Engaging Mathematics: TEKS-Based Activities Grade … · TEKS-Based Activities Grade 6 ISBN: ... Mean, Activity 1 ..... 300 Mean, ... Rectangular sheet of paper Colored pencils

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TEKS-BasedTEKS-BasedActivitiesActivities

Grade 6Grade 6

ISBN: 978-1-934950-68-5

www.theansweris4.net

Engaging Mathematics:TEKS-Based Activities

Grade 6

Teacher Edition

Product ID: 407-1601

Creating solutions that are the worldwide standard for

educational excellence®

Revolutionizing education to inspire and advance future

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SAMPLE

Table of Contents Introduction ........................................................................................................ i–viii

Overview of Materials ............................................................................................ i References ........................................................................................................... iii Texas Essential Knowledge and Skills (TEKS) Alignment Chart .......................... iv

Number, Operation, and Quantitative Reasoning ........................................... 1–95 Integers, Activity 1 ................................................................................................ 2 Integers, Activity 2 ................................................................................................ 4 Equivalent Fractions and Decimals, Activity 1 ...................................................... 6 Equivalent Fractions and Decimals, Activity 2 ...................................................... 8 Equivalent Fractions and Decimals, Activity 3 .................................................... 10 Equivalent Fractions and Decimals, Activity 4 .................................................... 14 Compare and Order Fractions and Decimals, Activity 1 ..................................... 18 Compare and Order Fractions and Decimals, Activity 2 ..................................... 20 Prime Factors ..................................................................................................... 22 Common Factors ................................................................................................ 24 Greatest Common Factor ................................................................................... 26 Common Multiples .............................................................................................. 28 Least Common Multiple ...................................................................................... 30 Order of Operations, Activity 1 ............................................................................ 32 Order of Operations, Activity 2 ............................................................................ 34 Modeling Fractions With Common Denominators .............................................. 36 Estimating Sums of Fractions ............................................................................. 38 Estimating Sums and Differences of Fractions ................................................... 40 Modeling Addition of Fractions, Activity 1 ........................................................... 42 Modeling Addition of Fractions, Activity 2 ........................................................... 44 Addition and Subtraction of Fractions ................................................................. 46 Estimating Sums and Differences of Mixed Numbers, Activity 1 ........................ 48 Estimating Sums and Differences of Mixed Numbers, Activity 2 ........................ 52 Modeling Addition and Subtraction of Mixed Numbers, Activity 1 ....................... 56 Modeling Addition and Subtraction of Mixed Numbers, Activity 2 ....................... 58 Modeling Addition and Subtraction of Mixed Numbers, Activity 3 ....................... 62 Addition and Subtraction of Mixed Numbers Without Regrouping ...................... 64 Addition and Subtraction of Mixed Numbers, Activity 1 ...................................... 66 Addition and Subtraction of Mixed Numbers, Activity 2 ...................................... 68 Addition and Subtraction of Mixed Numbers, Activity 3 ...................................... 70 Addition and Subtraction of Mixed Numbers, Activity 4 ...................................... 72 Addition and Subtraction of Mixed Numbers: Validating Conclusions ................ 74 Application Problems Using Mixed Numbers, Activity 1 ..................................... 76 Application Problems Using Mixed Numbers, Activity 2 ..................................... 78 Application Problems Using Mixed Numbers, Activity 3 ..................................... 82 Addition and Subtraction of Decimals ................................................................. 84 Application Problems Using Decimals, Activity 1 ................................................ 86 Application Problems Using Decimals, Activity 2 ................................................ 88 Application Problems Using Fractions and Decimals, Activity 1 ......................... 90 Application Problems Using Fractions and Decimals, Activity 2 ......................... 94

