- 80 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
About This Book
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
Frequently asked questions
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Answers
Construction Malfunction
- 1.1 The Founding of the FoundationA1 = 5 × 15 = 75 m2A2 = 15 × 10 = 150 m2total area = 225 m2
- 1.2 Up Against the Walls6 boards per frame 22 framestotal = 132 boards
- 1.3 Dry Wall My Walleach needs to put up 37 sheetsClever - 37 × 7 = 259 minutesSmart - 37 × 9 = 333 minutestotal = 592 minutes592 ¸ 60 = 9 hours 52 minutes= 10 hours
- 1.4 Debating on Painting4 buckets of exterior paintexterior cost - $33.75 × 4 = $135.00interior cost - $13.50 × 15 = $202.50total cost = $337.50
- 1.5 Winter WorriesA1 = 5 × 15 = 75 m2A2 = 15 × 10 = 150m2total attic area = 225 m2area of insulation - 3 × 1.5 = 4.5 m2225 ¸ 4.5 = 50 rolls needed$15.00 × 50 = $750
- 1.6 The White Roomarea each wall - 8 × 12 = 96 ft2total area = 96 × 4 = 384 ft2area door - 6.5 × 3.5 = 22.75 ft2area window - 4 × 5 = 20 ft2total area less window and door = 341.25 ft2two coats of paint = 682.50 ft2need 4 gallons of paint4 × $23.75 = $95.00
- 1.7 Carpeting the Stairseach step needs 18” of carpeting18 × 14 = 252” for all stepslanding = 60”total carpeting needed = 252 + 60 = 312”converting to yards = 8.66 or 9 yards
- 1.8 Roof Over Their Heads2025 ¸ 100 = 21 bundlescost of shingles - $171.95 × 21 = $3610.95specialist installs 10.5 bundlesspecialist hourly costs - $25.00 × 10.5 = 262.50specialists total costs - $262.50 + $500.00 = $762.50Total costs $762.50 + $3610.95 = $4373.45
- 1.9 Live Wireneed 261 feet of wire = about 87 yards87 yards is 3 boxes of wire$14.85 × 3 = $44.85
- 1.10 Plenty of Pipescopper tubing - $514.80elbow joints - $60.30Tee joints - $96.2545° joints - $34.20shut off valves - $56.70total cost - $762.25
Making Ends Meet
- 2.1 Figuring Out the Furniturenumber of payments - 36monthly cost to rent - $80total rental cost - $80 × 36 = $2880total cost to buy - $1427difference - $1453Buying furniture from Big Buy is the best deal.
- 2.2 Checking and BalancingClever’s income - $608Smart’s income - (608 × 1.5) – 30 = $882total monthly income - $1490total expenses - $1432$58 left over, enough to buy game
- 2.3 Catching the Bus40(x + 15) = 60x4x + 60 = 6x60 = 2 x30 = xClever reached the bus after driving 30 minutessee drawing below
- 2.4 Dirty Laundry2/3 of the job already done2/3 = 8/xtotal number of loads = 12loads left to do - 4
- 2.5 More Dirty Laundry50% of 24 = 12 loads12.5% of 24 = 3 loadstotal colored and delicate = 15 loads
- 2.3 drawing
- 2.6 Mall Madnessoveralls 1$43 × 25% = $10.75 savingsdiscounted price = $32.25overalls 2$43 less 15% = 36.55$36.55 less 15% = $31.07The second set of overalls is the best deal.
- 2.7 Ticket to Ridetrain - 12:15 (20 minutes) gets to subway at 12:35subway - 12:45 (8 minutes) gets to monorail at 12:53monorail - 12:55 (5 minutes) gets to the museum at 1:00They need to take the 12:15 PM train.
- 2.8 Lots of Lottery TicketsThere 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 1001/100 - 2.9 Food for Thoughtmeals = $24performance = $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