Naming Fractions NS4-45 Students will: JUMP Math™ Copyright © 2018 JUMP Math Teacher Resource 4.2 Unit 9 Number Sense pp. L-3–7 New Canadian Edition NS4-45 Naming Fractions Students will: • name fractions shown by pictures divided into equal areas and record fractions using standard fractional notation. AB: required BC: required MB: required ON: required AP Book 4.2 pp. 19–20

See p. L-3 for details.

This is one of two pieces. Is this half of the banana? Review "half." This is one of two pieces. Is this half of the banana? See p. L-3 for details.

Whole numbers count whole objects. Fractions are numbers that count part of an object. See p. L-3 for details.

one third, one fourth, one fifth, one sixth, Continue the pattern: one third, one fourth, one fifth, one sixth, ______________, ______________ See p. L-3 for details. What is each part called if there are ... 9 equal parts? 10 equal parts? 13 equal parts?

Exercises: Write the names for these fractions. a) one of 11 equal parts b) one of 15 equal parts c) one of 32 equal parts d) one of 100 equal parts Bonus: one of 10 000 equal parts

How many equal parts are shaded? See p. L-4 for details.

Exercises: Count all the parts. Write the name of the parts. Write how much is shaded. a) b) c) d) Bonus: e) f)

Written with numbers, a fraction has a top number and a bottom number. 5 sixths a) 7 ninths b) 2 thirds c) 3 fourths d) See p. L-4 for details.

Write in fraction notation. See p. L-4 for details. What does the bottom number count? What does the top number count?

Exercises: 1. Write the top and bottom parts for the shaded fraction. a) b) c) d)

2. Write the fraction as a top and bottom number. a) three eighths b) one half c) four tenths Bonus: seventeen hundredths

3. Write the fraction using words. 4 9 a) 6 8 b) 2 3 c) 3 4 d) 19 23 Bonus:

Activity: Picking Pairs. This activity is essential. Activity: Picking Pairs. Use the cards from BLM Fractions Memory (pp. L-38–40). See p. L-5 for details.

The top and bottom numbers have special names. 1 4 numerator denominator See p. L-5 for details.

Pretend each circle represents a whole cake. Which would you rather have? 1 small cake = 1 large cake Is this true? See p. L-5 for details.

Are these pairs of cakes equal? Hint: Look at the number and the size.

What fraction of each square is shaded? small cake = large cake 1 2 Is this true? See p. L-5 for details.

Complete "Are the Shaded Amounts Equal?" Complete a) as a class. Exercise: Complete "Are the Shaded Amounts Equal?" Distribute BLM Are the Shaded Amounts Equal? (p. L-41).

1. Use pattern blocks to answer. Extensions: 1. Use pattern blocks to answer. a) What fraction of the hexagon is the trapezoid? b) What fraction of the hexagon is the rhombus? c) What fraction of the hexagon is the triangle? d) What fraction of the trapezoid is the triangle? Bonus: What fraction of the trapezoid is the rhombus? See p. L-6 for details.

2. Add lines to make the parts equal. What fraction is shaded? a) b) c) d)

3. Use tangram pieces to answer. a) What fraction of the large tangram square is the smallest tangram triangle? b) Find three pieces that all look different but are all the same size as two small triangles. What fraction of the whole are each of these shapes? See p. L-7 for details.

AP Book 4.2 pp. 19–20 New Canadian Edition

Comparing Fractions to Benchmarks JUMP Math™ Copyright © 2018 JUMP Math Teacher Resource 4.2 Unit 9 Number Sense pp. L-8–13 New Canadian Edition NS4-46 Comparing Fractions to Benchmarks Students will: • compare fractions using the common benchmarks 0, , and 1. 1 2 AB: required BC: required MB: required ON: required AP Book 4.2 pp. 21–22

See p. L-8 for details.

What fraction is shaded? See p. L-8 for details. Now what fraction is shaded? Draw a horizontal line across the circle. What changed? What didn't change?

