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

Lesson 6.56.5 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

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 m in 14m + 35
Algebraic ExpressionSpanish: Expresión algebraica A math phrase that has at least one letter. 14m + 35
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. In 14m, the coefficient is 14.
ConstantSpanish: Constante A fixed number in an expression or equation that does not change. the 35 in 14m + 35
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. For s = 30: 4.25s + 23.50 → 4.25 × 30 + 23.50

How it worksWorked examplewriting an expression with a variable

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

A club buys a $14 shirt for each member and pays one $35 setup fee. Write an expression for the total cost.

  1. Name the unknown. Let m = the number of members.
  2. Write the part that changes. $14 for each member → 14m
  3. Write the part that stays the same. one-time fee → 35
  4. Join them with the operation the story needs. 14m + 35

Answer: The expression is 14m + 35, where m stands for the number of members.

Now you trySame steps, your turn

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

A camp charges $9 for each craft kit and one $20 registration fee. Write an expression for the total cost.

  1. Name the unknown. Let = the number of craft kits.
  2. Write the part that changes. $9 for each kit →
  3. Write the part that stays the same.
  4. Join them with the operation.
Answer:expression for the total cost

Say it and write itSentence starters

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

  • I let stand for .
  • The coefficient shows the amount for each .
  • The constant happens only .
  • My expression for this situation is .

Word bank variablealgebraic expressioncoefficientconstanttermeachone-timeperstands fordefinetotalunknown

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 6.56.5 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    mPlan A: 10m + 15Plan B: 13m
    3??
    8??
    Substitute each value of m into both expressions.

    Plan A costs 10m + 15 dollars for m months. Plan B costs 13m dollars. Which plan costs less for 3 months? For 8 months?

    1. 1Substitute m = 3 into both. Which plan costs less?
    2. 2Substitute m = 8 into Plan A. What is the cost?
    3. 3Substitute m = 8 into Plan B. What is the cost?
    Final answer:
  2. 2Complete each step, then write the final answer.
    WordsMath
    starts with 30 markers30
    4 markers for each group− 4g
    Start with 30. Take away 4 for each group.

    A class has 30 markers. Each group takes 4 markers. Let g be the number of groups. Write an expression for the markers left. Evaluate it for 5 groups.

    1. 1Write the expression for the markers left.
    2. 2Substitute g = 5. How many markers are left?
    3. 3Why is it 30 − 4g and not 4g − 30?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Evaluate 3.5k − 2 when k = 8.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    The expression 6n + 5 has a value of 41. Try n = 5, 6 and 7. Which value of n works?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A phone repair costs $45 for the visit, plus $28.50 for each hour of work. Let h be the number of hours. Write an expression. Then find the cost for 3 hours.

    Show your work
    Final answer:
  6. 6Circle 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

Explain your thinkingPlan A has a fee and Plan B does not. Why can the cheaper plan change when the number of months changes?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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