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

Lesson 6.46.4 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers, 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 6.4. 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
Numerical expressionSpanish: Expresión numérica A math phrase built from numbers and operations, with no equal sign and no variable. 4 × 9 + 3 × 6
EvaluateSpanish: Evaluar To find the single value an expression is worth by carrying out its operations in order. 3 × 6 = 18
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. 8 × 8 = 8^2
BaseSpanish: Base In a power, the number being multiplied by itself. In 2³ the base is 2. In 8^2, the base is 8.
ExponentSpanish: Exponente In a power, the small raised number that says how many times the base is used as a factor. In 8^2, the exponent is 2.

How it worksWorked example

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

Ms. Ortiz buys 4 pizzas at $9 each and one $6 salad. Write an expression for the total. Evaluate it.

  1. Pizzas are equal groups: 4 × 9.
  2. Add the salad: 4 × 9 + 6.
  3. Evaluate: 36 + 6 = 42.

Answer: 4 × 9 + 6 = $42

Now you trySame steps, your turn

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

Each student ticket costs 2³ dollars. Evaluate 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.

  • The word tells me to multiply by .
  • The expression for this situation is .
  • I used a power because the same factor repeats times.
  • An expression has no equal sign, so I only it.

Word bank numerical expressionevaluatepowerbaseexponentproductsumdifferenceeachin alloperationvalue

Watch out!A common mistake

A common mistake with powers is multiplying the base by the exponent: reading 3² as 3 × 2 = 6 instead of 3 × 3 = 9. A second is evaluating strictly left to right, so 3 + 4 × 2 becomes 14 instead of 11. The order of operations exists so one expression has exactly one value: grouping symbols, then powers, then × and ÷ left to right, then + and − left to right.

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

Lesson 6.46.4 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers, 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 6.4. 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.
    PartExpression
    Pizzas2 × 4²
    Whole bill2 × 4² + 4
    Each share(2 × 4² + 4) ÷ 4
    Find the whole bill first. Then split it.

    Four friends order 2 pizzas at 4² dollars each, plus a $4 tip. They split the bill equally. Write one expression for each friend's share. Evaluate it.

    1. 1Write the whole bill. Put it in parentheses. Divide by 4.
    2. 2Work inside the parentheses. What is the whole bill?
    3. 3Divide. How much does each friend pay?
    Final answer:
  2. 2Complete each step, then write the final answer.
    ExpressionFirst step
    (2 × 4² + 4) ÷ 4the whole bill
    2 × 4² + 4 ÷ 4the power 4²
    Same numbers. The parentheses change the order.

    Now evaluate 2 × 4² + 4 ÷ 4 with no parentheses. Compare it with the pizza share.

    1. 1Find the power. Then multiply and divide, left to right.
    2. 2Add. What is the value?
    3. 3Why do you get 33 here, but 9 with parentheses?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Evaluate 50 − 2 × 3³ ÷ 6.

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

    A number is squared. The result is multiplied by 2. Then 5 is added. The final value is 37. What is the number?

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

    A club buys 3 packs of 10 stickers and 2 boxes with 5² stickers each. They share all the stickers equally among 8 students. How many stickers does each student get?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Jay says 4 × 3² is 144, because 4 × 3 = 12 and 12² = 144. Find the correct value of 4 × 3².

    Show your work
    Final answer:

Explain your thinkingThe pizza share was 9 with parentheses and 33 without. When do parentheses change the value of an expression?

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