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Patterns, Relationships, and Algebraic Thinking ........................................ 96–173 Percents Introduction .......................................................................................... 96 Modeling Percents, Activity 1 .............................................................................. 98 Modeling Percents, Activity 2 ............................................................................ 102 Percents, Activity 1 ........................................................................................... 104 Percents, Activity 2 ........................................................................................... 108 Modeling Ratios, Activity 1 ................................................................................ 110 Modeling Ratios, Activity 2 ................................................................................ 112 Ratios, Activity 1 ............................................................................................... 116 Ratios, Activity 2 ............................................................................................... 120 Ratios, Activity 3 ............................................................................................... 124 Multiple Representations, Activity 1 .................................................................. 126 Multiple Representations, Activity 2 .................................................................. 130 Multiple Representations, Activity 3 .................................................................. 132 Multiple Representations, Activity 4 ................................................................. 134 Multiple Representations, Activity 5 .................................................................. 138 Proportional Relationships, Activity 1 ................................................................ 142 Proportional Relationships, Activity 2 ................................................................ 144 Proportional Relationships, Activity 3 ................................................................ 148 Proportional Relationships, Activity 4 ................................................................ 150 Expressions, Activity 1 ...................................................................................... 152 Expressions, Activity 2 ...................................................................................... 156 Writing an Equation, Activity 1 .......................................................................... 160 Writing an Equation, Activity 2 .......................................................................... 162 Sequences, Activity 1 ........................................................................................ 164 Sequences, Activity 2 ........................................................................................ 166 Sequences, Activity 3 ........................................................................................ 170

Geometry and Spatial Reasoning ............................................................... 174–213 Classifying Angles, Activity 1 ............................................................................ 174 Classifying Angles, Activity 2 ............................................................................ 178 Triangles, Activity 1 ........................................................................................... 182 Triangles, Activity 2 ........................................................................................... 184 Triangles, Activity 3 ........................................................................................... 186 Quadrilaterals, Activity 1 ................................................................................... 190 Quadrilaterals, Activity 2 ................................................................................... 194 Quadrilaterals, Activity 3 ................................................................................... 196 Circles Introduction ........................................................................................... 198 Circle Relationships, Activity 1 .......................................................................... 200 Circle Relationships, Activity 2 .......................................................................... 202 Circle Relationships, Activity 3 .......................................................................... 204 Coordinate Plane, Activity 1 .............................................................................. 208 Coordinate Plane, Activity 2 .............................................................................. 210

Measurement ................................................................................................ 214–275 Measurement Conversions, Activity 1 ............................................................... 214 Measurement Conversions, Activity 2 ............................................................... 218 Measurement Conversions, Activity 3 ............................................................... 220

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Perimeter, Activity 1 .......................................................................................... 222 Perimeter, Activity 2 .......................................................................................... 224 Perimeter, Activity 3 .......................................................................................... 226 Perimeter, Activity 4 .......................................................................................... 228 Patterns in Perimeter ........................................................................................ 230 Formulas for Area, Activity 1............................................................................. 232 Formulas for Area, Activity 2............................................................................. 236 Estimating the Area of Circles .......................................................................... 238 Selecting Area Formulas .................................................................................. 240 Application Problems Involving Circumference ................................................. 244 Volume, Activity 1 ............................................................................................. 246 Volume, Activity 2 ............................................................................................. 248 Volume, Activity 3 ............................................................................................. 250 Application Problems Involving Measurement Concepts, Activity 1 .................. 254 Application Problems Involving Measurement Concepts, Activity 2 .................. 256 Application Problems Involving Measurement Concepts, Activity 3 .................. 260 Application Problems Involving Measurement Concepts, Activity 4 .................. 262 Measuring Angles, Activity 1............................................................................. 266 Measuring Angles, Activity 2............................................................................. 270 Measuring Angles, Activity 3............................................................................. 272

Probability and Statistics ............................................................................ 276–311 Sample Spaces, Activity 1 ................................................................................ 276 Sample Spaces, Activity 2 ................................................................................ 280 Probability of Simple Events, Activity 1 ............................................................. 282 Probability of Simple Events, Activity 2 ............................................................. 284 Representing Data, Activity 1 ........................................................................... 288 Representing Data, Activity 2 ........................................................................... 290 Circle Graphs, Activity 1 ................................................................................... 292 Circle Graphs, Activity 2 ................................................................................... 294 Circle Graphs, Activity 3 ................................................................................... 296 Mean, Activity 1 ................................................................................................ 300 Mean, Activity 2 ................................................................................................ 304 Statistics, Activity 1 ........................................................................................... 306 Statistics, Activity 2 ........................................................................................... 308 Statistics, Activity 3 ........................................................................................... 310

