Grade 7 · The Number System · MAT-07-NS-003
Multiply Integers
Represent and solve multiply integers problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve multiply integers problems using precise mathematical notation, models, and reasoning.
- Explain why a method for multiply integers works, interpret the result in context, and verify it independently.
Prerequisite check
Make sure the foundation is ready.
The new lesson depends on this prerequisite as active knowledge.
Learn
Build the idea from meaning, not memorization.
Mathematical meaning
Multiply Integers extends arithmetic to signed, fractional, decimal, or coordinate quantities. Operations must preserve both magnitude and direction.
Represent the relationship
The Math Box uses rational number line to expose the structure. Change one input, predict the result, then connect the visual change to an equation, table, graph, number line, or geometric model.
Calculate, interpret, and verify
Verify with an inverse operation, equivalent representation, estimate, or second method so both the calculation and reasoning are auditable.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Rational Number Line
Move through positive and negative halves and compare distance from zero.
- Model one example of multiply integers in the Math Box.
- Change one input, predict the effect, and test the prediction.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
Compute (-2)(-3).
-2 × -3 = 6Same signs give a positive product; different signs give a negative product.
Compute (3)(5).
3 × 5 = 15Same signs give a positive product; different signs give a negative product.
Compute (-4)(7).
-4 × 7 = -28Same signs give a positive product; different signs give a negative product.
Compute (5)(-9).
5 × -9 = -45Same signs give a positive product; different signs give a negative product.
Compute (-6)(4).
-6 × 4 = -24Same signs give a positive product; different signs give a negative product.
Compute (7)(6).
7 × 6 = 42Same signs give a positive product; different signs give a negative product.
Compute (-8)(-8).
-8 × -8 = 64Same signs give a positive product; different signs give a negative product.
Compute (9)(3).
9 × 3 = 27Same signs give a positive product; different signs give a negative product.
Compute (-2)(5).
-2 × 5 = -10Same signs give a positive product; different signs give a negative product.
Compute (3)(-7).
3 × -7 = -21Same signs give a positive product; different signs give a negative product.
Compute (-4)(9).
-4 × 9 = -36Same signs give a positive product; different signs give a negative product.
Compute (5)(4).
5 × 4 = 20Same signs give a positive product; different signs give a negative product.
Compute (-6)(-6).
-6 × -6 = 36Same signs give a positive product; different signs give a negative product.
Compute (7)(8).
7 × 8 = 56Same signs give a positive product; different signs give a negative product.
Compute (-8)(3).
-8 × 3 = -24Same signs give a positive product; different signs give a negative product.
Compute (9)(-5).
9 × -5 = -45Same signs give a positive product; different signs give a negative product.
Compute (-2)(7).
-2 × 7 = -14Same signs give a positive product; different signs give a negative product.
Compute (3)(9).
3 × 9 = 27Same signs give a positive product; different signs give a negative product.
Compute (-4)(-4).
-4 × -4 = 16Same signs give a positive product; different signs give a negative product.
Compute (5)(6).
5 × 6 = 30Same signs give a positive product; different signs give a negative product.
Practice
Guided practice with hints
01Compute (-6)(8).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: -6 × 8 = -48
02Compute (7)(-3).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 7 × -3 = -21
03Compute (-8)(5).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: -8 × 5 = -40
04Compute (9)(7).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 9 × 7 = 63
05Compute (-2)(-9).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: -2 × -9 = 18
06Compute (3)(4).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 3 × 4 = 12
Practice
Independent practice
01Compute (-4)(6).
Answer: -4 × 6 = -24
02Compute (5)(-8).
Answer: 5 × -8 = -40
03Compute (-6)(3).
Answer: -6 × 3 = -18
04Compute (7)(5).
Answer: 7 × 5 = 35
05Compute (-8)(-7).
Answer: -8 × -7 = 56
06Compute (9)(9).
Answer: 9 × 9 = 81
07Compute (-2)(4).
Answer: -2 × 4 = -8
08Compute (3)(-6).
Answer: 3 × -6 = -18
Common mistakes
Learn to catch the error, not just the answer.
Use a number line, context, or inverse operation.
For negatives, values closer to zero are greater.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Model temperature, elevation, debt, gains and losses, coordinates, and measurements beyond whole numbers.
- Compute accurately with fractions, decimals, and signed quantities while checking magnitude and sign.
Challenge problems
Compute (-4)(8).
-4 × 8 = -32
Compute (5)(3).
5 × 3 = 15
Compute (-6)(-5).
-6 × -5 = 30
Compute (7)(7).
7 × 7 = 49
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve multiply integers problems accurately and justify each result with a valid check.
Practice
Mastery check
01Compute (-8)(9).
Answer: -8 × 9 = -72
02Compute (9)(-4).
Answer: 9 × -4 = -36
03Compute (-2)(6).
Answer: -2 × 6 = -12
04Compute (3)(8).
Answer: 3 × 8 = 24
05Compute (-4)(-3).
Answer: -4 × -3 = 12
06Compute (5)(5).
Answer: 5 × 5 = 25
07Compute (-6)(7).
Answer: -6 × 7 = -42
08Compute (7)(-9).
Answer: 7 × -9 = -63
Terminology
Words to know
- rational number
- A number expressible as a ratio of two integers with nonzero denominator.
- absolute value
- Distance from zero on a number line.
- opposite
- A number the same distance from zero on the other side.
- coordinate
- A number locating a point relative to an axis.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Middle-school instructional guidance, mathematical practices, modeling, and coherent progression.Common Core State Standards for Mathematics — Grade 7
Grade-level expectations for ratios, number systems, algebra, geometry, statistics, and probability.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.