Mixed Numbers. represent the same amount. They are equivalent. An improper fraction shows an amount greater than 1 whole. is an improper fraction.

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1 UNIT 5 STUDENT BOOK Mixed Numbers LESSO N Quick Review At At Home Sc h o o l Tyla arranged trapezoids. Her arrangement shows It also shows whole halves of a hexagon: hexagons plus half: and represent the same amount. They are equivalent. = An improper fraction shows an amount greater than whole. is an improper fraction. A mixed number has a whole number part and a fraction part. is a mixed number. Try These. Write an improper fraction and a mixed number for each picture. a) b) c) 58

2 Practice. Draw pictures to show each improper fraction. Write the mixed number. 5. Draw pictures to show each mixed number. Write the improper fraction Sofia took piano lessons for 8 months. How many years is that? Show your work. Stretch Your Thinking Henry drank glasses of juice. Ethan drank 9 glasses of juice. Who drank more juice? Explain how you know. 59

3 UNIT 5 STUDENT BOOK LESSO N Converting between Mixed Numbers and Improper Fractions Quick Review At At Home Sc h o o l These plates have sandwiches. These plates have 5 sandwiches. and 5 represent the same amount. 5 is a mixed number. is an improper fraction. To write 8 as an improper fraction, 8 6 multiply the whole number by the 6 denominator and add the numerator. So, 8 8 To write as a mixed number, divide 6 R the numerator by the denominator. So, 6 Try These. Write each mixed number as an improper fraction. a) 9 b) 6 c) d). Write each improper fraction as a mixed number. a) 8 5 b) 9 c) 8 9 d)

4 Practice Play this game with a partner. You will need number cube, game markers, and small counters Decide who will be player A and who will be player B. Put your markers on Start. Take turns to roll the number cube. Move that number of spaces in either direction. Put a counter on your strip on the improper fraction that names the same amount as the mixed number you landed on. If you can t place a counter on your strip, the other player takes your turn. The first player to cover the full strip wins START Player A Player B Stretch Your Thinking Sadie says she has dollars. How much money does she have? Explain. 6

5 UNIT 5 STUDENT BOOK LESSO N Comparing Mixed Numbers and Improper Fractions Quick Review At At Home Sc h o o l You can compare and order mixed numbers and improper fractions. Order, 9 8, and from least to greatest. Use number lines of equal length The order from least to greatest is 9 8,,. 0 Compare and. Write as an improper fraction: 5 Write 5 as an equivalent fraction with denominator : 5 5 Try These Compare So, 5 and : 5. Use these number lines to order 5, 6, and from least to greatest Write,, or. a) 8 b) 5 5 c) 5 6 6

6 Practice. Write,, or. a) 0 9 b) 8 c) d) 6 e) f) Use a mixed number to complete each question. a) 9 b) 9 c) d) e) 0 f). Order the numbers in each set from greatest to least. a) 8,, b) 0 6, 8 8, c) 9 5, 0 8, 0 d), 6, Use these number lines to order 5,, and 6 from greatest to least Write each time period as a mixed number and as an improper fraction. a) h 0 min: h; h b) h 0 min: h; h c) h 5 min: h; h d) h 0 min: h; h Stretch Your Thinking Jeremiah thinks 8 9 is equivalent to 5 8. Is he correct? Explain how you know. 6

7 UNIT 5 STUDENT BOOK Exploring Ratios LESSO N Quick Review At At Home Sc h o o l A ratio is a comparison of quantities with the same unit. Here are squares and 5 circles. Here are some ways to compare the shapes. Part-to-Part Ratios squares to circles is to 5 or : 5. circles to squares is 5 to or 5 :. Part-to-Whole Ratios squares to shapes is to 8 or : 8 or 8. circles to shapes is 5 to 8 or 5 : 8 or 5 8. The numbers and 5 are the terms of the ratio. You can write a part-to-whole ratio as a fraction. Try These. Write each ratio in as many ways as you can. a) balls to bats b) bats to balls c) balls to all toys d) bats to all toys 6

8 Practice. Use the numbers in the box to write each ratio. a) odd numbers to even numbers b) numbers less than 0 to all numbers c) multiples of 5 to multiples of d) prime numbers to composite numbers. Write a word that has each ratio of vowels to consonants. a) : 5 b) : c) : 6. What is being compared in each ratio? a) to b) : 6 c) : d) 6 e) 6. Draw some acorns and some oak leaves. Write as many ratios as you can for your drawing. cup cup cup sugar flour flour cup cup cup flour oatmeal oatmeal Stretch Your Thinking Ask 5 people to name the sport they enjoy watching the most. Write as many ratios as you can to compare the responses. Tell what each ratio compares. 65

