➕ 7th Grade Math · Unit 1

Operations with Rational Numbers

22 short narrated lessons in 5 chapters, each with pictures, a quiz with a hint and a second try, and an explanation for every answer.

Standards: 7.NS.A.1 7.NS.A.2 7.NS.A.3

7th Grade Math · 6 units
  1. 1Operations with Rational Numbers
  2. 2Expressions and Equations
  3. 3Ratios and Proportional Relationships
  4. 4Geometry
  5. 5Statistics
  6. 6Probability
Picture from the lesson “Opposites Make Zero”
Opposites Make Zero
Picture from the lesson “Adding Integers on a Number Line”
Adding Integers on a Number Line
Picture from the lesson “Rules for Adding Integers”
Rules for Adding Integers

What your child will learn

Adding integers

  1. Opposites Make ZeroExplain why a number and its opposite, like five and negative five, combine to make zero.
  2. Adding Integers on a Number LineAdd positive and negative integers by moving right or left on a number line.
  3. Rules for Adding IntegersAdd integers with the same sign or different signs using absolute value.
  4. Adding Integers Review ReviewReview opposites, zero pairs and adding integers with the same and different signs.

Subtracting integers

  1. Subtracting by Adding the OppositeRewrite a subtraction like three minus negative four as the addition three plus four and solve it.
  2. Distance Between Two NumbersFind the distance between two numbers on a number line as the absolute value of their difference.
  3. Adding and Subtracting Fractions and Decimals with SignsAdd and subtract positive and negative fractions and decimals using the integer rules.
  4. Subtracting Integers Review ReviewReview subtracting by adding the opposite, distance on a number line and adding and subtracting rational numbers.

Multiplying and dividing integers

  1. Multiplying IntegersMultiply positive and negative integers and decide the sign of the product.
  2. Why a Negative Times a Negative Is PositiveExplain with patterns and the distributive property why negative two times negative three equals positive six.
  3. Dividing IntegersDivide positive and negative integers and explain why dividing by zero is not defined.
  4. Multiplying and Dividing Rational NumbersMultiply and divide positive and negative fractions and decimals.
  5. Multiplying and Dividing Integers Review ReviewReview sign rules for multiplying and dividing integers and other rational numbers.

Rational numbers as decimals

  1. Fractions to Decimals with Long DivisionChange a fraction like three eighths into a decimal by dividing the numerator by the denominator.
  2. Terminating and Repeating DecimalsTell whether a fraction becomes a decimal that ends or one that repeats forever.
  3. Order of Operations with Rational NumbersEvaluate expressions with positive and negative fractions and decimals using the order of operations.
  4. Rational Numbers as Decimals Review ReviewReview converting fractions to decimals, repeating and terminating decimals and order of operations.

Rational number problems

  1. Temperature and Elevation ProblemsSolve real-world problems about temperatures and elevations using positive and negative numbers.
  2. Money Problems with Signed NumbersSolve problems about deposits, withdrawals and debts using rational number operations.
  3. Multi-Step Rational Number ProblemsSolve multi-step word problems using all four operations with rational numbers.
  4. Rational Number Problems Review ReviewReview solving real-world problems with the four operations on rational numbers.
  5. Unit 1 Test: Operations with Rational NumbersShow what you learned in the whole unit (Adding integers, Subtracting integers, Multiplying and dividing integers, Rational numbers as decimals, Rational number problems) by answering mixed questions.

Try a question from this unit

From the lesson “Opposites Make Zero”

What is the opposite of -12?

  • -12
  • 12
  • 0
  • 1/12
Show the answer

12. The number -12 is 12 units left of zero, so its opposite is 12 units right of zero, which is 12. Choosing -12 keeps the same side, and 1/12 mixes up opposites with flipping a fraction.

Hint kids see after a wrong try: “The opposite is the same distance from zero, on the other side of zero.”

Key words

  • opposite
  • additive inverse
  • integer
  • number line
  • absolute value
  • sum
  • difference
  • distance
  • rational number
  • product
  • sign
  • distributive property
  • quotient
  • undefined
  • reciprocal
  • long division
  • decimal
  • terminating decimal
  • repeating decimal
  • order of operations
  • elevation
  • sea level
  • deposit
  • withdrawal
All 7th Grade Math units Expressions and Equations →

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