Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.156.4–6.15 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 6.4–6.15 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 6.4–6.15: 6.4 Write and Evaluate Numerical Expressions with Exponents, 6.5 Write and Evaluate Algebraic Expressions, 6.6 Identify Equivalent Algebraic Expressions, 6.7 Find Factors and Multiples, 6.8 Generate Equivalent Expressions, 6.9 Divide Whole Numbers by Fractions, 6.10 Divide Mixed Numbers, 6.11 Fraction Division Problem Solving, 6.12 Least Common Multiple, 6.13 Prime Factorization, 6.14 The Distributive Property, 6.15 Simplify Algebraic Expressions. Work one example from each lesson, then prove you're caught up in the mixed practice.

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 × 20 is an expression; 4 × 20 = 80 is an equation
EvaluateSpanish: Evaluar To find the single value an expression is worth by carrying out its operations in order. Evaluate 3 + 2 × 4 → 3 + 8 = 11
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. 2³ = 2 × 2 × 2 = 8
BaseSpanish: Base In a power, the number being multiplied by itself. In 2³ the base is 2. 2³ — the 2 is the base
ExponentSpanish: Exponente In a power, the small raised number that says how many times the base is used as a factor. 2³ — the 3 is the exponent

How it worksWorked example

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

Evaluate 2 × 15 + 4 × 20 + 8 × 2³.

  1. Find the power first: 2³ = 2 × 2 × 2 = 8
  2. Multiply, left to right: 30 + 80 + 64
  3. Add, left to right: 30 + 80 + 64 = 174
  4. The value is 174.
  5. Tickets cost $12 each, plus a $50 fee one time. Write an expression for t tickets. Then find the cost of 25 tickets.
  6. Write the cost for t tickets: 12t
  7. Add the fee one time: 12t + 50
  8. Replace t with 25. Evaluate: 12 × 25 + 50 = 300 + 50 = 350
  9. The expression is 12t + 50. For 25 tickets, the cost is $350.
  10. Are 3x + 2x + 10 and 5x + 10 equivalent?
  11. Combine the like terms 3x and 2x: 3x + 2x + 10 → 5x + 10
  12. Check by testing x = 4 in both: 12 + 8 + 10 = 30; 20 + 10 = 30
  13. Yes. They are equivalent.
  14. Find the GCF of 48 and 36.
  15. List the factors of each number: 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  16. Circle the factors in both lists: 1, 2, 3, 4, 6, 12
  17. Choose the greatest one: GCF = 12
  18. The GCF of 48 and 36 is 12.
  19. Show that 3 + 5 + 2 and 5 + 3 + 2 give the same total. Name the property.
  20. Add in the first order: 3 + 5 + 2 = 10
  21. Add in the new order: 5 + 3 + 2 = 10
  22. Name what changed: order → Commutative Property
  23. Both equal 10. This is the Commutative Property.
  24. Agent Park has 4 pounds of powder. Each bag holds 1/2 pound. How many bags can he fill?
  25. Keep 4, change ÷ to ×, and flip 1/2: 4 ÷ 1/2 = 4 × 2/1
  26. Multiply: 4 × 2 = 8
  27. He can fill 8 bags.
  28. Agent Chen has a route that is 31/2 miles long. She cuts it into 1/4-mile parts. How many parts are there?
  29. Change 31/2 to an improper fraction: 3 × 2 + 1 = 7 → 31/2 = 7/2
  30. Keep, change, flip. Then multiply: 7/2 × 4/1 = 28/2 = 14
  31. 31/2 ÷ 1/4 = 14. The route has 14 parts.
  32. Agent Torres has 2/3 gallon of dust. Each test uses 1/6 gallon. How many tests can she run?
  33. Write total ÷ size of one test: 2/3 ÷ 1/6
  34. Keep, change, flip. Then multiply: 2/3 × 6/1 = 12/3 = 4
  35. Check by multiplying back: 4 × 1/6 = 4/6 = 2/3
  36. She can run 4 tests.
  37. Find the least common multiple (LCM) of 4 and 6.
  38. List the multiples of each number: 4, 8, 12, 16, 20, 24; 6, 12, 18, 24
  39. Circle the first number in both lists: 12
  40. The LCM of 4 and 6 is 12.
  41. Find the prime factorization of 60.
  42. Split 60 into two factors: 60 = 6 × 10
  43. Split each factor until all are prime: 6 = 2 × 3 → 10 = 2 × 5
  44. Write 60 as a product of primes: 60 = 2 × 2 × 3 × 5
  45. 60 = 2 × 2 × 3 × 5, or 2² × 3 × 5.
  46. Each bundle has a $15 ticket and a $5 snack. Use the distributive property to find 3(15 + 5).
  47. Multiply 3 by each term inside: 3 × 15 + 3 × 5
  48. Multiply, then add: 45 + 15 = 60
  49. 3(15 + 5) = 60. The 3 bundles cost $60.
  50. Simplify 5x + 2 + 3x + 4.
  51. Find the like terms: 5x and 3x → 2 and 4
  52. Add the coefficients of the x terms: 5 + 3 = 8 → 8x
  53. Add the constants: 2 + 4 = 6
  54. The simplified expression is 8x + 6.

Now you trySame steps, your turn

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

Evaluate 5 + 3 × 2².

Answer:

Say it and write itSentence starters

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

  • Two terms are like terms when they have the same . You cannot combine and because they represent different .

