5-A-Day Math Review: Week 1 worksheet featuring math problems for Monday and Tuesday.

Let's go through each problem on the worksheet step by step and solve them with explanations.

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Monday

#### 1. Write and solve an expression for the following situation:
> "9 less than the product of 5 and 7"

Step-by-step:
- First, find the product of 5 and 7:
$ 5 \times 7 = 35 $
- Then, subtract 9 from that product:
$ 35 - 9 = 26 $

Expression:
$ (5 \times 7) - 9 = 26 $

✔ Answer: $ 26 $

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#### 2. Model and solve the problem:
> $ 0.4 \times 0.6 $

Step-by-step:
- Use a hundredths grid (10x10 grid). Each small square represents 0.01.
- Shade 0.4 in one direction (e.g., 4 columns), which is 40 squares.
- Shade 0.6 in the other direction (e.g., 6 rows), which is 60 squares.
- The overlapping area represents the product: $ 0.4 \times 0.6 = 0.24 $

Modeling:
- Shade a 4-column by 6-row rectangle → $ 4 \times 6 = 24 $ shaded squares
- So, $ 24 \times 0.01 = 0.24 $

✔ Answer: $ 0.24 $

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#### 3. Solve using area models:
> $ \frac{1}{2} + \frac{1}{4} $

We need to use area models to add these fractions.

Step-by-step:
- Draw two rectangles:
- First rectangle divided into 2 equal parts; shade 1 part → $ \frac{1}{2} $
- Second rectangle divided into 4 equal parts; shade 1 part → $ \frac{1}{4} $
- To add, convert $ \frac{1}{2} $ to fourths: $ \frac{2}{4} $
- Now add: $ \frac{2}{4} + \frac{1}{4} = \frac{3}{4} $

✔ Answer: $ \frac{3}{4} $

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#### 4. What is the value of the underlined digits?

Let’s assume the underlined digits are as follows (based on typical formatting):

- $ 17,\underline{9}28 $ → Underlined digit is 9, which is in the hundreds place
→ Value: $ 9 \times 100 = 900 $

- $ 2.\underline{8}716 $ → Underlined digit is 8, which is in the tenths place
→ Value: $ 8 \times 0.1 = 0.8 $

- $ 398,84\underline{7} $ → Underlined digit is 7, which is in the ones place
→ Value: $ 7 \times 1 = 7 $

- $ 12.86\underline{5} $ → Underlined digit is 5, which is in the thousandths place
→ Value: $ 5 \times 0.001 = 0.005 $

✔ Answers:
- 900
- 0.8
- 7
- 0.005

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#### 5. Standard Form: 2,873

Word Form:
"Two thousand eight hundred seventy-three"

Expanded Form:
$ 2,000 + 800 + 70 + 3 $

✔ Answer:
- Word Form: Two thousand eight hundred seventy-three
- Expanded Form: $ 2,000 + 800 + 70 + 3 $

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Tuesday

#### 1. Long Division Problems

##### a) $ 703 \div 4 $

Step-by-step:
- $ 4 \times 175 = 700 $, remainder 3
- $ 703 \div 4 = 175 $ R$ 3 $

```
175
------
4 | 703
-4
---
30
-28
---
23
-20
---
3
```

✔ Answer: $ 175 $ R$ 3 $

##### b) $ 3625 \div 24 $

Step-by-step:
- $ 24 \times 150 = 3600 $
- $ 3625 - 3600 = 25 $
- $ 24 \times 1 = 24 $, so $ 150 + 1 = 151 $, remainder 1

So: $ 3625 \div 24 = 151 $ R$ 1 $

✔ Answer: $ 151 $ R$ 1 $

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#### 2. Write the ordered pair for each point.

From the graph:

- Point A: x = 8, y = 7 → $ (8, 7) $
- Point B: x = 2, y = 9 → $ (2, 9) $
- Point C: x = 3, y = 3 → $ (3, 3) $
- Point D: x = 10, y = 2 → $ (10, 2) $

✔ Answers:
- A: $ (8, 7) $
- B: $ (2, 9) $
- C: $ (3, 3) $
- D: $ (10, 2) $

---

#### 3. Model and solve: $ 5 \times \frac{1}{2} $

Step-by-step:
- $ \frac{1}{2} $ means half of a whole.
- Multiply 5 times $ \frac{1}{2} $: $ 5 \times \frac{1}{2} = \frac{5}{2} = 2\frac{1}{2} $
- Model: Draw 5 circles, shade half of each → total shaded = 2 full circles + half circle

✔ Answer: $ 2\frac{1}{2} $ or $ \frac{5}{2} $

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#### 4. Compare the numbers:

a) $ 0.2 \quad \text{vs} \quad 0.21 $

- $ 0.2 = 0.20 $
- $ 0.20 < 0.21 $

→ $ 0.2 < 0.21 $

b) $ 0.17 \quad \text{vs} \quad 0.7 $

- $ 0.7 = 0.70 $
- $ 0.17 < 0.70 $

→ $ 0.17 < 0.7 $

✔ Answers:
- $ 0.2 < 0.21 $
- $ 0.17 < 0.7 $

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#### 5. Solve. Show your work.

a) $ 0.6 + 0.13 $

- Align decimals:
```
0.60
+ 0.13
------
0.73
```

✔ Answer: $ 0.73 $

b) $ 0.22 - 0.17 $

- Subtract:
```
0.22
- 0.17
------
0.05
```

✔ Answer: $ 0.05 $

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✔ Final Summary of Answers:

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Monday

1. Expression: $ (5 \times 7) - 9 = 26 $ → 26
2. $ 0.4 \times 0.6 = 0.24 $ → 0.24
3. $ \frac{1}{2} + \frac{1}{4} = \frac{3}{4} $ → $ \frac{3}{4} $
4. Values:
- 17,928 → 900
- 2.8716 → 0.8
- 398,847 → 7
- 12.865 → 0.005
5.
- Word Form: Two thousand eight hundred seventy-three
- Expanded Form: 2,000 + 800 + 70 + 3

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Tuesday

1.
- $ 703 \div 4 = 175 $ R$ 3 $
- $ 3625 \div 24 = 151 $ R$ 1 $
2. Ordered Pairs:
- A: $ (8, 7) $
- B: $ (2, 9) $
- C: $ (3, 3) $
- D: $ (10, 2) $
3. $ 5 \times \frac{1}{2} = 2\frac{1}{2} $ → $ 2\frac{1}{2} $
4. Comparisons:
- $ 0.2 < 0.21 $
- $ 0.17 < 0.7 $
5.
- $ 0.6 + 0.13 = 0.73 $
- $ 0.22 - 0.17 = 0.05 $

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