Mathability

Math in the Real World (Grades 5-8)

Michael Cain

• Publisher: Routledge
• Year: 2021
• eBook ISBN: 9781000494532
• Edition: 1
• Topic: Education
• Subtopic: Education General

Mathability gives students the experience and ability to analyze and solve real-life mathematical problems, and explain their methods for arriving at the solution. Mathability is an excellent resource for preparing students for the performance tasks of standards-based tests. The six units in this book each have 10 problems that deal with a variety of real-life situations, such as those at a construction site, on vacation, in a business, and at home. The open-ended problems let students hone their skills in geometry, probability, percentages, use of charts, algebra, number relations/operations, money, and decimals.

Open-ended performance tasks have become a mainstay of standards-based testing. It is one of the tasks that most students perform at below proficiency level. Much of this low performance is due to a student's lack of experience with writing explanations of the mathematics that made it possible to solve the problem. Mathabilty presents a systematic approach that will lead students to proficiency.

Within each unit, this book provides four different levels of problems. The Step-by-Step Level leads a student through the problem and provides a format for presenting their answers. The Prompted Level provides the format for presenting the solution and hints on how to solve the problem. The Independent Level allows students to solve and explain their answers on their own, and the Challenge Level problems present a venue for gifted and talented students to push their skills to a higher level.

Grades 5-8

Answers

Construction Malfunction

• 1.1 The Founding of the Foundation
  A₁ = 5 × 15 = 75 m²
  A₂ = 15 × 10 = 150 m²
  total area = 225 m²
• 1.2 Up Against the Walls
  6 boards per frame 22 frames
  total = 132 boards
• 1.3 Dry Wall My Wall
  each needs to put up 37 sheets
  Clever - 37 × 7 = 259 minutes
  Smart - 37 × 9 = 333 minutes
  total = 592 minutes
  592 ¸ 60 = 9 hours 52 minutes
  = 10 hours
• 1.4 Debating on Painting
  4 buckets of exterior paint
  exterior cost - $33.75 × 4 = $135.00
  interior cost - $13.50 × 15 = $202.50
  total cost = $337.50
• 1.5 Winter Worries
  A₁ = 5 × 15 = 75 m²
  A₂ = 15 × 10 = 150m²
  total attic area = 225 m²
  area of insulation - 3 × 1.5 = 4.5 m²
  225 ¸ 4.5 = 50 rolls needed
  $15.00 × 50 = $750
• 1.6 The White Room
  area each wall - 8 × 12 = 96 ft²
  total area = 96 × 4 = 384 ft²
  area door - 6.5 × 3.5 = 22.75 ft²
  area window - 4 × 5 = 20 ft²
  total area less window and door = 341.25 ft²
  two coats of paint = 682.50 ft²
  need 4 gallons of paint
  4 × $23.75 = $95.00
• 1.7 Carpeting the Stairs
  each step needs 18” of carpeting
  18 × 14 = 252” for all steps
  landing = 60”
  total carpeting needed = 252 + 60 = 312”
  converting to yards = 8.66 or 9 yards
• 1.8 Roof Over Their Heads
  2025 ¸ 100 = 21 bundles
  cost of shingles - $171.95 × 21 = $3610.95
  specialist installs 10.5 bundles
  specialist hourly costs - $25.00 × 10.5 = 262.50
  specialists total costs - $262.50 + $500.00 = $762.50
  Total costs $762.50 + $3610.95 = $4373.45
• 1.9 Live Wire
  need 261 feet of wire = about 87 yards
  87 yards is 3 boxes of wire
  $14.85 × 3 = $44.85
• 1.10 Plenty of Pipes
  copper tubing - $514.80
  elbow joints - $60.30
  Tee joints - $96.25
  45° joints - $34.20
  shut off valves - $56.70
  total cost - $762.25

Making Ends Meet

• 2.1 Figuring Out the Furniture
  number of payments - 36
  monthly cost to rent - $80
  total rental cost - $80 × 36 = $2880
  total cost to buy - $1427
  difference - $1453
  Buying furniture from Big Buy is the best deal.
• 2.2 Checking and Balancing
  Clever’s income - $608
  Smart’s income - (608 × 1.5) – 30 = $882
  total monthly income - $1490
  total expenses - $1432
  $58 left over, enough to buy game
• 2.3 Catching the Bus
  40(x + 15) = 60x
  4x + 60 = 6x
  60 = 2 x
  30 = x
  Clever reached the bus after driving 30 minutes
  see drawing below
• 2.4 Dirty Laundry
  2/3 of the job already done
  2/3 = 8/x
  total number of loads = 12
  loads left to do - 4
• 2.5 More Dirty Laundry
  50% of 24 = 12 loads
  12.5% of 24 = 3 loads
  total colored and delicate = 15 loads
• 2.3 drawing

  

• 2.6 Mall Madness
  overalls 1
  $43 × 25% = $10.75 savings
  discounted price = $32.25
  overalls 2
  $43 less 15% = 36.55
  $36.55 less 15% = $31.07
  The second set of overalls is the best deal.
• 2.7 Ticket to Ride
  train - 12:15 (20 minutes) gets to subway at 12:35
  subway - 12:45 (8 minutes) gets to monorail at 12:53
  monorail - 12:55 (5 minutes) gets to the museum at 1:00
  They need to take the 12:15 PM train.
• 2.8 Lots of Lottery Tickets
  There are 1000 different combinations between 000 and 999.
  There are 10 numbers ending in 46:

  046	146	246	346
  446	546	646	746
  846	946

  Clever’s chances of winning are 10 out of 1000 or 1 in 100
  1/100
• 2.9 Food for Thought
  meals = $24
  performance = $21
  $21 is 46.66% or 47% of the total package
• 2.10 Wear and Tear
  $5400 less 20$ = $4320
  $4320 less 20% = $3456 $...

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• Construction Malfunction
• Making Ends Meet
• A Well Deserved Vacation
• Care and Feeding
• Minding a Business
• Home Sweet Home
• Answers