Exercises: Write two fractions for the picture. Write an equal sign between the fractions. a) b) c)

So, you can double the numerator to get the denominator. In a picture showing one half, there are always twice as many parts in the whole as there are in the shaded part. So, you can double the numerator to get the denominator. See pp. L-8–9 for details.

Exercises: Write the missing denominator. a) = 1 2 5 b) = 1 2 7 c) = 1 2 12 Bonus: = 1 2 4132

If you know the denominator of a fraction equal to , you can divide by 2 to get the numerator. 1 2 See p. L-9 for details.

Exercises: Write the missing numerator. a) = 1 2 10 b) = 1 2 36 c) = 1 2 50 d) = 1 2 120

I'm going to pour some beans from the full glass into the empty glass. Did I pour more or less than half? See p. L-8 for details.

I'm going to give some to each volunteer. I have 8 counters. I'm going to give some to each volunteer. Did they each get half? Ask for two volunteers. See p. L-9 for details.

Are these fractions more or less than half? See p. L-9 for details. 2 6 < 1 5 8 > and

Exercises: What fraction is shaded? Is it more or less than half? a) b)

What fraction is shaded? Is that more or less than half? See p. L-9 for details.

6 10 How can you tell from the fraction, without even looking at the picture, how many pieces are: • shaded? • not shaded? See p. L-10 for details.

Exercises: How many pieces are shaded? How many pieces are not shaded? a) 3 7 ___ shaded ___ not shaded b) 5 9 ___ shaded ___ not shaded c) 11 20 ___ shaded ___ not shaded

If the number of parts that are ... 47 100 d) ___ shaded ___ not shaded e) 100 1000 ___ shaded ___ not shaded 600 1000 f) ___ shaded ___ not shaded If the number of parts that are ... • shaded > not shaded, the fraction is more than 1 2 1 2 • shaded < not shaded, the fraction is less than Hint: Look back at each fraction in this exercise. Is it more or less than half?

Exercises: Is the fraction more than half or less than half? a) 5 8 b) 11 20 c) 17 35 d) 22 45

Bonus: Which fractions are more than half? Write down the letters. What do they spell? O. 3 5 T. 3 7 R. 11 20 P. 5 16 A. 3 4 N. 25 40 G. 8 14 E. 52 100 Y. 12 30

Are these more or less than half? 3 8 2 3 See pp. L-10–11 for details. 1 2 < < How do and compare to each other? 3 8 2 Draw a number line if students are having trouble with this.

Compare the fractions. Write < or >. Exercises: Compare the fractions. Write < or >. Hint: First compare them both to . 1 2 a) 5 9 6 15 b) 2 3 4 10 c) 10 18 12 30 d) 4 9 5 8 Bonus: 6000 20 000 760 900

a) David walked of a kilometre. Word problems practice. Exercises: a) David walked of a kilometre. Is that more than or less than half a kilometre? 5 11

8 15 b) On a soccer team, of the players are girls. Are there more boys or girls on the team?

3 5 c) Luc gave away of a cake and kept the rest. Did he keep more or less than half?

6 11 4 9 d) Kate ate of a chocolate bar and Raj ate of the chocolate bar. Who had more?

The number 1 can also be written different ways. 1 = = = Hint: A whole pie is a whole pie, no matter how many pieces it has. See p. L-11 for details. A fraction is equal to 1 if the numerator is the same as the denominator. That means all the parts are shaded.

Exercises: Write the missing number in the box to make the fraction equal to 1. a) 7 b) 10 c) 6 d) 9 Bonus: 182

How do we shade this circle to show that it is one whole circle? See p. L-12 for details. How can we shade the second circle to show a little bit more than one whole?

This shows one whole and a little bit more: Here, the shaded piece is even smaller: Does it still show a bit more than one whole? See p. L-12 for details.

How much does this picture show? Shade all of the circle, then erase a little. Is it still one whole? See p. L-12 for details.

What other fractions are less than one whole? 9 10 Hint: This is approximate since there aren't any line showing the parts. See p. L-12 for details. What other fractions are less than one whole?

