Math Lab — Grade 6

UNIT 01

Ratios, Rates & Proportions

A ratio compares two quantities. A rate compares two quantities with different units (like miles per hour). A proportion says two ratios are equal.

Key idea: A ratio like 3:4 means "for every 3 of the first thing, there are 4 of the second." To find a unit rate, divide the top number by the bottom. To solve a proportion, cross-multiply or scale up/down.

$15 for 3 bottles → 15 ÷ 3 → $5 per bottle (unit rate)

Q 01

A car travels 180 miles in 3 hours. What is its speed in miles per hour?

Q 02

A recipe uses 2 cups of flour for every 3 cups of oats. To make a batch using 9 cups of oats, how many cups of flour are needed?

Set up: 2/3 = ?/9. Since 3 × 3 = 9, multiply the numerator by 3 too.

Q 03

A store sells 5 pencils for $1.25. At the same rate, how much do 12 pencils cost? (enter as a decimal, e.g. 3.00)

Unit price = $1.25 ÷ 5 = $0.25 per pencil. Then multiply by 12.

UNIT 02

Dividing Fractions by Fractions

Dividing by a fraction is the same as multiplying by its reciprocal. Flip the second fraction, then multiply straight across.

Key idea: To divide fractions, use Keep–Change–Flip: Keep the first fraction, Change ÷ to ×, Flip the second fraction. Then multiply numerators and denominators.

3/4 ÷ 1/2 → 3/4 × 2/1 → 6/4 → 3/2 = 1½

Q 04

What is 2/3 ÷ 1/3? (enter as a whole number or fraction)

Q 05

A ribbon is 5/6 of a yard long. It is cut into pieces that are each 1/6 of a yard. How many pieces are there?

5/6 ÷ 1/6 = 5/6 × 6/1 = 30/6 = 5

Q 06

3/4 ÷ 3/8 = ? (enter as a fraction or whole number)

3/4 × 8/3 = 24/12 = 2. The 3s cancel!

UNIT 03

Negative Numbers & Absolute Value

Negative numbers extend the number line below zero. Absolute value is simply the distance from zero — it's always positive or zero.

Key ideas: The opposite of 5 is −5. Both are the same distance from zero. |−8| = 8 and |8| = 8. On a number line, numbers get smaller as you move left — so −10 < −3.

|−15| → 15 | which is bigger: −2 or −7? → −2 (closer to zero)

Q 07

What is |−23|?

Q 08

The temperature on Monday was −4°F. On Tuesday it was −11°F. Which day was colder? Type Monday or Tuesday.

On the number line, −11 is farther left than −4, so −11 is the smaller (colder) value.

Q 09

Put these numbers in order from least to greatest: −5, 2, −1, 0, −9. What number comes third? (i.e. the middle value)

Order: −9, −5, −1, 0, 2. The middle (3rd) value is −1.

UNIT 04

Expressions & One-Step Equations

An expression uses numbers and variables (like x) to represent a value. An equation says two expressions are equal — you can solve it by doing the opposite operation to both sides.

Key idea: To solve x + 5 = 12, subtract 5 from both sides → x = 7. To solve 3x = 21, divide both sides by 3 → x = 7. Whatever you do to one side, you must do to the other.

x − 8 = 15 → x = 15 + 8 → x = 23

Q 10

Solve for x: x + 14 = 30

Q 11

Solve for x: 7x = 56

Q 12

Maria has some stickers. She gives away 13 and has 27 left. Write and solve an equation to find how many she started with.

Equation: s − 13 = 27. Add 13 to both sides: s = 40.

UNIT 05

Statistics: Mean, Median & Mode + Area of Triangles

Statistics help us describe a set of numbers. Mean is the average. Median is the middle value when sorted. Mode is the most common value. Area of a triangle = ½ × base × height.

Key idea (Stats): Given the data set 4, 7, 7, 9, 13: Mean = (4+7+7+9+13) ÷ 5 = 8. Median = middle value when sorted = 7. Mode = most frequent = 7.

Triangle: base=10, height=6 → ½ × 10 × 6 → 30 sq units

Q 13

Find the mean of these quiz scores:

Student	Score
Ava	82
Ben	90
Cal	78
Dani	96
Eva	74

Add all scores: 82+90+78+96+74 = 420. Divide by 5 students.

Q 14

What is the median of this data set? 3, 11, 7, 2, 9, 5, 8

Sort first: 2, 3, 5, 7, 8, 9, 11. With 7 values, the middle is the 4th value.

Q 15

A triangular garden has a base of 14 feet and a height of 9 feet. What is its area in square feet?

Area = ½ × 14 × 9 = ½ × 126 = 63 square feet.