

Problem(s)


and Adjustments


3.2.1

6.NS.5Understand 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.6.NS.6aRecognize 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.

Focus of the lesson is to familiarize students with opposites and movement on a number line. Make sure to discuss the “opposite of the opposite” as stated in the math notes.(3-91 and the Math Notes)

3-94 (6.NS.6a)3-98 (6.RP.1)

No pre-requisite standards taught in prior grades for 6.NS.5.

3.NF.A.2Understand a fraction is a number on the number line.




MS-CCRS Specific

Problem(s)


and Adjustments


3.2.2

6.NS.4Find 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 asum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).6.NS.5Understand 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.6.NS.6aRecognize 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.6.NS.6cFind 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.6.NS.7aInterpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

There are many standards being addressed in this lesson. All core problems have needed material in them. The overall lesson focuses on the number line and placement of positive and negative numbers and comparing them with an inequality symbol.

3-106 (6.NS.6a)

3-107 (6.NS.4)

3-108 (6.NS.6c)

Supplement:More practice is needed to ensure students are proficient with finding the LCM of two numbers. There is a brief lesson attached that teachers can use to review this concept before teaching section 3.2. *See note on sample pacing calendar.

5.OA.A.2Write simple expressions

4.OA.B.4Factors & multiples

No pre-requisite standards taught in prior grades for 6.NS.5.

3.NF.A.2Understand a fraction is a number on the number line.

5.G.A.1Define the coordinate system

No pre-requisite standards taught in prior grades for 6.NS.7a.

Lesson

MS-CCRS Taught Focus for Lesson MS-CCRS Specific

Problem(


and




s) Adjustments

3.2.3

6.NS.7bWrite, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3º C > –7º C to express the fact that –3º C is warmer than –7º C.6.NS.7cUnderstand 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. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.6.NS.7dDistinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

Introduction to absolute value and it’s meaning in a contextual problem is the focus for this lesson.(3-114, 3-115, and 3-116)

3-120 (6.NS.6c)

3-122 (6.NS.6c)

No pre-requisite standards taught in prior grades for 6.NS.7b, 6.NS.7c, or 6.NS.7d.




MS-CCRS Specific

Problem(s)


and Adjustments


3.2.4

6.NS.6bUnderstand 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.6.NS.6cFind 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.6.NS.8Solve 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.6.G.3Draw 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.

The focus for this lesson is for students to use the knowledge they have learned with a single number line and apply it to the coordinate grid. Students should gain a strong understanding of how to plot points and their relationships to one another.

All core problems tie directly to one or more of the intended standards.

3-128 (6.NS.7c)

3-129 (6.NS.8)

3-130 (6.NS.4)

CL 3-138 (6.NS.6c)

CL 3-141 (6.NS.4)

5.G.A.1Define the coordinate system

5.G.A.2Graphing in the first quadrant



Assessment Understanding According to PARCC (Section Quiz and Chapter Assessment)

MS-CCRSEOY or

PBA

Math Practic

eClarifications

Calculator or No

Calculator

Chapter Mastery

6.RP.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

EOY and PBA

2

Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers. No

calculator

NowRatios of quantities and dilations

Coming UpRatios to compare similar figures and non-geometric contexts (chap. 4)

6.RP.3c – 1Use 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.c. Find a percent of a quantity as a rate

per 100 (e.g., 30% of a quantity means 30/100 times the quantity).

EOY 2, 5, 7, and 8

The testing interface can provide students with a calculation aid of the specified kind for these tasks.

Pool should contain tasks with and without contexts

Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers.

Calculator

NowPercent as a way to compare portions of a whole

Coming UpPercentages are a heavy focus of chapter 9.

6.RP.3c – 2Use 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.c. Solve problems involving finding the

whole, given a part and the percent.

EOY 2, 5, 7, and 8


Pool should contain tasks with and without contexts

Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p 42.) The initial numerator and denominator should be whole numbers.

Calculator

NowPercent as a way to compare portions of a whole

Coming UpPercentages are a heavy focus of chapter 9.