9 UNIT 5 5 STUDENT BOOK Equivalent Ratios LESSO N Quick Review At At Home Sc h o o l The ratio : means that for every apples there are pears. The ratio 6 : means that for every 6 apples there are pears. : and 6 : are equal. : and 6 : are equivalent ratios. You can use a table and patterns to find equivalent ratios. The numbers in the Apples column are multiples of. The numbers in the Pears column are multiples of. The ratios of apples to pears are: :,6 :,9 :6, :8,5 :0,... Apples Pears Ratio : 6 6 : :6 8 : : 0 Try These. Write equivalent ratios for each ratio. a) 5 : b) : c) : 9 d) : e) : 6 f) 8 : 5 66

10 Practice. Play this game with a partner. You will need sheets of paper and a clock or watch with a second hand. Player A chooses a ratio and writes as many equivalent ratios as she can, as Player B times 0 s. Both players check Player A s ratios. Player A gets point for each correct ratio. Players switch roles and play again, using a different ratio. The player with the most points after 5 rounds wins. Ratios : : : 5 : 9 6 : : : 0 :5 8 : 6 : 8. Write an equivalent ratio with 0 as one of the terms. a) 5 : b) 8 : 5 c) : 6 d) : e) : 5 f) : g) : 0 h) 8 : 5. List all the ratios that are equivalent to : and have a first term that is less than 5.. Jillian is planting roses for every daisies in her garden. Complete the table to show how many daisies Jillian needs for 8,, and 6 roses. Write each ratio. Roses Daisies Ratio Stretch Your Thinking Mr. Tanaka has 56 students in his choir. The ratio of boys to girls is :. How many boys and how many girls are in Mr. Tanaka s choir? Explain. 6

11 UNIT 5 STUDENT BOOK Exploring Percents LESSO N Quick Review At At Home Sc h o o l This hundredths grid has 00 small squares. Each square represents 00 of the grid. Twenty-seven squares are shaded. You can describe the shaded part of the grid. out of 00 squares are shaded. 0 0 of the grid is shaded. 0. of the grid is shaded. % of the grid is shaded. Percent means per hundred or out of 00. This is a percent symbol. You read % as percent. Try These. Write a fraction with hundredths, a decimal, and a percent to describe the shaded part of each grid. a) b) c) d). Write a fraction with hundredths, a decimal, and a percent to describe the unshaded part of each grid in question. a) b) c) d) 68

12 Practice. Colour each hundredths grid to show the percent. a) % b) 5% c) 6%. a) Use the hundredths grid. Colour 5% blue, % red, 0% green, and the rest orange. b) Write a fraction and a decimal to describe each colour. blue red green orange c) What percent is orange?. Write as a percent and as a decimal. 6 a) 0 0 b) 00 c) d) 00 8 e) 00 f) 00. Write as a fraction and as a decimal. a) 9% b) % c) 9% d) % e) 00% f) % Stretch Your Thinking Draw a rectangle and an oval around groups of Xs so that all of the following statements are true. 6% of the Xs are not inside either figure. 8% of the Xs are inside both figures. 0% of the Xs are inside the rectangle only. 8% of the Xs are inside the oval only. 69

13 UNIT 5 8 STUDENT BOOK LESSO N Relating Fractions, Decimals, and Percents Quick Review Fractions, decimals, and percents are ways to describe parts of a whole. 0 of this shape is shaded % % of the shape is shaded. of the squares are shaded % % of the squares are shaded % At At Home Sc h o o l Try These. Write each fraction as a percent and as a decimal. 9 a) 00 b) 0 c) 5 d) 5 e) 5 0 f) 0. What percent is shaded? a) b) c) 0

14 Practice. a) Use the hundredths grid to make a design. Follow these rules: You can use only red, black, green, and blue. You must colour at least 0 of the squares. You must use: red for at least 6% of the squares. black for at least 5% of the squares. green and blue together for at least 0. of the squares. b) Complete the chart to describe the colours in your design. Colour Red Black Green Blue No Colour Number of Squares Fraction Decimal Percent of Grid c) What is the greatest percent of blank squares you could have in your design? Explain. d) What is the sum of your decimals? Percents? What do you think the sum of your fractions would be? Stretch Your Thinking What percent of Canada s 0 provinces begin with a vowel? With a consonant? Explain.

NUMBER, NUMBER SYSTEMS, AND NUMBER RELATIONSHIPS. Kindergarten:

Kindergarten: NUMBER, NUMBER SYSTEMS, AND NUMBER RELATIONSHIPS Count by 1 s and 10 s to 100. Count on from a given number (other than 1) within the known sequence to 100. Count up to 20 objects with 1-1