3rd Grade Fractions 2015-03-31 www.njctl.org Slide 3 / 215 Table - - PDF document

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3rd Grade Fractions

www.njctl.org 2015-03-31

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· Whole Number Fractions · Equal Parts · Fractions of a Group · Comparing Fractions with Same D enominators or Numerators · Equivalent Fractions

Table of Contents

· Fractions on a Number Line Click title to go to that section · Measurement to Nearest H alf and Quarter Inch · Benchmarks · Exploring Fractions with Pattern Blocks

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Links to PARCC sample questions

Non-Calculator #3 Non-Calculator #4 End of Year Performance Based Assessment Non-Calculator #5 Non-Calculator #7 Non-Calculator #17 Non-Calculator #8 Non-Calculator #13 Non-Calculator #17 Non-Calculator #23 Non-Calculator #28 Non-Calculator #30 Non-Calculator #35

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Equal Parts

Return to Table of Contents

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Fraction

• An expression that indicates the

quotient ( ) of two quantities. Numerator

• The number above the fraction bar.

The numerator answers the question "How many parts?" Denominator

• The number below the fraction
• bar. The denominator answers the question

"How many total?"

Key Terms

Numerator 3 Denominator 7 Fraction =

= ÷

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Where have you seen fractions? How do we use fractions? 96/100= A+

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These are halves. How do you write one half? numerator denominator

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These are thirds. How do you write one third?

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These are Fourths. How do you show and write two fourths?

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Sixths How do you show and write two sixths?

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Eighths How do you show and write eight eighths?

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What fractions are represented below?

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Internet links for more practice Fractions Naming Model Fractions Parts of a Whole Model

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1 Does this show ? Yes No

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2 What fraction of the whole is shaded?

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3 What fraction of the whole is white?

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4 What fraction could this picture show? A B C Both A and B D Neither A nor B

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5 How many more yellow pieces do I need to make this fraction ?

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6 Which of the following could be used to show ?

A B C D

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7 Bella cut her ribbon into 4 pieces that are the same

• length. The length of one piece of ribbon is what

fraction of the length of the ribbon?

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8 A whole is divided into 4 equal parts. Write the fraction that represents 3 parts of the whole.

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9 A whole is divided into 6 equal parts. Write the fraction that represents 1 part of the whole.

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10 A whole is divided into 7 equal parts. Write the fraction that represents 4 parts of the whole.

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11 Lee needs of a cup of sugar to make cookies. He will measure the sugar using a cup scoop. How many times will Lee need to fill the cup scoop in

• rder to measure of a cup of sugar?

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12 Sasha needs of a cup of mix to make pancakes She will measure the mix using a cup scoop. How many times will Sasha need to fill the cup scoop in order to measure of a cup of mix?

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13 Which three shapes have parts that are the area of their whole shape. A B C D E Drag and drop the correct three shapes into the box.

From PARCC sample test

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14 Select the two shapes that have parts that are each

• f the area of the whole shape.

A B C D E

From PARCC sample test

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15 A flower garden is divided into equal parts. The color

• f the flowers planted in each part of the garden is

shown. Select the three statements that are true. A There are red or yellow flowers in of the garden. B Purple flowers are planted in of the garden. C Pinks flowers are planted in of the garden. D Each part of the garden is of the whole garden. E There are yellow flowers in of the garden. F Red flowers are planted in of the garden.

From PARCC sample test

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16 Each model equals one whole divided into equal

• parts. Which models show shaded?

Select the three correct answers. A B C D E F

From PARCC sample test

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17 An artist plans to paint a wall in a room. The wall is divided into 6 equal parts so that each part can be painted a different color. Part A The artist goes to the store to buy brushes and small cans of paint. He pays a total of $94. · He buys 8 brushes that cost $5 each. · The rest of the money is used for the 6 cans of paint. Each can of paint costs the same amount. How much does each can of paint cost?

(Show your work on paper at your desk and be ready to explain)

From PARCC sample test

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18 Part B The artist starts painting the wall. The parts of the wall that look white are not painted yet. Which statements about the wall are correct? Select the two correct statements. A Each painted part it of the whole wall. B Each painted part it of the whole wall. C Each painted part it of the whole wall. D The fraction of the wall not yet painted is . E The fraction of the wall not yet painted is . F The fraction of the wall not yet painted is .

