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Math Homework Review: Problem-Solving Techniques and Examples

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This document provides a comprehensive review of math problems involving expanded form, simplification, and operations analysis. Students are encouraged to fill in their planners and HWRS activities for thorough understanding. It includes step-by-step examples, such as calculating totals, understanding operations, and representing real-world scenarios in equations. The importance of rounding, managing expenses, and calculating totals with tax and discounts is emphasized. Ideal for practice and mastery of mathematical concepts and operations.

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Math Homework Review: Problem-Solving Techniques and Examples

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  1. Quick Start Expectations Fill in planner and HWRS HW: AN P. 86-92; #2, 4, 6, 14,18, 46, 66 Get a signatureon your HWRS On desk: math journal, HWRS, pencil, pen Warm Up: A. Write in expanded form. -12(x - 6) = B. Simplify. -3 [2 + (-10)] – 22 = -12(x) – (-12)(6) 20

  2. What operation(s) do you need to solve the problem, and how do you know?

  3. No, she has 20 items. 4(2 + 3) = 4(5) = 20 What do each of those numbers represent? 4 hikers (2 waters +3 trail mix) 4 x 2 + 4 x 3 or (4 x 2) + (4 x 3) What do each of those numbers represent? (4 hikers need 2 water each) + (4 hikers need 3 trail mix ea.) (4 x 2) +(4x 3) 8 + 12 = 20

  4. 4( 2 x 1.50) + 4(3 x 3.75) = 4( 3) + 4(11.25) = 12+ 45= $57 Yes, she will spend $57.

  5. Note: Retailers round up to the nearest cent when adding tax. ($2.19 +$2.69) + ($2.19+$2.69) (0.04) +3.95 −5 = (4.88) +(4.88) (0.04) +3.95 −5 = (4.88) + (.20) +3.95 −5 = (5.08) + 3.95 −5 = 9.03 −5 = = $4.03

  6. ($2.19 +$2.69) + ($2.19+$2.69) (0.04) +$3.95−5 = $5.08 +$3.95 −5 = $4.03 Yes; here are three more ways. Total = 2.19 +0.04(2.19) +2.69 + 0.04(2.69) +3.95−5 Total=1.04(2.19) +1.04(2.69) +3.95−5 Total=1.04(2.19+2.69) +3.95−5 Possible explanation: 4% of an amount is the same as 0.04 times the amount. You add the prices of the items and the sales tax to get a subtotal. You subtract the amount of the coupon from the subtotal to arrive at the final bill.

  7. Possible answer: −$5.75−$4.75−$3.75+$13.50+$24.70+$13.15+$19.50=$56.60 . Yes, the class made $56.60. Yes, you can add all the amounts separately, with expenses as negative numbers and amounts of money the class raised as positive numbers. Or, you can find the total amount raised and subtract the total of the expenses. Possible explanation: Amounts of money raised are positive numbers, so add those together. Expenses, which are negative numbers, can be grouped together as well. Adding the positive funds raised and the negative expenses will result in finding the profit.

  8. Possible Answer: Super Brains: −50+150−100+250−150=100 Rocket Scientists: −150+250−50−50+100=100 The two teams are tied at this stage of the game. Possible answer: Super Brains: (150+250)−(50+100+150)=100 Rocket Scientists: (250+100)−(150+50+50)=100

  9. 38,500 gallons Possible answer: 4(5,000)+7(4,000)−3(7,500)+6.5(5,000)−6.5(3,000) = 38,500 gallons

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