Resources .................................................................................................... 312–314 Centimeter Grid Paper ...................................................................................... 312 Grade 6 Conversion Chart ................................................................................ 313 Grade 6 Formula Chart ..................................................................................... 314

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Engaging Mathematics: Grade 6 TEKS-Based Activities

© Region 4 Education Service Center All rights reserved

Activity Objective The student will model addition situations involving fractions with objects, pictures, words, and numbers.

Materials Have Cake and Eat It, Too Rectangular sheet of paper Colored pencils

Facilitation Questions How can you fold the paper so that you have four equal parts?

Answers may vary. Possible answers: I could fold the paper in half two times. When I unfold the paper, the folds divide the paper into four equal parts. I could shade one of

those parts to represent 1

4.

How could you use the same sheet of paper to model eighths? Answers may vary. Possible answer: I could fold the paper in half twice in the same way that I folded it before, and then I could fold it one more time. When I unfold the paper, the folds now divide the paper into eight equal parts. I could shade three of those parts

to represent 3

8.

How do the additional folds change the representation of 1

4?

Answers may vary. Possible answer: The additional folds divide the part of the paper

that represents 1

4 into two equal parts. I could name the part

2

8 because

2

8 is

equivalent to 1

4.

Answers

Sketch of your paper model

Portion of cake eaten by Harvey

Portion of cake eaten by Ted

Use words to describe your solution. Five out of eight parts of the paper are

shaded, so Harvey and Ted ate 5

8 of

the cake.

Use numbers to represent the problem situation and your solution.

1 2 2 3 5

4 8 8 8 8

Modeling Addition of Fractions, Activity 2

44

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Student Name: ________________________________________ Date: ________________

Have Cake and Eat It, Too

Harvey made a cake to share with his friend Ted. Harvey ate 1

4 of the cake, and Ted ate

3

8 of

the cake. 1. Use one sheet of paper. Fold the paper into fourths and then shade the paper to represent

the portion of the cake that Harvey ate. 2. Fold the same sheet of paper into eighths. Using a different color, shade the paper to

represent the portion of the cake that Ted ate. 3. Use the shaded portions on the sheet of paper to determine the portion of the cake Harvey

and Ted ate altogether. Sketch of your paper model

Use words to describe your solution. Use numbers to represent the problem situation and your solution.

Communicating About Mathematics How does the paper model verify the solution to the problem situation?

45

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Activity Objective The student will represent ratios and percents with concrete models, fractions, and decimals.

Materials Fractions and Percents Color Tiles

Facilitation Questions Does the total number of tiles in the set represent the numerator or denominator

of a fraction? Why? Answers may vary. Possible answers: The total number of tiles in the set would be the denominator of a fraction because it represents the entire set.

Does the number of blue tiles in the set represent the numerator or denominator of a fraction? Why? Answers may vary. Possible answers: The total number of blue tiles in the set would be the numerator of a fraction because it represents a part of the entire set.

If you divided 100 into 4 equal parts, what would be the value of each equal part? Answers may vary. Possible answer: 100 4 25 , so each part would have a value equal to 25%.

If the blue tiles represent 3 of the 4 equal parts and 1 part is equal to 25%, how could you use multiplication to determine the percentage of tiles in the set that are blue? Answers may vary. Possible answer: If one part is equal to 25%, then I could multiply 3 25 75 to determine that the blue tiles are 75% of the entire set.

Answers

Blue Green

Set Picture

1 Tile

Represents ___% of Set

Fraction of Set

% of Set Fraction

of Set % of Set

3 blue tiles 1 green tile

BBBG 25% 3

4 75%

1

4 25%

2 blue tiles 3 green tiles

BBGGG 20% 2

5 40%

3

5 60%


BBBBBBBBGG

10% 8

10or

4

5 80%

2

10 or 20%

Modeling Percents, Activity 2

102

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Fractions and Percents

Use square tiles to make each of the sets described below. Complete each table using the data from each set of square tiles.

