Grade 7 · The Number System · MAT-07-NS-001
Add Integers
Represent and solve add integers problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve add integers problems using precise mathematical notation, models, and reasoning.
- Explain why a method for add 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
Add 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 add 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 -12 + 7.
-12 + 7 = -5Add signed quantities by combining direction and magnitude.
Compute -11 + 6.
-11 + 6 = -5Add signed quantities by combining direction and magnitude.
Compute -10 + 5.
-10 + 5 = -5Add signed quantities by combining direction and magnitude.
Compute -9 + 4.
-9 + 4 = -5Add signed quantities by combining direction and magnitude.
Compute -8 + 3.
-8 + 3 = -5Add signed quantities by combining direction and magnitude.
Compute -7 + 2.
-7 + 2 = -5Add signed quantities by combining direction and magnitude.
Compute -6 + 1.
-6 + 1 = -5Add signed quantities by combining direction and magnitude.
Compute -5 + 0.
-5 + 0 = -5Add signed quantities by combining direction and magnitude.
Compute -4 + -1.
-4 + -1 = -5Add signed quantities by combining direction and magnitude.
Compute -3 + -2.
-3 + -2 = -5Add signed quantities by combining direction and magnitude.
Compute -2 + -3.
-2 + -3 = -5Add signed quantities by combining direction and magnitude.
Compute -1 + -4.
-1 + -4 = -5Add signed quantities by combining direction and magnitude.
Compute 0 + -5.
0 + -5 = -5Add signed quantities by combining direction and magnitude.
Compute 1 + -6.
1 + -6 = -5Add signed quantities by combining direction and magnitude.
Compute 2 + -7.
2 + -7 = -5Add signed quantities by combining direction and magnitude.
Compute 3 + 7.
3 + 7 = 10Add signed quantities by combining direction and magnitude.
Compute 4 + 6.
4 + 6 = 10Add signed quantities by combining direction and magnitude.
Compute 5 + 5.
5 + 5 = 10Add signed quantities by combining direction and magnitude.
Compute 6 + 4.
6 + 4 = 10Add signed quantities by combining direction and magnitude.
Compute 7 + 3.
7 + 3 = 10Add signed quantities by combining direction and magnitude.
Practice
Guided practice with hints
01Compute 8 + 2.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 8 + 2 = 10
02Compute 9 + 1.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 9 + 1 = 10
03Compute 10 + 0.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 10 + 0 = 10
04Compute 11 + -1.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 11 + -1 = 10
05Compute 12 + -2.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 12 + -2 = 10
06Compute 13 + -3.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: 13 + -3 = 10
Practice
Independent practice
01Compute 14 + -4.
Answer: 14 + -4 = 10
02Compute 15 + -5.
Answer: 15 + -5 = 10
03Compute 16 + -6.
Answer: 16 + -6 = 10
04Compute 17 + -7.
Answer: 17 + -7 = 10
05Compute 18 + 7.
Answer: 18 + 7 = 25
06Compute 19 + 6.
Answer: 19 + 6 = 25
07Compute 20 + 5.
Answer: 20 + 5 = 25
08Compute 21 + 4.
Answer: 21 + 4 = 25
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 22 + 3.
22 + 3 = 25
Compute 23 + 2.
23 + 2 = 25
Compute 24 + 1.
24 + 1 = 25
Compute 25 + 0.
25 + 0 = 25
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve add integers problems accurately and justify each result with a valid check.
Practice
Mastery check
01Compute 26 + -1.
Answer: 26 + -1 = 25
02Compute 27 + -2.
Answer: 27 + -2 = 25
03Compute 28 + -3.
Answer: 28 + -3 = 25
04Compute 29 + -4.
Answer: 29 + -4 = 25
05Compute 30 + -5.
Answer: 30 + -5 = 25
06Compute 31 + -6.
Answer: 31 + -6 = 25
07Compute 32 + -7.
Answer: 32 + -7 = 25
08Compute 33 + 7.
Answer: 33 + 7 = 40
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.