Grade 4 math worksheet focusing on place value and addition, part of the EngageNY curriculum.

It looks like you've uploaded a math worksheet titled "Lesson 12 Problem Set" from the EngageNY curriculum, which focuses on place value and decimal operations, specifically working with tenths and hundredths.

Let’s go through each problem step by step and solve them.

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Problem 1: Complete the number sentence by representing each part using tape diagrams. Model using the place value chart, as shown in Part (a).

We are given three expressions involving tenths and hundredths, and we need to convert them into equivalent values in hundredths.

#### a. 3 tenths + 5 hundredths = ___ hundredths

- 3 tenths = 3 × 10 hundredths = 30 hundredths
- 5 hundredths = 5 hundredths
- So:
$$
30 + 5 = 35 \text{ hundredths}
$$

✔ Answer: 35 hundredths

#### b. 7 tenths + 1 hundredth = ___ hundredths

- 7 tenths = 7 × 10 = 70 hundredths
- 1 hundredth = 1 hundredth
- So:
$$
70 + 1 = 71 \text{ hundredths}
$$

✔ Answer: 71 hundredths

#### c. 1 tenth + 12 hundredths = ___ hundredths

- 1 tenth = 10 hundredths
- 12 hundredths = 12 hundredths
- So:
$$
10 + 12 = 22 \text{ hundredths}
$$

✔ Answer: 22 hundredths

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Problem 2: Solve by converting all addends to hundredths before solving.

We will convert all parts to hundredths first, then add.

#### a. 3 tenths + 3 hundredths = ___ hundredths = 3 hundredths + 3 hundredths = ___ hundredths

Wait — this seems to have a typo or formatting issue. Let's interpret it carefully:

It says:
> 3 tenths + 3 hundredths = ___ hundredths = 3 hundredths + 3 hundredths = ___ hundredths

But that second part is incorrect because 3 tenths ≠ 3 hundredths.

So likely, the intended expression is:
> 3 tenths + 3 hundredths = ___ hundredths

Convert:
- 3 tenths = 30 hundredths
- 3 hundredths = 3 hundredths
- Total: $ 30 + 3 = 33 $ hundredths

Now, the equation should probably be:
> 3 tenths + 3 hundredths = 33 hundredths

But the next part says: "= 3 hundredths + 3 hundredths", which is 6 hundredths — clearly wrong.

Possibility: There may be a typo. Perhaps it meant:
> 3 tenths + 3 hundredths = ___ hundredths = 30 hundredths + 3 hundredths = ___ hundredths

That would make sense.

So correct version:
$$
3 \text{ tenths} + 3 \text{ hundredths} = 30 \text{ hundredths} + 3 \text{ hundredths} = 33 \text{ hundredths}
$$

✔ Answer: 33 hundredths

#### b. 5 tenths + 12 hundredths = ___ hundredths = ___ hundredths + ___ hundredths = ___ hundredths

Convert:
- 5 tenths = 50 hundredths
- 12 hundredths = 12 hundredths
- So:
$$
50 + 12 = 62 \text{ hundredths}
$$

Now fill in:
> 5 tenths + 12 hundredths = 62 hundredths = 50 hundredths + 12 hundredths = 62 hundredths

✔ Answer: 62 hundredths

#### c. 7 tenths + 27 hundredths = ___ hundredths = ___ hundredths + ___ hundredths = ___ hundredths

Convert:
- 7 tenths = 70 hundredths
- 27 hundredths = 27 hundredths
- Total: $ 70 + 27 = 97 $ hundredths

So:
> 7 tenths + 27 hundredths = 97 hundredths = 70 hundredths + 27 hundredths = 97 hundredths

✔ Answer: 97 hundredths

#### d. 27 hundredths + 7 tenths = ___ hundredths = ___ hundredths + ___ hundredths = ___ hundredths

Note: Order doesn't matter.
- 27 hundredths = 27 hundredths
- 7 tenths = 70 hundredths
- Total: $ 27 + 70 = 97 $ hundredths

So:
> 27 hundredths + 7 tenths = 97 hundredths = 27 hundredths + 70 hundredths = 97 hundredths

✔ Answer: 97 hundredths

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✔ Final Answers Summary:

#### Problem 1:
a. 35 hundredths
b. 71 hundredths
c. 22 hundredths

#### Problem 2:
a. 33 hundredths = 30 hundredths + 3 hundredths = 33 hundredths
b. 62 hundredths = 50 hundredths + 12 hundredths = 62 hundredths
c. 97 hundredths = 70 hundredths + 27 hundredths = 97 hundredths
d. 97 hundredths = 27 hundredths + 70 hundredths = 97 hundredths

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🔍 Explanation:

This lesson emphasizes understanding decimal place value:
- 1 tenth = 10 hundredths
- So when adding tenths and hundredths, convert tenths to hundredths first to add easily.
- This builds foundational skills for decimal arithmetic.

You can model these using tape diagrams or place value charts (as suggested), where:
- Tenths column → each unit = 10 hundredths
- Hundredths column → individual units

For example, 3 tenths = 30 hundredths → represented as 3 blocks of 10 in the tenths column.

Let me know if you'd like a visual explanation or help drawing the tape diagrams!