From PARCC sample test

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Fractions of a Group

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The last lesson focused on dividing a whole shape into fractions. This lesson focuses on fractions of group of objects. 1 2 1 2 1 of the group of apples 2 1 of the whole 2

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What fraction of the shapes are circles? Step 1: Count the circles. This is your numerator. Step 2: Count all of the shapes. This is the denominator.

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What fraction of the nickels are heads up? What fraction of the nickels are on tails?

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What fraction of the faces are happy? What fraction of the faces are sad?

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Circle of the mice. Circle of the frogs. Circle of the lions.

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Click the cookie to practice fractions of a group.

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19 Are of the lions in the triangle? Yes No

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20 What fraction of the frogs are boxed below? A B C D

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21 What fraction is not circled?

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22 of the dogs are wearing a bow. True False

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23 What fraction of the flowers are not in the vase?

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Exploring Fractions with Pattern Blocks

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Groups of students need:

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How many are in one ?

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The is what fraction of the ?

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24 How many green triangles are in one red trapezoid?

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25 The green triangle is what fraction of the red trapezoid?

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26 How many green triangles are in one yellow hexagon?

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27 The green triangle is what fraction of the yellow hexagon?

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28 How many blue rhombuses are in one yellow hexagon?

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29 The blue rhombus is what fraction of the yellow hexagon?

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30 How many red trapezoids are in one yellow hexagon?

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31 The red trapezoid is what fraction of the yellow hexagon?

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Small group/ individual practice with online pattern blocks. Click for web site.

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Pattern block activity Groups need a container of pattern blocks and will use pattern blocks to represent fractions of a group.

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In this group

• f 8 pattern

blocks, 3 of them are triangles.

Drag blocks needed down into work space.

WORK SPACE

• f the

group is triangles

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Make a group

• f 5 pattern

blocks, with 2 of them squares.

Drag blocks needed down into work space.

WORK SPACE Fraction =

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Make a group

• f 7 pattern

blocks, with 6 of them trapezoids.

Drag blocks needed down into work space.

WORK SPACE Fraction =

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Make a group

• f 3 pattern

blocks, with 2 of them hexagons.

Drag blocks needed down into work space.

WORK SPACE Fraction =

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32 What fraction of this group of pattern blocks is squares?

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33 What fraction of this group of pattern blocks is triangles?

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34 What fraction of this group of pattern blocks is hexagons?

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35 What fraction of this group of pattern blocks is trapezoids?

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36 What fraction of this group of pattern blocks is triangles?

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Fractions on a Number Line

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There are numbers between 0 and 1. 1 What is a number that is greater than 0 but less than 1?

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1 How did you know what the number was? The number line was divided into 2 equal sections.

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What denominator would you use if the number line was divided into 3 equal parts? 1

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What denominator would you use if the number line was divided into 4 equal parts? 1

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37 Should you use a 6 in the denominator for this number line? Yes No

1

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38 What denominator would you use to represent the lines on this number line?

1

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39 What denominator would you use to represent the lines on this number line?

1

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40 What denominator would you use to represent the lines on this number line?

1

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41 What denominator would you use to represent the lines on this number line?

1

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1

Move the fractions to label the lines on the number line.

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1

Divide the number line into 7 equal parts and label it.

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1

Divide the number line into 5 equal parts and label it.

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Click for Number Line Game

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42 What fraction is missing from the number line? A B C D 0 1 3 4 1 5 5 5

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43 What is the fraction for the red dot?

1

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44 What is the fraction for the red dot?

1

? Slide 84 / 215

45 What is the fraction for the red dot?

1

? Slide 85 / 215

46 Where should be placed? A B C 1

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47 What fraction should be placed with point Z? A B C 1 X Y Z

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48 The point on the number line below represents the fraction . Which point shows ?

A B C D

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49 The point on the number line below represents the fraction . Which point shows 1?

A B C D

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50 The point on the number line below represents the fraction . Which point shows 0?

A B C D

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51 Which letter shows where would be plotted on the number line? A B C D

From PARCC sample test

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52 Which letter is positioned at ? A B C D

From PARCC sample test

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53 A fraction is shown on the number line. Which letter is positioned on the number line to show a fraction that is equivalent to the fraction shown on the other number line? A B C D

From PARCC sample test

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54 Which letter is positioned at ? A B C D

From PARCC sample test

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55 Mia placed point P on the number line. What is the value of P as a fraction? A B C D What does the denominator of your fraction represent on the number line? What does the numerator of your fraction represent

• n the number line?

