General Math Unit 2. Proportional Reasoning. Solving equations arising from a context
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1 General Math Unit 2 Proportional Reasoning Solving equations arising from a context
2 Day 1 U2D1 I can explain what a ratio is I can use ratio tables to solve problems involving ratios
3 Math Notes Ratios U2D1 A ratio is a relationship between two quantities. A ratio may look like a fraction, but it is not a number. It describes a relationship! A ratio can be written 3 ways 4:5 4 to A ratio may may be reduced like you would a fraction... but don t turn it into a mixed number.
4 Writing Ratios U2D1 What is the ratio of triangles to circles? What is the ratio of circles to triangles? What is the ratio of total objects to circles? What is the ratio of total objects to triangles?
5 What are equal ratios? U2D1 2 to 3 is the same as 4 to 6 2 to 3 is the same as 10 to 15 is 4 to 6 the same as 10 to 15
6 Ratio Tables U2D1 Suppose a necklace of red and green beads has 21 beads total. The ratio of red to green beads is 3 to 4. How many red beads are there? How many green Red Green Total
7 Ratio Table U2D1 If 3 t-shirts cost $15. How much will 30 shirts cost? What about 7 shirts? # T-Shirt Cost
8 Using Ratio tables to solve problems U2D1 4 out of 5 dentist prefer crest toothpaste. If 52 dentists in the survey said they prefer crest, how many total dentists were surveyed? How many did not like crest?
9 Ratios U2D1 Nadia and Keisha take a road trip where they take turns driving. The ratio of the number of miles that Nadia drives to the number of miles that Keisha drives is 4:3. If Nadia drives 112 miles, what was the length of the trip?
10 U2D1 A piece of wire was cut into 2 pieces in the ratio of 4 : 7. The longer piece was 42cm. Find the length of the shorter piece.
11 Ratio U2D1 The French Club had 76 members, with the ratio of boys to girls at 9:10. When four more boys joined the club, what was the new ratio of boys to girls?
12 U2D1 Independent Practice U2D1
13 U2D2 U2D2 I can find missing sides by using proportions in similar figures I can solve contextual problems using ratios
14 Computational Warmup U2D2 4
15 Review Ratio Table problems U2D2 If 5 apples cost $1.00. How much will 73 apples cost? # apples Cost
16 These triangles are similar... they have the same shape and their sides are proportional. Find the missing side. U2D2
17 U2D2 These quadrilaterals are similar. Find the value of x
18 U2D2 These quadrilaterals are similar. Find the value of x
19 U2D2 If it takes 16 yards of material to make 3 costumes of a certain size, how much material will be needed to make 8 costumes of that same size?
20 U2D2 If a person earns $2340 in 6 weeks, how much can the person earn in 13 weeks at the same rate of pay?
21 U2D2 If there are 12 inches in 1 foot, how many inches are there in 8 feet?
22 Independent Practice U2D2 U2D2
23 Let s see how we re doing Draw a ratio table and solve on a piece of NBP: 1. A piece of wire was cut into 2 pieces in the ratio of 4 : 7. The longer piece was 42cm. Find the length of the shorter piece. 2. The ratio of miles to inches on a map scale is 5:1. If the distance between two cities on a map is 6 inches, how many miles are there between the two cities? 3. These figures are similar. Find the missing side length, x
24 U2D3 Solving more proportional reasoning problems involving unit rates
25 U2D3 Concept Review 3. Assume these shapes are similar. Find x, y, z lar figures. 8 y z x 5
26 U2D3 Unit Rates ask how many for 1? If apples sell for 6 for $1.50, how much does one apple cost?
27 Problem Solving U2D3 Socks are sold in packs of 6. If a package of socks costs $8.32, how much does one pair of socks cost? Use what you know about equivalent fractions to help you solve this.
28 U2D3 more... A 2-pack of sweatshirts costs $ What is the unit price?
29 U2D3 Which is the better buy? 2-foot roll of yellow fabric for $ foot roll of yellow fabric for $10.08
30 U2D3 An automobile travels 180 miles on 8 gallons of gasoline. How far can the car go on one gallon of gas? How far can it go on a tankful of gasoline if the tank holds 15 gallons?
31 U2D3 Mrs. Rush asked her students to find out their heart rate by counting beats in a 15 second period. Tyson counted 38 beats in the 15 second period. Calculate his heart rated (beats/minute)
32 U2D3 Independent Practice ICP U2 D3
33 U2D4 More on proportional reasoning
34 Computational Review U2D4 m n ) o Sup er Tea c her Worksheets - ertea c he 15)
35 U2D4 A real, bona-fide, really real, true and real SAT question:
36 U2D4 Solve two different ways Then find a third way to solve it:)
37 U2D4 Solve two ways: A piece of cloth was cut into 2 pieces in the ratio of 3 : 5. The longer piece was 45cm. Find the length of the shorter piece. How long was the piece before it was cut in two?
38 U2D4 Luis mixed 6 oz. of cherry syrup with 53 oz. of water to make a drink. Martin mixed 5 oz. of syrup with 42 oz. of water. Who has a stronger cherry taste? Write a complete sentence explaining what you did to solve this problem.
39 U2D4 Marine biologists capture, tag, and release 132 Florida manatees into a protected region. Several months later biologists capture another 90 manatees in this same region. 6 of them have tags. Estimate the population of Florida manatees in the protected region.
40 U2D4 Problem Solving The gauge of an oil tank indicated that it was 1/7 full. After 240 gallons were added, the gauge indicated that the tank was now 4/7 full. How many gallons does the tank hold?
41 U2D4 If a person earns $4340 in 6 weeks, how much can the person earn in 13 weeks at the same rate of pay?
42 U2D4 Independent Practice ICP U2D4
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