Communicating About Mathematics How does knowing the total number of items in a set help determine the percentage represented by each item in the set?

Blue Green

Set Picture

1 Tile

Represents ___% of

Set

Fraction of Set

% of Set

Fraction of Set

% of Set

3 blue tiles 1 green tile



103

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Activity Objective The student will use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates.

Materials Measurement Equivalences Measurement Equivalence Cards Tape or glue Scissors

Facilitation Questions How could you generate an equivalent ratio?

Answers may vary. Possible answers: I could multiply or divide the numerator and denominator by the same number to create a ratio equivalent to a given ratio.

What is the relationship between inches to feet in .48 in

4 ft?

Answers may vary. Possible answers: The relationship is 12 inches to every 1 foot.

How could you use this relationship to find an equivalent ratio? Answers may vary. Possible answer: I could look for other ratios that have a relationship of 12 inches to every 1 foot.

Answers

Relationship: Inches to Feet

12

1 48

4 60

5

84

7

Relationship: Ounces to Cups

8

1

16

2

24

3

40

5

Relationship: Quarts to Gallons

20.5

4

1 8

2

12

3

Ratios, Activity 2

120

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Measurement Equivalences

1. Cut apart the Measurement Equivalence Cards. 2. Match the Measurement Equivalence Cards to the correct relationships below. 3. Tape or glue the equivalent ratios.

Relationship: Inches to Feet

Relationship: Ounces to Cups

Relationship: Quarts to Gallons

Communicating About Mathematics Pick one set of matched cards. Explain how you determined that the cards represented equivalent ratios.

121

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Measurement Equivalence Cards

Cut along the bold dotted lines. Two sets of cards are provided.

48

4

12

3 40

5

24

3

8

1

4

1 2

0.5

8

2

12

1

84

7

16

2

60

5

48

4

12

3 40

5

24

3

8

1

4

1 2

0.5

8

2

12

1

84

7

16

2

60

5

122

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Activity Objective The student will define attributes of circles.

Materials Circles: Find Someone Who . . .

Facilitation Questions What do you know about the parts of a circle?

Answers may vary. Possible answers: Circles have an outside curved edge that is the distance around the circle. I could draw a line through the center of a circle to show the length across the circle.

How could you draw the radius? Answers may vary. Possible answer: I could draw a circle and then draw a line from the center of the circle to the outer edge of the circle.

How could you describe circumference? Answers may vary. Possible answer: Circumference is the distance around a circle.

Answers

can draw and label the diameter of a circle.

can draw and label the radius of a circle.

can draw and label the circumference of a circle.

Answer:

Answer:

Answer:

can define diameter. can define radius. can define circumference.

Answer: Diameter is a line segment that passes through the center of a circle and has both endpoints on the circle.

Answer: A radius is half the length of the diameter or a line segment from the center of a circle to a point on the circle.

Answer: Circumference is the distance around a circle.

Circles Introduction

198

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Circles: Find Someone Who . . . 1. Find a student who can draw or define the given part of a circle. 2. Ask him or her to draw or define the given part of a circle and sign his or her name. 3. Continue this process until your paper is complete. 4. Each student may only answer one problem on your paper.

can draw and label the diameter of a circle.

can draw and label the radius of a circle.

can draw and label the circumference of a circle.

Answer: Answer: Answer:

Signature:

Signature: Signature:

can define diameter. can define radius. can define circumference.

Answer:

Answer: Answer:

Signature:

Signature: Signature:

Communicating About Mathematics How are circumference and perimeter similar? How are they different?

199

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Documents

Engaging Mathematics: TEKS-Based Activities Grade … · TEKS-Based Activities Grade 6 ISBN: ... Mean, Activity 1 ..... 300 Mean, ... Rectangular sheet of paper Colored pencils