From PARCC sample test

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Comparing Fractions

Return to Table of Contents

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To compare fractions, you could use pictures or number lines to determine which fractions are greater. By using these strategies, you will come up with some rules to remember.

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Let's compare 4/5 and 2/5. Which one is greater? How do you know? 1 5 1 What rule could you use when comparing fractions with the same denominator?

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Slide each problem over to the blue side to see if you are correct. 1 < 2 2 2 2 < 4 6 6 4 > 2 5 5 3 > 2 4 4 1 < 2 3 3 Compare each set of fractions. (Drag fraction to box on right to see the inequality symbol)

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56 A < B > C =

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57 A < B > C =

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58 A < B > C =

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59 A < B > C =

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60 Classroom A has of the students buying school lunch. Classroom B has

• f the students buying lunch. Which

classroom has the larger fraction of the students buying lunch?

A

Classroom A

B

Classroom B

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1 2

Let's compare 1/5 and 1/2. Which one is greater? How do you know? 1 What rule could you use when comparing fractions with the same numerator? 1 5

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Compare each set of fractions. Move the magnifying glass to see if you are correct. 1 > 1 2 3 6 < 6 12 10 3 > 3 4 5 4 > 4 6 8 5 < 5 9 7 2 < 2 5 2

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61 is less than . Yes No

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62 Which fraction is greater than ? A B C Both A and B D Neither A Nor B

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63 A < B > C =

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64 A < B > C =

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65 A < B > C =

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Click the fish to practice comparing fractions with the same denominators or the same numerators.

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66 Enter a fraction larger than .

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67 Enter a fraction larger than .

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68 Enter a fraction less than .

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69 Enter a fraction less than .

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70 Which three comparisons are true? A = B = C = D = E =

From PARCC sample test

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71 A B C D E

<

Select the three fractions that make this comparison true.

From PARCC sample test

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Benchmark Fractions

Return to Table of Contents

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1

This circle has

• f it shaded.

This is very close to zero. This circle has

• f it shaded.

This is very close to one.

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1

<

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1

This rectangle has of it shaded. This is very close to zero. This rectangle has of it shaded. This is very close to one.

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1

<

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1

This group has

• f it sharks.

This is very close to zero (or none

• f the group).

This group has

• f it dogs.

This is very close to one (or the whole group).

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1

<

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72 Which fraction is closest to zero?

A B C D

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73 Which fraction is closest to zero?

A B C D

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74 Which fraction is closest to one?

A B C D

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75 Which fraction is closest to one?

A B C D

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1

We can also see if a fraction is equal to

• r close to .

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1

< <

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1

Very close to zero. Very close to . Very close to one whole.

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1

< <

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1

This group has

• f it pink

hearts, this is very close to of the group. This group has

• f it blue

triangles, this is very close to the whole group. This group has

• f it purple

stars, this is very close to zero.

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1

< <

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Move the magnifier to find the fractions that are close to half.

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79 Which fraction is closest to ?

A B C D

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80 Which fraction is closest to ?

A B C D

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81 Which fraction is closest to ? A B C D

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82 Which group shows about of it as stars?

A B C Slide 143 / 215

83 Which group shows about of it as circles?

A B C Slide 144 / 215

Equivalent Fractions

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Key Term Equivalent Fractions- Fractions that represent the same number or are equal to one another.

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1/4 pieces 1/6 pieces 1/8 pieces 1/2 How many 1/4 pieces fit in the 1/2 piece? Write as a fraction. How many 1/6 pieces fit in the 1/2 piece? How many 1/8 pieces fit in the 1/2 piece? These fractions are equivalent.

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1/3 1/6 pieces How many 1/6 pieces fit in a 1/3? We show equivalence by writing both fractions with an equal sign. =

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1 9 1 9 1 9

What do you notice about the denominators in each set of equivalent fractions? The fraction bars below are equivalent because they are the same size.

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Drag the red rectangle to see equivalent fractions on number lines. What do you notice about the numerators and denominators?

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To create equivalent fractions, multiply (or divide) the numerator and denominator by the same number. 2 x 3 = 6 4 x 3 = 12 6 ÷ 3 = 2 21 ÷ 3 = 7

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Practice finding equivalent fractions with this

• game. Click the star to play!

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84 Are the shaded areas equivalent?

Yes No

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85 Which fraction is equivalent to ?

A B C D

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86 Write a fraction equivalent to . 1 3

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87 Which set of fractions is equivalent?

