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.

Why This Matters This is your challenge small group for Lesson 6.5. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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 example

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

A taxi charges $3 to start plus $2 for each mile. Write an expression for the fare for m miles.

  1. Let m = the number of miles.
  2. $2 repeats each mile: 2m.
  3. The $3 start fee happens once. Join: 2m + 3.

Answer: 2m + 3 dollars

Now you trySame steps, your turn

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

The committee buys one $4.25 item for each student, plus $23.50 shipping one time. Write an expression. Find the cost for 30 students.

Answer:

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 out!A 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

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.

Why This Matters This is your challenge small group for Lesson 6.5. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  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.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help