MS-CCRSEOY or

PBA

Math Practic

eClarifications

Calculator or No

Calculator

Chapter Mastery

6.NS.3 – 1Fluently add multi-digit decimals using the standard algorithm for each operation.

EOY -

Tasks do not have a context. Only the sum is required. Prompts do not include visual models.

The answer sought is a number, not a picture.

The given addends are such as to require an efficient/standard algorithm (e.g., 72.63+4.875). Addends in the task do not suggest any obvious ad hoc or mental strategy (as would be present for example in a case such as 16.999+3.501).

Each addend is greater than or equal to 0.001 and less than or equal to 99.999.

No calculator

NowAdding and subtracting

Coming UpMultiplying and dividing are in chapters 5 and 7.

6.NS.3 – 2Fluently subtract multi-digit decimals using the standard algorithm for each operation.

EOY -

Tasks do not have a context. Only the difference is required. Prompts do not include visual models.


The given subtrahend and minuend are such as to require an efficient/standard algorithm (e.g., 177.3-72.635). The subtrahend and minuend do not suggest any obvious ad hoc or mental strategy (as would be present for example in a case such as 20.5-3.501).

The subtrahend and minuend are each greater than or equal to 0.001 and less than or equal to 99.999. Positive differences only. (Every included subtraction problem is an unknown-addend problem included in 6.NS.3-1.)

No calculator





MS-CCRSEOY or

PBA

Math Practic

eClarifications

Calculator or No

Calculator

Chapter Mastery

6.NS.3 – 3Fluently multiply multi-digit decimals using the standard algorithm for each operation.

EOY -

Tasks do not have a context. Only the product is required. Prompts do not include visual models.


The given factors are such as to require an efficient/standard algorithm (e.g., 72.3×4.87). Factors in the task do not suggest any obvious ad hoc or mental strategy.

Problems are effectively 3-digit by 3-digit or 2-digit by 5-digit. (For example, 7.68×15.3 or

0.35×18.241.)

No calculator



6.NS.3 – 4Fluently divide multi-digit decimals using the standard algorithm for each operation.

EOY -

Tasks do not have a context. Only the quotient is required. Prompts do not include visual models. The

answer sought is a number, not a picture. The given dividend and divisor are such as

to require an efficient/standard algorithm (e.g., 177.3÷0.36). The dividend and divisor do not suggest any obvious ad hoc or mental strategy.

Problems are effectively 4-digit divided by 2-digit or 3-digit3-digit. (For example, 14.28÷0.68 or 2.394÷0.684)

Every quotient is a whole number or a decimal terminating at the tenths, hundredths, or thousandths place. Every included division problem is an unknown-factor problem included in 6.NS.3-3.

No calculator





MS-CCRSEOY or

PBA

Math Practic

eClarifications

Calculator or No

Calculator

Chapter Mastery

6.NS.4 - 1Find the greatest common factor of two whole numbers less than or equal to 100;Find the least common multiple of two whole numbers less than or equal to 12.

EOY NA

Tasks do not have context Tasks require students to find the

greatest common factor or the least common multiple only. No

calculator

NowHeavy focus of LCM. All can be assessed now.

Coming UpNA

6.NS.4 - 2Use 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. For example, express 36 + 8 as 4 (9 + 2).

EOY 7

Tasks do not have a context

No calculator

NowHeavy focus of LCM. All can be assessed now.

Coming UpNA

6.NS.5Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperatures 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.

EOY and PBA

2 and 5

Tasks do not require students to perform any computations.

Students may be asked to recognize the meaning of 0 in the situation, but will not be asked to explain. No

Calculator

NowEntire standard is taught in chapter 3.

Coming UpNA



MS-CCRSEOY or

PBA

Math Practic

eClarifications

Calculator or No

Calculator

Chapter Mastery

6.NS.6aUnderstand 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.a. 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.

EOY and PBA

3, 4, 5, 6, and 8

Tasks have “thin context” or no context. 6.C.4 - Base explanations/reasoning on a

number line diagram (whether provided in the prompt or constructed by the student in her response).