A B C D

1 2 2 2 = 4 1 8 4 1 3 3 6 3 9 7 21 = = =

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88 Write a fraction equivalent to . 5 9

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Whole Number Fractions

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Numerator = How many parts? Denominator = How many total?

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This is read as 3 over 1. It is 3 parts of 1 total.

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If each circle is one whole, then this picture shows that 3 wholes are shaded.

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The fraction bar means division. If you take the whole number 3 and divide it by 1. What would your answer be?

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89 What whole number is equal to?

A B C

4

D

1

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90 What whole number is equal to?

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91 What whole number is equal to?

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92 What fraction is equal to the whole number 7?

A B C D

7

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93 What fraction is equal to the whole number 8?

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94 What fraction is equal to the whole number 3?

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Measurement to the Nearest Half and Quarter Inch

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Inch

Small units of length are called inches. Depending on how big your thumb is, your thumbnail can be about 1 inch. The abbreviation of inch is in. Can you think of some things you could measure in inches?

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Follow these steps to measure something correctly: · Determine the unit you are measuring in. · Choose the correct tool. · Correctly line up the measuring tool. · Measure to the nearest unit. · Label your measurement.

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Let's measure this line in inches.

Determine the unit you are measuring in. Choose the correct tool. Correctly line up the measuring tool. Measure to the nearest unit. Label your measurement.

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Let's measure this line in inches.

Determine the unit you are measuring in. Choose the correct tool. Correctly line up the measuring tool. Measure to the nearest unit. Label your measurement.

x

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Let's measure this line in inches.

Determine the unit you are measuring in. Choose the correct tool. Correctly line up the measuring tool. Measure to the nearest unit. Label your measurement.

x x

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Let's measure this line in inches.

Determine the unit you are measuring in. Choose the correct tool. Correctly line up the measuring tool. Measure to the nearest unit. Label your measurement.

x x x

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Let's measure this line in inches.

Determine the unit you are measuring in. Choose the correct tool. Correctly line up the measuring tool. Measure to the nearest unit. Label your measurement.

x x x x

3 in.

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Click on The Ruler Game to practice measuring in inches.

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95 This line is 4 inches long.

Yes No

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96 How long is this line? _____ in.

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97 How many inches is this pencil? _____ in.

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98 How many inches is this crayon? _____ in.

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In between each of the numbers on a ruler are 1/2 inches.

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Let's measure in half inches.

Correctly line up the measuring tool. Measure to the nearest half inch. Label your measurement.

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Let's measure in half inches.

Correctly line up the measuring tool. Measure to the nearest half inch. Label your measurement.

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Let's measure in half inches.

Correctly line up the measuring tool. Measure to the nearest half inch. Label your measurement.

3 1/2 in.

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Let's measure in half inches.

Correctly line up the measuring tool. Measure to the nearest half inch. Label your measurement.

3 1/2 in.

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Click on The Ruler Game to practice measuring in half inches.

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100 This line is inch long.

Yes No

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101 How many inches is this comb? _____ in.

A

3 1/2 in.

B

2 in.

C

2 1/2 in.

D

1/2 in.

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102 How many inches is this card? _____ in.

A

3 1/2 in.

B

2 in.

C

2 1/2 in.

D

1/2 in.

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103 How long is this line? _____ in.

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When measuring an object, we can get a more exact measurement using inch increments.

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What do you notice about inch?

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104 Is inches equivalent to inches?

Yes No

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105 Is in. equivalent to in.?

Yes No

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Let's measure in quarter inches.

Correctly line up the measuring tool. Measure to the nearest quarter inch. Label your measurement.

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Let's measure in quarter inches.

Correctly line up the measuring tool. Measure to the nearest quarter inch. Label your measurement.

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Let's measure in quarter inches.

Correctly line up the measuring tool. Measure to the nearest quarter inch. Label your measurement.

in.

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Click to practice measuring in quarter inches.

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106 Measure the line.

Students type their answers here

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107 Measure the line.

Students type their answers here

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108 Measure the line.

Students type their answers here

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109 Measure the line.

Students type their answers here

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110 Measure the object.

Students type their answers here

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111 Measure this object.

Students type their answers here

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112 Measure this object.

Students type their answers here

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113 Measure this object.

Students type their answers here

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114 Measure this object.

Students type their answers here

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115 Measure this object.

Students type their answers here

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116 Measure this object.

Students type their answers here

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117 Measure this object.

Students type their answers here

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118 Measure this object.

Students type their answers here

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119 Measure this object.

Students type their answers here

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