6•4 Lesson 1

Lesson 1: The Relationship of Addition and Subtraction

Lesson 1: The Relationship of Addition and Subtraction

Classwork

Opening Exercise

a. Draw a tape diagram to represent the following expression: 5 + 4.

b. Write an expression for each tape diagram. i.

ii.

Exercises

1. Predict what will happen when a tape diagram has a large number of squares, some squares are removed, and then the same amount of squares are added back on.

2. Build a tape diagram with 10 squares. a. Remove six squares. Write an expression to represent the tape diagram.

b. Add six squares onto the tape diagram. Alter the original expression to represent the current tape diagram.

A STORY OF RATIOS

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6•4 Lesson 1

Lesson 1: The Relationship of Addition and Subtraction

c. Evaluate the expression.

3. Write an equation, using variables, to represent the identities we demonstrated with tape diagrams.

4. Using your knowledge of identities, fill in each of the blanks. a. 4 + 5 − _____ = 4

b. 25 − _____ + 10 = 25

c. _____ + 16 − 16 = 45

d. 56 − 20 + 20 = _____

5. Using your knowledge of identities, fill in each of the blanks.

a. 𝑎𝑎 + 𝑏𝑏 − _____ = 𝑎𝑎

b. 𝑐𝑐 − 𝑑𝑑 + 𝑑𝑑 = _____

c. 𝑒𝑒 + _____ − 𝑓𝑓 = 𝑒𝑒

d. _____ − ℎ + ℎ = 𝑔𝑔

A STORY OF RATIOS

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6•4 Lesson 1

Lesson 1: The Relationship of Addition and Subtraction

Problem Set 1. Fill in each blank.

a. _____ + 15 − 15 = 21

b. 450 − 230 + 230 = _____

c. 1289 − ______ + 856 = 1289

2. Why are the equations 𝑤𝑤 − 𝑥𝑥 + 𝑥𝑥 = 𝑤𝑤 and 𝑤𝑤 + 𝑥𝑥 − 𝑥𝑥 = 𝑤𝑤 called identities?

A STORY OF RATIOS

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6•4 Lesson 1

Lesson 1: The Relationship of Addition and Subtraction

Name Date

Lesson 1: The Relationship of Addition and Subtraction

Exit Ticket

1. Draw tape diagrams to represent each of the following number sentences.a. 3 + 5 − 5 = 3

b. 8 − 2 + 2 = 8

2. Fill in each blank.

a. 65 + _____ −15 = 65

b. _____ + 𝑔𝑔 − 𝑔𝑔 = 𝑘𝑘

c. 𝑎𝑎 + 𝑏𝑏 − _____ = 𝑎𝑎

d. 367 − 93 + 93 = _____

A STORY OF RATIOS

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Lección 1 Boleto de salidaUNA HISTORIA DE PROPORCIONES 6•4

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Lección 1:

Nombre Fecha

1. Dibuja diagramas de cinta para representar cada uno de los siguientes enunciados numéricos.

a. 3 + 5 − 5 = 3

b. 8 − 2 + 2 = 8

2. Llena los espacios en blanco.

a. 65 + − 15 = 65

b. + g − g = k

c. a + b − = b

d. 367 − 93 + 93 =

La relación de la suma y la resta

EM1_S_0604LPS_TopicA.indd 7 04-10-2019 00:49:32

6•4 Lesson 2

Lesson 2: The Relationship of Multiplication and Division

Lesson 2: The Relationship of Multiplication and Division

Classwork

Opening Exercise

Draw a pictorial representation of the division and multiplication problems using a tape diagram.

a. 8 ÷ 2

b. 3 × 2

Exploratory Challenge

Work in pairs or small groups to determine equations to show the relationship between multiplication and division. Use tape diagrams to provide support for your findings.

1. Create two equations to show the relationship between multiplication and division. These equations should be identities and include variables. Use the squares to develop these equations.

2. Write your equations on large paper. Show a series of tape diagrams to defend each of your equations.

Use the following rubric to critique other posters.

1. Name of the group you are critiquing 2. Equation you are critiquing 3. Whether or not you believe the equations are true and reasons why

A STORY OF RATIOS

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6•4 Lesson 2

Lesson 2: The Relationship of Multiplication and Division

Problem Set 1. Fill in each blank to make the equation true.

a. 132 ÷ 3 × 3 = _____

b. _____ ÷ 25 × 25 = 225

c. 56 × _____ ÷ 8 = 56

d. 452 × 12 ÷ _____ = 452

2. How is the relationship of addition and subtraction similar to the relationship of multiplication and division?

A STORY OF RATIOS

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6•4 Lesson 2

Lesson 2: The Relationship of Multiplication and Division

Name Date

Lesson 2: The Relationship of Multiplication and Division

Exit Ticket

1. Fill in the blanks to make each equation true.

a. 12 ÷ 3 × ______ = 12

b. 𝑓𝑓 × ℎ ÷ ℎ = ______

c. 45 × ______ ÷ 15 = 45

d. ______ ÷ 𝑟𝑟 × 𝑟𝑟 = 𝑝𝑝

2. Draw a series of tape diagrams to represent the following number sentences.a. 12 ÷ 3 × 3 = 12

b. 4 × 5 ÷ 5 = 4

A STORY OF RATIOS

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Lección 2:

Nombre Fecha

1. Llena los espacios en blanco para hacer que cada ecuación sea verdadera.

a. 12 ÷ 3 × = 12

b. f × h ÷ h =

c. 45 × ÷ 15 = 45

d. ÷ r × r = p

2. Dibuja una serie de diagramas de cinta para representar los siguientes enunciados numéricos.

a. 12 ÷ 3 × 3 = 12

b. 4 × 5 ÷ 5 = 4

La relación de la multiplicación y la división

EM1_S_0604LPS_TopicA.indd 19 04-10-2019 00:50:51

1 - problem set 1 English (2)2 - problem set 1 English3 - exit ticket 1 English (2)4 - exit ticket 1 Spanish (2)5 - problem set 2 English (4)6 - problem set 2 Spanish (5)7 - exit ticket 2 English (2)8 - exit ticket 2 Spanish (2)