AASA Grade 7 Math Word Problems and Mixed Practice

Arizona Grade 7 students take AASA mathematics as part of the statewide Grades 3-8 assessment program. Current assessment information should always come from the Arizona Department of Education AASA page, Arizona assessment resources, and Arizona mathematics standards page. This article is an independent practice guide focused on Grade 7 math word problems and mixed review.

Grade 7 word problems often combine rational numbers, rates, proportions, percents, expressions, equations, geometry, probability, and statistics. Students need more than formulas; they need a plan for translating a situation into math.

ViewMath is not affiliated with or endorsed by the Arizona Department of Education or AASA.

Why Grade 7 Word Problems Feel Hard

Many Grade 7 students know individual procedures but struggle when the problem does not name the procedure. A word problem might ask for a percent discount, but the word “discount” means the final price is less than the original. A scale drawing problem might look like multiplication, but students must first identify the scale factor. The goal is to train translation: situation to model, model to equation, equation to answer.

A Simple Word-Problem Method

Underline the question. Identify exactly what you need to find.
Circle important quantities. Include units, rates, percents, and totals.
Choose a model. Table, equation, ratio, diagram, number line, or graph.
Solve and label. A number without units is usually incomplete.
Check reasonableness. Ask whether the answer is too large, too small, or the wrong type.

Diagnostic Translation Check

Before a long practice set, ask the student to identify the model for each sentence without solving it.

“$45 after a 10% discount” means part-whole percent with the sale price as 90% of the original.
“3 inches represents 12 feet” means a scale relationship.
“$14 per hour plus a fee” means an expression with a rate and a starting amount.
“The temperature changed from -6 to 8” means signed-number movement on a number line.
“How likely is blue?” means probability: favorable outcomes over total outcomes.

If the student can choose the model, most remaining errors are arithmetic or vocabulary errors. If the student cannot choose the model, slow down and practice sorting problem types before solving.

Grade 7 Mixed Word Problems

A recipe uses 4 cups of flour for 10 servings. How many cups are needed for 25 servings?
A jacket costs $72 after a 20% discount. What was the original price?
Solve: 2.5x + 6 = 21.
The temperature was -4 degrees in the morning and rose 11 degrees by afternoon. What was the afternoon temperature?
A scale drawing uses 1 inch to represent 6 feet. A wall is 4.5 inches long on the drawing. What is the actual length?
A circle has radius 7 cm. Use 22/7 for pi. What is the circumference?
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble?
The numbers 14, 18, 21, 21, 26 have what mean?
A student earns $12 per hour plus a $30 bonus. Write an expression for earnings after h hours.
A store increases a $50 price by 12%. What is the new price?
Two angles are supplementary. One angle is 63 degrees. What is the other angle?
A car travels 135 miles in 2.5 hours. What is the average speed?
A phone plan charges $25 per month plus $0.10 per text message. Write an expression for c text messages.
A map scale says 2 cm represents 15 miles. Two cities are 7 cm apart on the map. How far apart are they?
A number is multiplied by -3 and then increased by 8. The result is 20. What is the number?
A spinner has 8 equal sections: 3 yellow, 2 blue, and 3 green. What is the probability of not landing on blue?

Answer Key and Explanations

10 cups. The rate is 4/10 cup per serving; for 25 servings, 25 x 0.4 = 10.
$90. If $72 is 80% of the original, 72 ÷ 0.8 = 90.
x = 6. Subtract 6 to get 2.5x = 15, then divide by 2.5.
7 degrees.
27 feet.
44 cm because C = 2 pi r = 2 x 22/7 x 7.
3/10.
20. The sum is 100, and 100 ÷ 5 = 20.
12h + 30.
$56.
117 degrees.
54 miles per hour.
25 + 0.10c.
52.5 miles. Since 2 cm represents 15 miles, 1 cm represents 7.5 miles, and 7 x 7.5 = 52.5.
-4. Write -3x + 8 = 20, subtract 8 to get -3x = 12, then divide by -3.
6/8 = 3/4. There are 6 sections that are not blue out of 8 total sections.

How to Review Mistakes

After a mixed set, do not only record the score. Label each missed question by type:

Translation error: The equation or setup did not match the story.
Computation error: The setup was correct, but arithmetic went wrong.
Vocabulary error: Words like discount, increase, circumference, supplementary, or probability caused confusion.
Unit error: The answer did not match the required unit or scale.
Reasonableness error: The student did not notice an impossible or unlikely answer.

Common Grade 7 Word-Problem Traps

Discount versus original price: If a price is “after a 20% discount,” the sale price is 80% of the original, not 20%.
Percent increase: Add the increase to the original. A 12% increase on $50 is $50 + $6, not just $6.
Scale drawings: Keep drawing units and real units separate until the final answer.
Signed numbers: Rising from -4 by 11 means moving right 11 spaces to 7.
Expressions: “Plus a bonus” or “plus a fee” usually adds a constant after the rate term.

Two-Week AASA Word-Problem Plan

Days	Focus	What to Practice
1-3	Ratios, rates, and proportional relationships	Ratio tables, unit rates, double number lines, and scale factors
4-5	Percent problems	Discount, tax, percent increase, percent decrease, and original price
6-7	Rational numbers and equations	Signed-number contexts, two-step equations, and expressions from stories
8-9	Geometry	Scale drawings, area, circumference, supplementary angles, and unit labels
10-11	Probability and statistics	Simple probability, mean, median, data interpretation, and reasonableness
12-14	Mixed practice	Timed sets, full corrections, and retakes of missed types from the error log

How ViewMath Resources Fit

Use a Grade 7 ViewMath study guide if the student needs explanations before mixed practice. Use a workbook when the student needs targeted repetition in ratios, percents, rational numbers, equations, geometry, or statistics. Use practice tests when the student can solve most topics separately but needs to build stamina with mixed questions. The best sequence is usually lesson, targeted practice, mixed set, correction, and retake.

Word-problem confidence grows from repeated translation practice. Have students explain the setup before solving. If the setup is correct, the arithmetic becomes much easier to fix.

Study materials