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

Lesson 6.5Evaluating Algebraic Expressions

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.

Start hereWords for this lesson

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

WordWhat it meansExample
VariableSpanish: Variable A letter that stands for a number that is unknown or can change. the b in 6b − 9
Algebraic ExpressionSpanish: Expresión algebraica A math phrase that has at least one letter. 3n + 7 means 'triple a number, then add 7' — it has a variable (n), a coefficient (3), and a constant (7)
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. In 6b, the coefficient is 6.
ConstantSpanish: Constante A fixed number in an expression or equation that does not change. In 3n + 7, the 7 never changes no matter what n is — like a flat fee that stays the same
Like termsSpanish: Términos semejantes Terms with the same letter raised to the same power, like 2x and 5x. 4x + 2x = 6x (like terms, same variable); but 4x + 2y cannot be combined (different variables)
SubstituteSpanish: Sustituir To replace a variable with a given number before working out the value. 6b when b = 7 → 6 × 7

How it worksWorked exampleevaluating an expression by substituting

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

Find the value of 6b − 9 when b = 7.

  1. Write the expression. 6b − 9
  2. Substitute the given value for the letter. 6 × 7 − 9
  3. Follow the order of operations. 42 − 9
  4. Evaluate. 33

Answer: When b = 7, the value of 6b − 9 is 33.

Now you trySame steps, your turn

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

Find the value of 2m + 11 when m = 12.

  1. Write the expression. 2m + 11
  2. Substitute the given value for the letter. 2 × + 11
  3. Follow the order of operations. +
  4. Evaluate.
Answer:value of 2m + 11 when m = 12

Say it and write itSentence starters

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

  • I substituted for the variable .
  • After substituting, the expression became .
  • I did first because of the order of operations.
  • The value of the expression is .

Word bank substituteevaluatevariablecoefficientconstantorder of operationsvaluereplaceless thanmore thantimesper

Watch outA common mistake

A common mistake in Write Algebraic Expressions is treating 'each' or 'per' as if it means add instead of multiply, and attaching the variable to the wrong number. For 'a $25 setup fee plus $8 per hour, h,' students often write 25 + 8 + h (adding all three numbers) or 25h + 8 (multiplying the flat fee by h) instead of the correct 8h + 25. Since $8 applies per hour, it must multiply the variable (8h), and the flat $25 fee is a constant added only once — check that the per-unit rate, not the flat fee, is the number multiplied by the variable.

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

Lesson 6.5Evaluating Algebraic Expressions

Apply Day · Version ASupported practice

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

Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.

  1. 1Complete each step, then write the final answer.

    Evaluate 4m + 6 when m = 5.

    Show your work

    Hint Put 5 in place of m. 4m means 4 × m.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Books cost $3 each. A bag costs $2, paid one time. Let b be the number of books. Write an expression for the total cost. Find the cost for 7 books.

    Show your work

    Hint The $3 is for each book, so write 3b. Add the $2 one time.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Evaluate 10 − 2y when y = 3.

    Show your work

    Hint Put 3 in place of y. Multiply before you subtract.

    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.6a

Lesson 6.5Evaluating Algebraic Expressions

Apply Day · Version BCore practice

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

Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.

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

    Rosa writes “4 less than a number n” as 4 − n. Which expression is correct?

    1. An − 4
    2. B4 − n
    3. C4n
    4. Dn + 4
    Show your work
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.

    Evaluate 3.5k − 2 when k = 8.

    Show your work
    Final answer:
  2. 3Complete each step, then write the final answer.

    Evaluate 9k + 4 when k = 3.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.6a

Lesson 6.5Evaluating Algebraic Expressions

Apply Day · ChallengeExtension

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

Learning target I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.

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

    A concert ticket costs 8 dollars. The website also charges one 5 dollar service fee for the whole order. Let t represent the number of tickets bought in one order. Which expression gives the total cost in dollars?

    1. A8t + 5
    2. B8 + 5t
    3. C8(t + 5)
    4. D13t
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Shop A charges 2.5p + 10 dollars for p posters. Shop B charges 4.5p dollars. Which shop costs less for 5 posters?

    1. AShop A
    2. BShop B
    3. CThey cost the same
    Show your work
  2. 3Complete each step, then write the final answer.

    Evaluate 12 + 2.5w when w = 6.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help