UNLOCK THE SECRET TO MASTERING FRACTION, RATIO AND PERCENTAGE CONCEPTS WITH BAR MODELING FROM SINGAPORE
The Common Core is loaded with standards that begin, “Solve real world problems involving …” Model drawing from Singapore provides a powerful method to demystify fraction, ratio and percentage problems. In this lively interactive session, you’ll learn to use a signature feature of math from Singapore to help your students work with these higher-level concepts with ease.
FRACTIONS 1. Erin cut a cake into 12 pieces. Larry at 4 pieces, Mac ate 5 pieces and Erin ate the rest of the cake. What fraction of the cake did Erin eat? Express your answer in its simplest form.
Larry Mac Erin = ?
Erin ate of the cake.
2. Mrs. Jones made 225 cookies for a party. The children ate of the
cookies and the adults ate 48 cookies. How many cookies were left?
225 cookies
children
How many cookies did the children eat? 3 units 225 cookies 225 cookies 1 unit → 225 cookies ÷ 3 = 135 cookies How many cookies are left? → children = 135 adults = 48 ? left 225 – 135 – 48 = 42 There are 42 cookies left.
3. Bob’s Bikes sold 96 bikes during the week and of what was left on
the weekend. After that, Bob still had of his bikes left. How many bikes did Bob have at first?
?
96 bikes
2 units 96 bikes
1 unit → 96 ÷ 2 = 48 bikes 6 units→ 48 bikes x 6 = 288 bikes Bob had 288 bikes at first. → 4. Michael bought 8 boxes of pencils. There were 36 pencils in each box. He lent 108 of the pencils to Glen, 42 to Maisy and some to Phil. He had of the colored pencils left. How many pencils did
Michael lend to Phil? ? pencils
36
1 unit 36 pencils 8 units 36 pencils x 8 = 288 pencils → 288 pencils Pencils left over are 1 unit → 6 units 288 left 1 unit 288 ÷ 6= 48 → Total pencils – Glen – Maisy – left = Phil → 288 – 108 – 42 – 48 = 90 Michael lent Phil 90 pencils. 5. Lily bought a car. It cost $24,000 plus of what Lily paid or it. Find the cost of Lily’s car.
?
= $24,000
or 4 units $24,000
→ or 1 unit $24,000 ÷ 4 = $6000
→ or 9 units $6000 x 9 = $54,000 Lily’s car cost $54,000.
→ 6. 117 children took part in a track meet. of girls that participated is
equal to the number of boys. How many girls took part in the track meet?
girls 117 children boys
13 units → 117 children
1 unit → 117 children ÷ 13 = 9 children Girls are 7 units 9 children x 7 = 63 63 girls were in the track meet.
→ PERCENTAGE
1. There were 200 people at the movie. 30% of them were children and the rest were adults. How many children were at the movie? How many adults?
100 % = 200 people
children adults
100% → 200 people 10% → 200 ÷ 10 = 20 people Children are 30% → 3 x 20 = 60 children Adults are 70% → 7x 20= 140 adults There are 60 children and 140 adults.
2. Colin bought an iPod, which cost $300. He had to pay 6% sales tax on the $300. How much was the sales tax?
3% 100 % = $300
?
100% → $300 or 3% x $300 .03 x $300 1% $300 ÷ 100 = $3 → → 3% → $3 x 3 = $9 The sales tax was $9.
3. Rick spent 20% of his monthly salary on rent, 25% of the rest on food and saved the rest. If he saved $600 each month, how much was his monthly income? ?
rent food Saved = $600
3 units → $600
1 unit → $600 ÷ 3 = $200
Total is 5 units → 4200 x 5 = $1000 Rick’s monthly income is $1000.
4. Camy, Dale and Rafe have 120 Pokémon cards altogether. If 40% of the cards are Camy’s and 25% of the remainder are Dale’s, how many Pokémon cards does Rafe have?
120 Pokémon cards
Camy Dale
Rafe = ?
100% → 120 Pokémon cards 10 % → 12 cards If Camy has 40%, then Dale & Rafe share 60% of the total → 12 x 6 = 72 cards 4 units → 72 cards 1 unit → 72 ÷ 4 = 18 Rafe has 3 units → 18 x 3 = 54 Rafe has 54 Pokemon cards.
5. An elementary school had 720 students last year. This year, there are 5% more students at the school. How many students attend the school this year?
100 % = 720 5%
105 % = ?
100% → 720 students
1% → 720÷ 100 = 7.2 students
105% → 7.2 x 105 = 756 students
OR 5% → 7.2 x 5 = 36 36 + 720 = 756 There are 756 students at school this year.
6. There were 120 peaches and plums in a basket. 20% of the peaches and 25% of the plums were equivalent to 28 fruits. Find the number of peaches in the basket.
peaches 120 fruits plums
28 fruits 28 fruits 28 fruits 28 fruits
4 groups of 28 fruits → 4 x 28 = 112 120 fruits – 112 fruits = 8 peaches 20% 8 peaches
100%→ 8 peaches x 5 = 40 peaches There were 40 peaches in the basket.
→ RATIO
1. The ratio of the number of boys to the number of girls in a class is 3 : 5. a. Express the number of boys as a fraction of the number of girls. b. Express the number of boys as a fraction of the number of the number of students in all.
boys
girls
a. b.
2. Cody’s height is 1 times that of Wade’s. Find the ratio of Cody’s height to Wade’s height.
Cody
Wade The ratio of Cody’s height to Wade’s height is 3:2.
3. Jim, Terry and Danny shared a sum of money in the ratio of 4 : 5 : 6. If Danny receives $80 more than Jim, find the sum of the money shared by the three boys.
Jim
Terry $ ?
Danny
$80
Danny 6 units
Jim 4→ units Difference is 2 units
2 units→ $80
1 unit → $80 ÷ 2 = $40
Total of→ 15 units 15 x $40 = $600 The boys had $300.
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