IM 5.2 Using Diagrams to Represent Addition and Subtraction

​Warm-up pg 13

Using Diagrams to
Represent Addition
& Subtraction

Lesson #2

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Let’s represent addition
and subtraction of
decimals.

Today’s Goals

❏ I can use diagrams to represent and reason

about addition and subtraction of decimals.

❏ I can use place value to explain addition and

subtraction of decimals.

❏ I can use vertical calculations to represent and

reason about addition and subtraction of
decimals.

​Today's Goals

Squares &
Rectangles

Activity 2.2

●MLR7: Compare & Connect

Study these diagrams. What do you notice
about how they are structured?

Open Ended

Here is the diagram that Priya drew to represent 0.13. Draw a different diagram that represents 0.13. Explain why your diagram and Priya’s diagram represent the same number.

Open Ended

Here is the diagram that Han drew to represent 0.025. Draw a different diagram that represents 0.025. Explain why your diagram and Han’s diagram represent the same number.

Draw

For each of these numbers, draw or describe two different diagrams that represent it.

a. 0.1                                            b. 0.02                                             c. 0.43

Draw

Use diagrams of base-ten units to represent the following sums and find their values. Think about how you could use as few units as possible to represent each number.

Let’s Talk About It

●Is it always helpful or important to use as few base-ten figures as
possible when representing addition of two numbers?

●When can you bundle a base-ten figure?

●What would a figure that represents 10 look like?

●Why might using base-ten diagrams for addition be cumbersome
with larger multi-digit numbers?

Finding Sums in
Different Ways

Activity 2.3

●MLR7: Compare & Connect

Answer the first question with your partner
and then pause.

Open Ended

Here are two ways to calculate the value of 0.26 + 0.07. In the diagram, each rectangle represents 0.1 and each square represents 0.01.

Use what you know about base-ten units and addition of base-ten numbers to explain:

a. Why ten squares can be “bundled” into a rectangle.

b. How this “bundling” is reflected in the computation.

Open Ended

Find the value of 0.38 + 0.69 by drawing a diagram. Can you find the sum without bundling? Would it be useful to bundle some pieces? Explain your reasoning.

Fill in the Blanks

Calculate 0.38 + 0.69. Check your calculation against your diagram in the previous question.

Fill in the Blanks

Find each sum. The larger square represents 1, the rectangle represents 0.1, and the smaller square represents 0.01.

Fill in the Blanks

Find each sum. The larger square represents 1, the rectangle represents 0.1, and the smaller square represents 0.01.

Let’s Talk About It

●In which place(s) did bundling happen when adding 0.38 and 0.69?

●How can the bundling process be represented in vertical
calculations?

●Which method of calculating is more efficient?

Are you ready for more?

A distant, magical land uses jewels for their bartering system. The jewels are valued and ranked in
order of their rarity. Each jewel is worth 3 times the jewel immediately below it in the ranking. The
ranking is red, orange, yellow, green, blue, indigo, and violet. So a red jewel is worth 3 orange jewels, a
green jewel is worth 3 blue jewels, and so on.

1.If you had 500 violet jewels and wanted to trade so that you carried as few jewels as possible,
which jewels would you have?

2.Suppose you have 1 orange jewel, 2 yellow jewels, and 1 indigo jewel. If youʼre given 2 green
jewels and 1 yellow jewels, what is the fewest number of jewels that could represent the value of
the jewels you have?

Representing
Subtraction

Activity 2.4

●Think Pair Share

●MLR3: Clarify, Critique, Correct

Fill in the Blanks

Here are diagrams that represent differences. Removed pieces are marked with Xs. For each diagram, write a numerical subtraction expression and determine the value of the expression.

Fill in the Blanks

Here are diagrams that represent differences. Removed pieces are marked with Xs. For each diagram, write a numerical subtraction expression and determine the value of the expression.

Fill in the Blanks

Here are diagrams that represent differences. Removed pieces are marked with Xs. For each diagram, write a numerical subtraction expression and determine the value of the expression.

Open Ended

Express each subtraction in words.

Fill in the Blanks

Find each difference by drawing a diagram and by calculating with numbers. Make sure the answers from both methods match. If not, check your diagram and your numerical calculation.

a. 0.05-0.02

Fill in the Blanks

Find each difference by drawing a diagram and by calculating with numbers. Make sure the answers from both methods match. If not, check your diagram and your numerical calculation.

b. 0.024-0.003

Fill in the Blanks

Find each difference by drawing a diagram and by calculating with numbers. Make sure the answers from both methods match. If not, check your diagram and your numerical calculation.

c. 1.26-0.14

Let’s Talk About It

●How are addition and subtraction of decimal numbers similar?

●Did anyone find different results when using diagrams versus when
calculating vertically?

●Why is it helpful to line up the decimal points when calculating
differences of decimals?

●Which is more efficient, using base-ten blocks or calculating the
difference?

Lesson Synthesis

● The addition of decimals beyond hundredths

works the same way as addition of whole
numbers and decimals up to hundredths.

● We can group 10 of any base-ten unit into 1 of

a base-ten unit that is 10 times as large.

Lesson Synthesis

●

How do the pieces representing ones, tens, hundreths,
etc of a base-ten diagram help us add two decimals?

●

When might we want to bundle some of the base-ten
pieces?

●

How is adding with vertical calculations similar to and
different from using base-ten diagrams?

●

When using vertical calculations, how do we make sure
that we add like base-ten units?

●

Which method of calculating is more efficient?

Today’s Goals

❏ I can use diagrams to represent and reason

about addition and subtraction of decimals.

❏ I can use place value to explain addition and

subtraction of decimals.

❏ I can use vertical calculations to represent and

reason about addition and subtraction of
decimals.

Why or Why Not?

Cool Down 2.5

Open Ended

Is this equation true?

$$0.025+0.17=0.042$$