For a fraction to be less than a whole, does the numerator have to be: • less than the denominator, • equal to the denominator, or • greater than the denominator? See p. L-12 for details.

Exercises: Circle the fractions that are not less than one whole. a) 5 8 b) 7 c) 11 429 d) 999 1000 e) 4306 f) 1 2

Extensions: 1. Estimate, very approximately, where the fraction goes. Write the letter above the number line. A. 1 10 B. 10 11 C. 4 10 D. 5 8 A

2. Write any number to make the fraction greater than , but less than 1. 1 2 a) 7 b) 12 c) 6 Bonus: 7

3. Write any number to make the fraction greater than 0, but less than . 1 2 a) 7 b) 4 c) 6 d) 3 e) 12 Bonus: 7

4. Place the "Fractions Memory" cards face down. Turn over a card and write a fraction for the part that is not named or shaded. Distribute BLM Fractions Memory Cards (pp. L-38–40). See p. L-13 for example.

5. Identify whether the fraction is closest to the benchmark 0, , or 1. 1 2 1 9 a) is closest to ____ 5 11 b) is closest to ____ 8 14 c) is closest to ____ 13 15 d) is closest to ____ 3 20 e) is closest to ____ 98 100 f) is closest to ____

AP Book 4.2 pp. 21–22 New Canadian Edition

Equivalent Fractions NS4-47 Students will: JUMP Math™ Copyright © 2018 JUMP Math Teacher Resource 4.2 Unit 9 Number Sense pp. L-14–17 New Canadian Edition NS4-47 Equivalent Fractions Students will: • find equivalent fractions using multiplication. AB: optional BC: optional MB: optional ON: required AP Book 4.2 pp. 23–25

See p. L-14 for details.

The child said he wanted two pieces, so the parent cut the cake again. A parent and a child were sharing a cake, so the parent divided it into two pieces. The child said he wanted two pieces, so the parent cut the cake again. Did the child get more cake by getting two pieces? See p. L-14 for details.

These fractions are equivalent because the pictures have the same amount shaded. 1 2 4 = See p. L-14 for details. Both people get twice as many pieces but the same amount of cake as before.

Exercises: Copy the picture in your notebook. Break each part in half to create equivalent fractions. a) b) c) d)

Have students signal their responses. How many times as many parts are in the first picture compared to the second picture? a) b) c) d) See p. L-15 for details.

Have students signal their responses. How many times as many shaded parts are in the first picture compared to the second picture? a) b) c) d) See p. L-15 for details.

Write equivalent fractions from these pictures. Exercises: Write equivalent fractions from these pictures. a) b) c) d) Point out how they are related by multiplication. See p. L-15 for details.

We can use the same picture to show two fractions. = Hint: You can look at the big parts or the small parts. See p. L-15 for details.

Exercises: Write two equivalent fractions from the picture. a) b) c)

Bonus: Write as many equivalent fractions as you can from the picture without adding more lines. a) b)

How many parts do I have to break each piece into to get 12 parts altogether? 3 = 12 See p. L-16 for details.

Exercises: Use multiplication to find the missing numerator. a) 1 5 = 15 b) 3 4 = 16 c) 5 6 = 12 d) 7 10 = 100 Bonus: e) = 1000 15 100

We can skip count to create equivalent fractions. 3 5 3 × 2 5 × 2 = 3 × 3 5 × 3 3 × 4 5 × 4 3 × 5 5 × 5 3 5 = See p. L-16 for details.

2 5 Exercises: Write four fractions equivalent to . Bonus: Write more fractions equivalent to . 2 5

Picking Pairs and Memory. This activity is optional. Activity: Picking Pairs and Memory. Use the cards from BLM Equivalent Fractions Memory (pp. L-43–45). See p. L-17 for details.

