FREE 6th Grade Daily Math Spiral Review • Teacher Thrive - Free Printable

Let's solve each problem on the 5-A-Day Math Review: Week 2 worksheet step by step, explaining the reasoning behind each answer.

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Monday

#### 1. Express the ratio in three different ways (grey to total).
There are 7 circles: 3 grey and 4 white.

- Fraction: $ \frac{3}{7} $
- Words: 3 to 7
- Colon notation: 3 : 7

✔ Answer:
$ \frac{3}{7} $, 3 to 7, 3 : 7

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#### 2. Use an integer to describe the situations.
- 5 degrees below 0 → negative → –5
- 32 degrees above 0 → positive → +32 or 32

✔ Answer:
–5, 32

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#### 3. Write an expression to represent: "6 more than y"
"More than" means addition. So, 6 added to y.

✔ Answer: $ y + 6 $

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#### 4. List all the factors. Circle the GCF.
- Factors of 5: 1, 5
- Factors of 10: 1, 2, 5, 10
→ Common factors: 1, 5 → Greatest common factor (GCF) is 5

Now list 5 multiples:
- Multiples of 4: 4, 8, 12, 16, 20
- Multiples of 6: 6, 12, 18, 24, 30
→ Common multiple: 12, 24, ... → Least common multiple (LCM) is 12

✔ Answer:
- Factors:
- 5: 1, 5
- 10: 1, 2, 5, 10 → Circle 5 (GCF)
- Multiples:
- 4: 4, 8, 12, 16, 20
- 6: 6, 12, 18, 24, 30 → Circle 12 (LCM)

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#### 5. Perform calculations:
- $ 1.44 ÷ 0.3 $
Multiply numerator and denominator by 10 to eliminate decimals:
$$
\frac{1.44}{0.3} = \frac{14.4}{3} = 4.8
$$

- $ 3.6 × 4.2 $
First ignore decimals: $ 36 × 42 = 1512 $
Count decimal places: 1 + 1 = 2 → So move decimal two places left: 15.12

✔ Answer:
1.44 ÷ 0.3 = 4.8
3.6 × 4.2 = 15.12

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Tuesday

#### 1. $33.00 for 11 pounds of meat
- Rate: $ \frac{33}{11} = 3 $ dollars per pound
- Unit rate: $3 per pound

✔ Answer:
rate = $33/11 lbs, unit rate = $3 per pound

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#### 2. Exponent Form → Expanded & Standard Form

| Exponent Form | Expanded Form | Standard Form |
|---------------|------------------------|----------------|
| $ 2^3 $ | $ 2 × 2 × 2 $ | 8 |
| $ 4^2 $ | $ 4 × 4 $ | 16 |
| $ 3^3 $ | $ 3 × 3 × 3 $ | 27 |

✔ Answer:
- $ 2^3 $: $ 2×2×2 $, 8
- $ 4^2 $: $ 4×4 $, 16
- $ 3^3 $: $ 3×3×3 $, 27

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#### 3. 3 is what percent of 10?
Use the formula:
$$
\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}
$$

So:
$$
\frac{3}{10} = \frac{x}{100} \Rightarrow x = \frac{3 × 100}{10} = 30
$$

✔ Answer:
Part → 3, Whole → 10 → $ \frac{3}{10} = \frac{30}{100} $ → 30%

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#### 4. Sebastian carried $ \frac{1}{2} $ liter of water. He drank $ \frac{2}{3} $ of it. How much did he drink?

Multiply:
$$
\frac{1}{2} × \frac{2}{3} = \frac{2}{6} = \frac{1}{3}
$$

✔ Answer: He drank $ \frac{1}{3} $ liter of water.

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#### 5. Write an equation for each table

Table 1:
| x | y |
|---|---|
| 2 | 7 |
| 3 | 8 |
| 4 | 9 |
| 5 | 10 |
| 6 | 11 |

Look at pattern: y increases by 1 when x increases by 1 → slope = 1
When x = 2, y = 7 → so y = x + 5 (because 2 + 5 = 7)

Check:
x = 3 → 3 + 5 = 8 ✔
x = 4 → 4 + 5 = 9 ✔

✔ Equation: y = x + 5

Table 2:
| x | y |
|---|---|
| 0 | 3 |
| 1 | 4 |
| 2 | 5 |
| 3 | 6 |
| 4 | 7 |

Again, y increases by 1 when x increases by 1 → slope = 1
When x = 0, y = 3 → y-intercept = 3

✔ Equation: y = x + 3

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✔ Final Answers Summary:

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Monday

1. $ \frac{3}{7} $, 3 to 7, 3:7
2. –5, 32
3. $ y + 6 $
4.
- Factors:
- 5: 1, 5
- 10: 1, 2, 5, 10 → GCF: 5
- Multiples:
- 4: 4, 8, 12, 16, 20
- 6: 6, 12, 18, 24, 30 → LCM: 12
5. 1.44 ÷ 0.3 = 4.8, 3.6 × 4.2 = 15.12

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Tuesday

1. Rate = $33/11 lbs, Unit rate = $3 per pound
2.
- $ 2^3 $: $ 2×2×2 $, 8
- $ 4^2 $: $ 4×4 $, 16
- $ 3^3 $: $ 3×3×3 $, 27
3. $ \frac{3}{10} = \frac{30}{100} $ → 30%
4. $ \frac{1}{2} × \frac{2}{3} = \frac{1}{3} $ → $ \frac{1}{3} $ liter
5.
- Table 1: y = x + 5
- Table 2: y = x + 3

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