Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.156.4–6.15 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 6.4–6.15 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Write and Evaluate Numerical Expressions with ExponentsSpanish: Escribir y evaluar expresiones numéricas con exponentes Turning a situation into a number sentence without an equal sign, then finding its value in the correct order. 2 × 15 + 4 × 20 + 8 × 2³ = 174
Numerical expressionSpanish: Expresión numérica A math phrase built from numbers and operations, with no equal sign and no variable. 4 × 20 is an expression; 4 × 20 = 80 is an equation
EvaluateSpanish: Evaluar To find the single value an expression is worth by carrying out its operations in order. Evaluate 3 + 2 × 4 → 3 + 8 = 11
Order of operationsSpanish: Orden de las operaciones The agreed order for evaluating: grouping symbols, then exponents, then multiply and divide left to right, then add and subtract left to right. 3 + 4 × 2² → 3 + 4 × 4 → 3 + 16 = 19
PowerSpanish: Potencia A short way to write repeated multiplication of the same factor, such as 2³ for 2 × 2 × 2. 2³ = 2 × 2 × 2 = 8
BaseSpanish: Base In a power, the number being multiplied by itself. In 2³ the base is 2. 2³ — the 2 is the base

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Lesson 6.4 — Write and Evaluate Numerical Expressions with Exponents: Evaluate in this order: grouping symbols, then powers, then multiplication and division left to right, then addition and subtraction left to right.

  1. Lesson 6.5 — Write and Evaluate Algebraic Expressions: Words like “each” or “per” mean multiply and attach to the variable; a one-time amount is a constant. Once the variable has a number, substitute it in and evaluate using the order of operations.
  2. Lesson 6.6 — Identify Equivalent Algebraic Expressions: Equivalent expressions give the same answer for every value of the variable.
  3. Lesson 6.7 — Find Factors and Multiples: GCF = the biggest number that divides BOTH — use it to split into equal groups. LCM = the smallest number BOTH divide into — use it to find when cycles meet again.
  4. Lesson 6.8 — Generate Equivalent Expressions: Changing the order or the grouping of numbers being added or multiplied does not change the answer.
  5. Lesson 6.9 — Divide Whole Numbers by Fractions: Dividing by a fraction is the same as multiplying by its reciprocal (the fraction flipped over).
  6. Lesson 6.10 — Divide Mixed Numbers: Always convert a mixed number to an improper fraction first, then divide using Keep, Change, Flip.
  7. Lesson 6.11 — Fraction Division Problem Solving: Total goes first (dividend), group size goes second (divisor): total ÷ group size. Then check your answer by multiplying it back.
  8. Lesson 6.12 — Least Common Multiple: The LCM is the FIRST number that shows up in both numbers' multiple lists.
  9. Lesson 6.13 — Prime Factorization: Keep breaking a number apart until every factor is a prime number you cannot split anymore.
  10. Lesson 6.14 — The Distributive Property: The number outside the parentheses gets "shared" with every term inside.
  11. Lesson 6.15 — Simplify Algebraic Expressions: Only combine terms that have the same variable part; numbers without a variable combine with each other.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

From 6.4: Suppose the student tickets cost 2³ dollars each instead of $2. The expression becomes 2 × 15 + 4 × 20 + 8 × 2³.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • Two terms are like terms when they have the same . You cannot combine and because they represent different .

Word bank Write and Evaluate Numerical Expressions with ExponentsNumerical expressionEvaluateOrder of operationsPowerBasevariablelike termscoefficientcombinesame variabledifferent

Watch outA common mistake

A common mistake in Simplify Algebraic Expressions is sweeping a constant into the variable terms — for example, simplifying 6x + 4 + 2x as 12x by adding all three numbers (6 + 4 + 2 = 12) instead of recognizing that 4 has no variable and cannot combine with 6x and 2x. The correct simplified expression is 8x + 4 (combine 6x + 2x = 8x, and let the 4 stay on its own). Before you submit, check that every term you combined has the exact same variable part.

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.156.4–6.15 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 6.4–6.15 by using each lesson's big idea in mixed practice.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 6.4) What does 2³ mean?

    1. A2 × 2 × 2
    2. B2 × 3
    3. C2 + 2 + 2
    4. D3 × 3

    Hint Which number is the base, and which is the exponent?

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 6.5) Which expression represents 'the product of 6 and a number n'?

    1. A6n
    2. B6 + n
    3. Cn − 6
    4. Dn ÷ 6

    Hint Underline the key word 'product.' Every operation has a code word — which operation does 'product' name?

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 6.5) Which expression represents '9 less than a number y'?

    1. Ay − 9
    2. B9 − y
    3. Cy + 9
    4. D9y

    Hint 'Less than' is a tricky phrase — it flips the order of what you write.

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 6.6) Which expression is equivalent to 4x + 3x?

    1. A7x
    2. B7x²
    3. C12x
    4. D43x

    Hint 4x and 3x share the exact same variable, x — that makes them like terms.

    Show your work
Part 2Apply itreal-world problems
  1. 5Circle the letter of the best answer. Show how you know.

    (Lesson 6.4) Evaluate 3 + 4 × 2.

    1. A9
    2. B11
    3. C14
    4. D24

    Hint Which operation comes first in the order of operations?

    Line up the place values
    1. 1Line upPoints under points.
    2. 2Fill gapsWrite in the zeros.
    3. 3OperateRight to left.
    4. 4Bring the point downStraight down.

Explain your thinkingWhat rule determines whether two terms are 'like terms'? Why can't you combine unlike terms?

Sentence starter Two terms are like terms when they have the same ___. You cannot combine ___ and ___ because they represent different ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help