6th Grade All Year Math Review

Number Sense

100

Order these numbers from least to greatest: 3/4, 0.7, -0.2

-0.2, 0.7, 3/4

200

What is the opposite of -7?

7

300

Find the Greatest Common Factor (GCF) of 48 and 72.

24

400

Evaluate the expression using order of operations: 

3+2 x (4² - 6)

1st: 4² = 16 (4² - 6) --> 3+2 x (16-6)

2nd: Compute inside parentheses (16-6) = 3+2 x10

3rd: Multiply: 2 x 10 = 3+20

4th: Add: 23

500

Express 36 as a product that shows a common factor using the distributive property (for example, write 36 as a sum that factors).

Example: 36 = 4(9) = 4(5+4) --> 4x5 =20 4x4=16 20+16=36

Ratios & Proportional Reasoning

100

Write the ratio 8 to 2 in simplest form.

4:1 or 4/1

200

If a recipe uses 3 cups flour for every 2 cups sugar, how many cups of flour for 6 cups sugar?

For 6 cups sugar, flour = 3:2 --> ?:6 --> (multiply by sides by 3), therefore it would be 9 cups flour (9:6)

300

Find the unit rate: 150 miles in 3 hours (miles per hour)

150 divided by 3 = 50 mph

400

Convert 3/5 to a decimal and a percent.

3 divided by 5 = 0.6 = 60%

500

Use variables: Write an equation relating total cost C and number of items n if each item costs $4.25. Then find C when n = 12.

Equation: C = 4.25n For n = 12, C = 4.25 x 12 = 51.00

Algebra & Functions

100

Evaluate the expression 3x + 5, when x = 2

3(2) + 5 = 11

200

Write an expression for "five more than twice a number x."

2x + 5

300

Solve the equation x +7 = 15

x = 8

400

Determine whether the value x = 3 makes the equation 2x - 4 = 2 true.

Plug in: 2(3) - 4 = 6 - 4 = 2 , so it is true

500

Graphing/coordinate: Plot the points (2,3) and (2, -1). What is the distance between them? (Explain using coordinates or absolute value)

Points have same x so distance = [3 - (-1)] = 4

Geometry & Measurement

100

Convert 24 inches to feet.

24 inches = 2 feet

200

Find the area of a rectangle with length 7 cm and width 4 cm.

Area = 7 x 4 = 28 cm²

300

Find the sum of the interior angles of a quadrilateral.

Sum = 360 degrees

400

Find the volume of a rectangular prism with length = 5 cm, width = 3 cm, height = 2 cm.

Volume = 5 x 3 x 2 = 30 cm³

500

A composite shape is formed by joining two rectangles: one 6 cm  x 4 cm and one 3 cm x 4 cm along the 4 cm side. Find the total area.

Total area = (6 x 4) + (3 x 4) = 24 + 12 = 36 cm²

Data & Statistics

100

Which graph type is appropriate to show the distribution of students' test scores: line plot, histogram or scatter plot? (Choose one and justify briefly).

Histogram for distribution of scores

200

Given data: 3, 7, 7, 10, 10, 16

Median = 7

300

Create a line plot idea: Describe a simple measurement and how you would display five students' results on a line plot.

Example answer: Measure pencil lengths in inches for five students; mark Xs above number line at each length to make a line plot.

400

Calculate the mean of: 6, 8, 10, 10, 16

Mean = (6 + 8 + 10 + 10 + 16)/5 = 50/5 = 10

500

Interpret data: A box plot shows a median of 12, first quartile 8, third quartile 18. Describe the spread and identify any possible outliers if one data point is 2.

IQR = 10 (18-8). Median 12 centered, value of 2 is far below lower quartile and is likely an outlier.