Extensions: 1. Use multiplication to find the missing denominator. a) 3 4 = 15 b) 1 8 = 7 c) 5 6 = 30 d) 4 10 = 40 Bonus: 3000 = 3 1000 e) = 2200 22 100 f)

2. Is there a fraction equivalent to with an odd denominator? Explain. 3 8

AP Book 4.2 pp. 23–25 New Canadian Edition

Comparing and Ordering Fractions JUMP Math™ Copyright © 2018 JUMP Math Teacher Resource 4.2 Unit 9 Number Sense pp. L-18–24 New Canadian Edition NS4-48 Comparing and Ordering Fractions Students will: • compare and order fractions based on the size and the number of fractional parts; and • compare and order fractions using number lines and fraction strips. AB: required BC: required MB: required ON: required AP Book 4.2 pp. 26–29

See p. L-18 for details.

Let's compare these fractions. See p. L-18 for details.

Which strip has a greater amount shaded? 3 6 5 6 See p. L-19 for details. 3 6 5

Exercises: Write < or >. a) 2 5 4 b) 3 4 2 c) 6 10 9 Bonus: 37 59 27

How can we make this relationship correct? 4 9 > Ask for all possibilities. See p. L-19 for details. 7 10 <

Exercises: Write any number in the blank that makes the relationship correct. a) 6 10 > b) 2 5 < c) 1 2 < d) 7 >

Activity 1: Least to greatest. Hint: Group yourselves by denominator. This activity is essential. Activity 1: Least to greatest. Hint: Group yourselves by denominator. Use BLM Fraction Cards (p. L-46–48). See p. L-19 for details.

We can also order fractions using a number line. Hint: Start by marking each fraction on the number line. 6 1 2 3 4 5 1 6 2 4 < See pp. L-19–20 for details.

1. Use the number line to order the fractions. Exercises: 1. Use the number line to order the fractions. Hint: Draw an "X" for each fraction. a) 1 9 2 5 8 7 4 9 1 2 3 5 4 8 6 7

b) 5 2 3 5 1 2 3 4

2. Write a fraction that is between the two fractions. a) and 3 9 8 b) and 1 5 c) and 1 4 3 d) and 5 10 8

Can you order these fractions without a number line? 1 6 2 4 < Hint: What does the denominator "6" mean? See p. L-20 for details.

Exercises: Order the fractions from least to greatest. a) 2 9 7 5 8 1 4 b) 5 3 2

Which of these fractions is greatest? Hint: Are the strips the same length? Do they have the same number and size of parts? See p. L-21 for details.

The more parts something is divided into, the smaller each part is. Which fraction is greater? 1 4 9 3 8 5 See p. L-21 for details.

Exercises: 1. Write < or >. a) 1 8 3 b) 1 2 10 c) 1 5 4 d) 1 10 100

e) 2 5 8 f) 7 20 8 g) 6 12 16 Bonus: 35 1000 40

2. Write any number in the blank that makes the relationship correct. 1 10 12 > b) 3 7 5 < c) 5 9 > Bonus: 172 983 <

Activity 2: Least to greatest. Hint: Group yourselves by numerator. This activity is essential. Activity 2: Least to greatest. Hint: Group yourselves by numerator. Use BLM Fraction Cards (p. L-46–48). See p. L-19 for details.

Now let's order fractions with the same numerator. 1 10 2 5 4 3 Hint: Can you match each fraction to a fraction strip? See p. L-22 for details.

Complete "Ordering with Fraction Strips." Exercise: Complete "Ordering with Fraction Strips." Distribute BLM Ordering with Fraction Strips (p. L-49).

Order the fractions from greatest to least. 2 5 4 10 3 < Hint: What does the numerator "2" mean? See p. L-22 for details.

Exercises: Order the fractions in part a) from least to greatest, and the fractions in part b) from greatest to least. < 3 18 11 21 5 a) > 10 15 31 12 b)

Name several fractions between 0 and , and then between and 1. 1 2 Hint: Pick any denominator. 1 2 Select a fraction from each side and have students compare them. See p. L-23 for details.