6.C.5 - Base explanations/reasoning on a coordinate plane diagram (whether provided in the prompt or constructed by the student in her response).

No Calculator

Yes on PBA


Coming UpNA

6.NS.6b – 1Understand 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.b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.

EOY and PBA

3, 4, 5,and 6

Tasks have “thin context” or no context. Students need not recognize or use

traditional notation for quadrants (such as I, II, III, IV).

Coordinates are not limited to integers. 6.C.4 - Base explanations/reasoning on a



No Calculator

Yes on PBA

NowFocus is primarily on integers only.

Coming UpCheckpoint 6 has students plot rational numbers on a number line.

6.NS.6b – 2Understand 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.b. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

EOY and PBA

3, 4, 5, 6, and 8


traditional notation for quadrants (such as I, II, III, IV).




No Calculator

Yes on PBA


Coming UpNA

MS-CCRS EOY or

Math Practic

Clarifications Calculator or No

Chapter Mastery



PBA e Calculator

6.NS.6c – 1Understand 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.c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram.

EOY and PBA

3, 4, 5,and 6

Tasks have “thin context” or no context. Coordinates are not limited to integers. 6.C.4 - Base explanations/reasoning on a



No Calculator

Yes on PBA



6.NS.6c – 2Understand 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.c. Find and position pairs of integers and other rational numbers on a coordinate plane.

EOY and PBA

3, 4, 5,and 6


traditional notation for quadrants (such as I, II, III, or IV).




No Calculator

Yes on PBA



6.NS.7aUnderstand ordering and absolute value of rational numbers.a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.

EOY and PBA

2, 3, 4, 5, and 6

Tasks do not have a context. Tasks are not limited to integers. 6.C.4 - Base explanations/reasoning on a



No Calculator

Yes on PBA


Coming UpNA



MS-CCRSEOY or

PBA

Math Practic

eClarifications

Calculator or No

Calculator

Chapter Mastery

6.NS.7bUnderstand ordering and absolute value of rational numbers.b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3°C > -7°C to express the fact that -3°C is warmer than -7°C.

EOY and PBA

2, 3, 4, 5,

and 6

Tasks are not limited to integers. Tasks do not require students to explain. 6.C.4 - Base explanations/reasoning on a



No Calculator

Yes on PBA


Coming UpNA

6.NS.7c – 1Understanding ordering and absolute value of rational numbers.c. Understand the absolute value of a rational number as its distance from 0 on the number line.

EOY and PBA

2, 3, 4, 5, and 6




No Calculator

Yes on PBA


Coming UpNA

6.NS.7c – 2Understand ordering and absolute value of rational numbers.c. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |−30|=30to describe the size of the debt in dollars.

EOY and PBA

2, 3, 4, 5,

and 6




No Calculator

Yes on PBA


Coming UpNA



MS-CCRSEOY or

PBA

Math Practic

eClarifications

Calculator or No

Calculator

Chapter Mastery

6.NS.7dUnderstand ordering and absolute value of rational numbers.d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

EOY and PBA

2, 3, 4, 5, and 6

Pool should contain tasks with and without contexts.

Tasks are not limited to integers. Prompts do not present students with a

number line diagram, but students may draw a number line diagram as a strategy.

6.C.4 - Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response).


No Calculator

Yes on PBA


Coming UpNA

6.NS.8Solve 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.

EOY and PBA

1, 2, 3, 4, 5, and 6

Pool should contain tasks with and without contexts.

Finding distances is limited to points with integer coordinates.


No Calculator

Yes on PBA


Coming UpNA

6.G.3Draw 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.

EOY 1 and 5


Calculator

NowStandard is introduced in 3.2.4

Coming UpSection 4.2 has practice of plotting polygons on the coordinate grid.


Documents

images.pcmac.orgimages.pcmac.org/Uploads/DesotoCSD/DesotoCSD... · Web viewThe teacher notes state that these two lessons could be combined into one day. This is a foundational strategy