Word bank Numerical expressionEvaluateOrder of operationsPowerBaseExponentvariablelike termscoefficientcombinesame variabledifferent

Watch out!A common mistake

A common mistake in Simplify Algebraic Expressions is sweeping a constant into the variable terms

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.AT.7

Lesson 6.156.4–6.15 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 6.4–6.15 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 6.4–6.15: 6.4 Write and Evaluate Numerical Expressions with Exponents, 6.5 Write and Evaluate Algebraic Expressions, 6.6 Identify Equivalent Algebraic Expressions, 6.7 Find Factors and Multiples, 6.8 Generate Equivalent Expressions, 6.9 Divide Whole Numbers by Fractions, 6.10 Divide Mixed Numbers, 6.11 Fraction Division Problem Solving, 6.12 Least Common Multiple, 6.13 Prime Factorization, 6.14 The Distributive Property, 6.15 Simplify Algebraic Expressions. Work one example from each lesson, then prove you're caught up in the mixed practice.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    Find 2 ÷ 1/4.

    Show your work

    Hint Flip 1/4 to get 4. Then multiply 2 × 4.

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

    Find 5 ÷ 1/2.

    Show your work

    Hint Flip 1/2 to get 2. Then multiply 5 × 2.

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

    Find 1 1/4 ÷ 1/4.

    Show your work

    Hint Change 1 1/4 to 5/4. Then multiply by 4.

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

    Find 2 1/2 ÷ 1/4.

    Show your work

    Hint Change 2 1/2 to 5/2. Then multiply by 4.

    Final answer:
Part 2Apply itreal-world problems
  1. 5Complete each step, then write the final answer.

    Evaluate 3 + 2 × 4².

    Show your work

    Hint Find 4² first. Then multiply. Add last.

    Final answer:
  2. 6Complete each step, then write the final answer.

    There are 5 boxes with 2³ apples in each box. 6 apples are bad. Evaluate 5 × 2³ − 6 to find the good apples.

    Show your work

    Hint Find 2³ first. Then multiply by 5. Subtract last.

    Final answer:
  3. 7Complete 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:
  4. 8Complete 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:
  5. 9Complete each step, then write the final answer.

    Fill in the box: 3x + 5x + 4 is equivalent to ☐x + 4. What number goes in the box?

    Show your work

    Hint Combine 3x and 5x. The 4 stays the same.

    Final answer:
  6. 10Complete each step, then write the final answer.

    Are 4x + 2x and 6x equivalent? Find the value of each when x = 5.

    Show your work

    Hint Put 5 in for x in both expressions.

    Final answer:
  7. 11Complete each step, then write the final answer.

    Find the GCF of 15 and 25.

    Show your work

    Hint List the factors of 15 and of 25.

    Final answer:
  8. 12Complete each step, then write the final answer.

    Find the LCM of 3 and 4.

    Show your work

    Hint Skip-count by 3 and by 4. Find the first number in both lists.

    Final answer:
  9. 13Complete each step, then write the final answer.

    Use properties to find 6 + 8 + 4. Add the friendly pair first.

    Show your work

    Hint 6 and 4 make a ten.

    Final answer:
  10. 14Complete each step, then write the final answer.

    Which property does 5 × 9 = 9 × 5 show? Type commutative or associative.

    Show your work

    Hint Did the order change, or only the parentheses?

    Final answer:
  11. 15Complete each step, then write the final answer.

    A jug has 3/5 gallon of water. Each cup holds 1/5 gallon. How many cups can you fill?

    Show your work

    Hint Write total ÷ size of one cup.

    Final answer:
  12. 16Complete each step, then write the final answer.

    Agent Torres has 2 pounds of clay. Each cast uses 1/3 pound. How many casts can she make?

    Show your work

    Hint The total is 2 pounds. Divide 2 by 1/3.

    Final answer:
  13. 17Complete each step, then write the final answer.

    Find the LCM of 2 and 3.

    Show your work

    Hint Skip count by 3: 3, 6. Which one is also a multiple of 2?

    Final answer:
  14. 18Complete each step, then write the final answer.

    Find the LCM of 5 and 10.

    Show your work

    Hint Skip count by 10. Is 10 already a multiple of 5?

    Final answer:
  15. 19Complete each step, then write the final answer.

    Fill in the blank: 20 = 2 × 2 × ___.

    Show your work

    Hint Start with 20 = 4 × 5. Then split 4.

    Final answer:
  16. 20Complete each step, then write the final answer.

    Fill in the blank: 66 = 2 × 3 × ___.

    Show your work

    Hint Start with 66 = 6 × 11. Then split 6.

    Final answer:
  17. 21Complete each step, then write the final answer.

    Use the distributive property to find 2(10 + 5).

    Show your work

    Hint Write 2 × 10 + 2 × 5. Then multiply and add.

    Final answer:
  18. 22Complete each step, then write the final answer.

    Expand 2(x + 9). Fill in the blank: 2x + ___.

    Show your work

    Hint The 2 multiplies the x and the 9. What is 2 × 9?

    Final answer:
  19. 23Complete each step, then write the final answer.

    Simplify 3k + 5k. How many k's do you have?

    Show your work

    Hint Both terms have k, so add the coefficients: 3 + 5.

    Final answer:
  20. 24Complete each step, then write the final answer.

    Simplify 2w + 6 + 4w + 1. What is the coefficient of w?

    Show your work

    Hint Add only the w terms: 2w + 4w.

    Final answer:

Explain your thinkingWhat rule determines whether two terms are 'like terms'? Why can't you combine unlike terms?

Sentence starter Two terms are like terms when they have the same ___. You cannot combine ___ and ___ because they represent different ___.

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