1 2 Between and 1 Between 0 and Repeat, using a table instead of a number line. 1 2 Between and 1 Between 0 and See p. L-23 for details.

a) Marla thinks that of a cake is equal to Word problems practice. Exercises: a) Marla thinks that of a cake is equal to of the moon, but Cathy doesn't think that is true. She explained why to her teacher, who said her explanation was correct. What was Cathy's explanation? 1 2

b) Arsham doesn't think that of a cherry pie can weigh the same as a whole apple pie. Is he correct? Explain. 1 2

1. Complete "Ordering Fractions." This Extension is required for the ON curriculum. Extensions: 1. Complete "Ordering Fractions." Distribute BLM Ordering Fractions (pp. L-50–51).

2. Use two number lines to decide if the fraction is closer to 0, , or 1. 1 2 Hint: Write 0, , or 1. 1 2 5 7 a) is closer to _____ 1 7 b) is closer to _____ 6 7 c) is closer to _____

3. Compare the fractions and by comparing how much of a whole pie is left if the given amounts are eaten. 3 4 5 Hint: The smaller fraction is from the pie with a bigger piece left over.

4. Write the fractions in order from least to greatest. 1 5 6 8 3

AP Book 4.2 pp. 26–29 New Canadian Edition

Equal Parts of Sets NS4-49 Students will: JUMP Math™ Copyright © 2018 JUMP Math Teacher Resource 4.2 Unit 9 Number Sense pp. L-25–29 New Canadian Edition NS4-49 Equal Parts of Sets Students will: • name fractions of a set and recognize that equal parts of a set do not have to have the same area. AB: required BC: required MB: required ON: required AP Book 4.2 p. 30

See p. L-25 for details.

What can we take a fraction of? See p. L-25 for details.

We can take a fraction of a set of objects. What fraction of the circles are shaded? See p. L-25 for details.

Can we still say that of the circles are shaded? 3 8 See p. L-25 for details. What fraction of the circles are big?

Exercises: Find the fraction of the shapes that are … a) circles b) triangles c) shaded d) not shaded

Bonus: e) circles f) small g) shaded h) not shaded i) big j) triangles

Exercises: What does the fraction describe? a) of the shapes are ______________ 3 8 1 8 b) of the shapes are ______________ Bonus: of the shapes are ______________ 1 2

Bonus: a) Describe the picture using the fraction in two different ways. 3 5 b) Describe the picture using the fraction in three different ways. 3 5

What fraction of the shapes are … See note on p. L-26. Exercises: What fraction of the shapes are … a) circles b) squares c) circles or squares d) not circles e) not triangles Bonus: f) Which two parts above have the same answer? g) Make up another question that has the same answer as part d).

We can take a fraction of any kind of set, not just shapes. What fraction of your fingers are thumbs? See p. L-26 for details.

Now I will ask questions about you! What fraction of the students in our class wear glasses? See p. L-26 for details. What fraction play a musical instrument?

A basketball team played five games and won two of them. What fraction of the games did the team win? See p. L-27 for details.

What fraction of their games did the team win? Exercises: What fraction of their games did the team win? a) Team A played 6 games and won 4. b) Team B won 5 games and lost 3. c) Team C played 9 games and won 7. d) Team D won 4 games and lost 5. See p. L-27 for follow-up questions.

1 2 5 10 Extensions: 1. Explain how you can use your hands to show that is equivalent to .

2. What word do you get when you combine … 1 2 a) the first of sun and the first of person? 3 b) the first of grease and the first of ends? 1 2 c) the first of wood and the last of arm? 1 2 3 Bonus: Try making up your own such questions.

3. a) Write as many equivalent fractions as you can for the picture.

b) Make a model (using counters) of a fraction that can be described in two ways. 1 2 of the counters are white 3 6 Example:

c) Using 10 counters of one colour and 10 counters of a different colour, make a model of a fraction that can be described in at least three different ways. Then write the three fractions.

4. Draw a set of five shapes (circles and squares) so: 2 5 One circle is shaded are shaded are squares b) 3 5 2 No circle is shaded are shaded are squares c) 3 5 are squares are shaded 1 of the squares are shaded

3 5 are squares Bonus: 3 5 are shaded 2 5 are big 1 3 of the squares is big 2 3 of the squares are shaded No shaded shape is big

AP Book 4.2 p. 30 New Canadian Edition