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

Lesson 6.56.5 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can write an algebraic expression for a real situation and evaluate it for a given value of the variable — one step at a time, with support.

Why This Matters This is your support small group for Lesson 6.5. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

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 field day committee buys one $4.25 item for each student. Shipping costs $23.50, paid one time. Write an expression for the total cost. Then 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 1

Group 1Supported practice

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

Learning target With my small group, I can write an algebraic expression for a real situation and evaluate it for a given value of the variable — one step at a time, with support.

Why This Matters This is your support small group for Lesson 6.5. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

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

    Hint Try a number. If n is 10, what is 4 less than 10?

    Show your work
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    WordsMath
    $8 for each class8c
    $20 to join, one time+ 20
    Turn each part of the words into math.

    A gym costs $20 to join, paid one time. Each class costs $8. Let c be the number of classes. Write an expression for the total cost. Then find the cost for 6 classes.

    1. 1Write the cost of c classes.
    2. 2Add the join fee one time. What is the expression?
    3. 3Substitute c = 6. What is the total cost?
    Final answer:
  2. 3Complete each step, then write the final answer.
    WordsMath
    starts with 50 gallons50
    loses 3 gallons each hour− 3h
    This time the changing part is taken away.

    A tank has 50 gallons of water. It loses 3 gallons each hour. Let h be the number of hours. Write an expression for the water left. Then find the water left after 4 hours.

    1. 1How much water is lost in h hours?
    2. 2Write the expression for the water left.
    3. 3Substitute h = 4. How many gallons are left?
    Final answer:
  3. 4Complete each step, then write the final answer.

    Evaluate 5n + 2 when n = 7.

    Show your work

    Hint Put 7 in place of n. 5n means 5 × n.

    Final answer:
  4. 5Complete each step, then write the final answer.

    Evaluate 4.5m + 12 when m = 8.

    Show your work

    Hint Replace m with 8. Multiply 4.5 × 8 before you add.

    Final answer:
  5. 6Complete each step, then write the final answer.
    p1.75p + 4.50
    10?
    Put 10 in place of p.

    Each slice of pizza costs $1.75. Delivery costs $4.50, paid one time. Let p be the number of slices. The cost is 1.75p + 4.50 dollars. What is the cost for 10 slices?

    Show your work

    Hint Replace p with 10. Multiply 1.75 × 10. Then add the delivery fee.

    Final answer:

Explain your thinkingIn 8c + 20, why is the 8 next to the c, but the 20 is added alone?

Sentence starter The 8 is next to c because ___. · The 20 is added one time because ___.

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