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Add mentally:

2.1 Properties and Operations. Add mentally:. 4 + 5 + 3 + 7 + 6 + 8 + 5 What method did you use to find your solution faster?. How many questions can you solve on the Mental Math sheet in 5 minutes???. In your notebook, write down any shortcut methods you used to find the solutions.

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Add mentally:

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  1. 2.1 Properties and Operations Add mentally: 4 + 5 + 3 + 7 + 6 + 8 + 5 What method did you use to find your solution faster?

  2. How many questions can you solve on the Mental Math sheet in 5 minutes???

  3. In your notebook, write down any shortcut methods you used to find the solutions.

  4. Answer these next two questions mentally: How long is your commute to Science Park?

  5. Who are the people you associate with in grade 7?

  6. In English, commute means to change locations, and associate means to group together. These words have similar meanings in mathematics. • Turn to pg 63 in lesson 2.1 and copy the box that has the Commutative and Associative Properties. (you do not need to copy the Algebra examples if they do not make sense to you)

  7. Identify the following properties: 8 x (-5) = -5 x 8 (3 x 10) x 4 = 3 x (10 x 4) 3 x 10 x 4 = 3 x 4 x 10 (ab)c = a(bc) Write the answers in your notebook

  8. Use the chart to identify which properties could be used on the Mental Math sheet to make the solutions easier or faster.Record a c for commutative or an a for associative beside each question.

  9. Using properties of addition: Read through these next two examples. Take notes if you need to. You buy a portable CD player for $48, rechargeable batteries with charger for $25, and a CD case for $12. Find the total cost.

  10. Using properties of addition: You buy a portable CD player for $48, rechargeable batteries with charger for $25, and a CD case for $12. Find the total cost. 48 + 25 + 12 =

  11. Using properties of addition: You buy a portable CD player for $48, rechargeable batteries with charger for $25, and a CD case for $12. Find the total cost. 48 + 25 + 12 = (48 + 25) + 12 (order of operations) = (25 + 48) + 12 (??)

  12. Using properties of addition: You buy a portable CD player for $48, rechargeable batteries with charger for $25, and a CD case for $12. Find the total cost. 48 + 25 + 12 = (48 + 25) + 12 (order of operations) = (25 + 48) + 12 (commutative property)

  13. Using properties of addition: You buy a portable CD player for $48, rechargeable batteries with charger for $25, and a CD case for $12. Find the total cost. 48 + 25 + 12 = (48 + 25) + 12 (order of operations) = (25 + 48) + 12 (commutative property) = 25 + (48 + 12) (??)

  14. Using properties of addition: You buy a portable CD player for $48, rechargeable batteries with charger for $25, and a CD case for $12. Find the total cost. 48 + 25 + 12 = (48 + 25) + 12 (order of operations) = (25 + 48) + 12 (commutative property) = 25 + (48 + 12) (associative property)

  15. Using properties of addition: You buy a portable CD player for $48, rechargeable batteries with charger for $25, and a CD case for $12. Find the total cost. 48 + 25 + 12 = (48 + 25) + 12 (order of operations) = (25 + 48) + 12 (commutative property) = 25 + (48 + 12) (associative property) Answer: The total cost is $85.

  16. Using properties of multiplication: Evaluate 4xy when x = -7 and y = 25. 4xy =

  17. Using properties of multiplication: Evaluate 4xy when x = -7 and y = 25. 4xy = 4 (-7)

  18. Using properties of multiplication: Evaluate 4xy when x = -7 and y = 25. 4xy = 4 (-7)(25)

  19. Using properties of multiplication: Evaluate 4xy when x = -7 and y = 25. 4xy = 4 (-7)(25) = (-7 x 4)(25)

  20. Using properties of multiplication: Evaluate 4xy when x = -7 and y = 25. 4xy = 4 (-7)(25) = (-7 x 4)(25) Commutative property

  21. Using properties of multiplication: Evaluate 4xy when x = -7 and y = 25. 4xy = 4 (-7)(25) = (-7 x 4)(25) Commutative property = -7 [(4)(25)]

  22. Using properties of multiplication: Evaluate 4xy when x = -7 and y = 25. 4xy = 4 (-7)(25) = (-7 x 4)(25) Commutative property = -7 [(4)(25)] Associative property

  23. Using properties of multiplication: Evaluate 4xy when x = -7 and y = 25. 4xy = 4 (-7)(25) = (-7 x 4)(25) Commutative property = -7 [(4)(25)] Associative property Which one makes multiplying this question easier?

  24. Complete the Checkpoint on p.64 # 1 to 4 in your notebook.

  25. Checkpoint Answers • 1) 66. Commutative Property of Addition (17+13)+36 • 2) -120. Commutative Prop of Mult 8(5)(-3) • 3) 20.7 Comm. And Associative Props of Addition 3.4+7.6+9.7changes to (3.4+7.6)+9.7 • 4) 3600. Comm and Associative Props of Mult (5)(20)36

  26. Read through Example 3 on p.64 using variables. Complete the Checkpoint on p.64 # 5 to 8.

  27. Checkpoint Answers • 5) m + 14 • 6) 18k • 7) x + 3 • 8) -10r

  28. 1) 3.382) 1103) -10,000 Copy down the identity properties at the bottom of page 64. Use mental math to evaluate the following expressions. Justify each of your steps. • 1.25 + 1.38 + 0.75 • 44 + 19 + 16 + 31 • 4(20)(25)(-5)

  29. Can the commutative and associative properties work for subtraction and division?

  30. Can the commutative and associative properties work for subtraction and division? Test your theory on the following questions: 8 – 3 10 ÷ 5 (15 – 9) – 4 (48 ÷ 6) ÷ 2

  31. Green ~Pgs 66-67: 1-14all, 16-19all, 28-31all, 36, 37, 40 Blue/Black ~Read through example #5 on pg 65 in lesson 2.1 ~Pgs 66-68: 21-35odd, 44-51all

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