# Bansho – Fractions

Bansho – Fractions

Expectations:

• Represent, compare, and order fractional amounts with like denominators, including proper (3/4) and improper (5/4) fractions and mixed numbers (1 3/5) (using a variety of tools and standard fractional notation).

• Demonstrate and explain the concept of equivalent fractions (using concrete materials).

• Describe multiplitive relationships between quantities by using simple fractions and decimals.

• Determine and explain, through investigation using concrete materials, drawings, and calculators, the relationship between fractions (i.e., with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) and their equivalent decimal forms. – use calculator

Review:

• Fractions are part of a whole

• Vocabulary (half, thirds, quarters, fifths, etc…)

Content Knowledge:

• Model fractions as parts of a whole

- Using area models (this model represents 2/6)

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- Using set models (a collection of objects represent a whole – in this case the red crayons represent 2/5)

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- Using linear models (4/10)

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- Finding the missing part gives the student an understanding of the whole

- If 12 counters represent the whole set, how many counters are ¾ of the set? (set model)

- If the blue rod is the whole, what fraction of the whole is the green rod? (linear model)

• Relate fractions to the benchmarks of 0, ½, and 1

- This is rounding off to the nearest benchmark

• Compare and order fractions (2 strategies: Using concrete materials and using reasoning)

- Using circle fractions to discover that 7/8 of a pizza is greater than ¾.

- Using reasoning:

- 4/6 ? 5/6 – same size parts (sixths) therefore 4/6 < 5/6

- ¾ ? 3/6 – same number of parts, but different sized parts. Fourths are larger, therefore ¾ > 3/6

- 4/6 ? 3/8 – Nearness to ½: 4/6 is greater than ½ and 3/8 is smaller than ½ therefore 4/6 > 3/8

- 7/8 ? ¾ - Nearness to the whole: eights are smaller than fourths, so 7/8 is closer to one whole than ¾, therefore 7/8 > ¾

• Determine equivalent fractions

- Use a drawing (pizza) and cut it in half and then in half and then in half and write the fractions (1/2 = 2/4 = 4/8 etc…)

- Arrange a set of 12 red counters and 4 yellow counters in equal size groups. All the counters within the group must be the same colour. How many different size groups can you make? For each arrangement, record a fraction that represents the part that each colour is of the whole set.

|Number of Groups |Fraction Red |Fraction Blue |

|4 |3/4 |¼ |

|8 |6/8 |2/8 |

|16 |12/16 |4/16 |

- Using paper strips to find equivalent fractions, create a poster that shows different sets of equivalent fractions

Tangrams Problem: (From the Guide to Effective Instruction)

Many years ago, in China, there lived a man called Mr. Tan. Of all his possessions, he most treasured an exquisite porcelain square tile. One day, he heard that the Emperor of China was coming to his village. To show his great admiration for and loyalty to the Emperor, Mr. Tan decided to offer his very precious tile to the Emperor as a gift. In great excitement, he began to polish his tile so that it would shine. As he handled the tile, however, he dropped it. The tile broke into the 7 pieces of the tangram puzzle. Mr. Tan was so very unhappy. As he wiped away his tears he tried to put it together into a square again. He thought it would be easy, but it took him a long time. While he was trying to form the square he discovered lots of interesting shapes.

(Identify the shapes)

Problem: Put the pieces back together into a square. How many different ways can you do it?

Using BLM:

How many large triangles would you need to cover the square?)

Therefore what fraction does 1 large tangram represent?

¼

Find the fractional equivalent of all the other pieces.

Medium triangles 1/8

Small triangles 1/16

Square 1/8

Parallelogram 1/8

Explain how you figured them out (especially the square and the parallelogram)

Label BLM3

BLM4

- Cover ¼ of the large square with identical tangram pieces

- Arrange the identical pieces on another sheet of paper and trace around each piece

- Cut out the arrangement as a whole (one large triangle)

- Label each piece as a fraction (right on the paper)

- Glue the triangle in your math book and label the entire fraction underneath

How many eighths are in ¼?

How many sixteenths are in ¼?

Describe the pattern they discover

LESSONS

Lesson 1

Activation: Review vocabulary (half, third, quarter, fifth, etc…)

Problem: Represent 2/6 as many possible ways as you can. (Be sure to have a variety of manipulatives available to students)

Consolidation: organize according to three models (area model, set model, linear model)

HW: Copy notes and give an example of each fraction model

Lesson 2

Activation:

Problem: Arrange a set of 12 red counters and 4 yellow counters in equal size groups. All the counters within the group must be the same colour. How many different size groups can you make? For each arrangement, record a fraction that represents the part that each colour is of the whole set.

Example answer:

|Number of Groups |Fraction Red |Fraction Blue |

|4 |3/4 |¼ |

|8 |6/8 |2/8 |

|16 |12/16 |4/16 |

Consolidation: Discussion of equivalent fractions

HW: Text 337 #3-6

Lesson 3 and 4

“Tangrams Problem” activity from above.

Day one – arrange the tangrams in as many ways as you can to make the square.

Day two – label each piece of the tangram as a part of the whole

Focus on Area Model

Lesson 5

Activation: How many different ways can you write (drawing of 1 ½ pizzas). Bring out vocabulary of proper, improper, mixed fractions.

Problem: There are 7 people at a party. They ordered a bunch of pizzas. The first person ate ¼ of a pizza. The second 2/4, the third ¾, 4/4, 5/4, 6/4, and the last 7/4 of a pizza. How many pizzas did they order?

Extension: If each pizza had 6 slices, how many pieces did each person eat?

Consolidation: Review improper and mixed fractions

HW: ONW page 10 and 11

Lesson 6 (optional)

Same as lesson 4, but 1/6 to 11/6

Lesson 7

Activation: Take up HW

Problem: 3 ½ pizzas were ordered by Mr. Wendler. Each pizza had 8 pieces. Mrs. Sarte-Dance ate ½ of everything and Mr. Wendler ate the other ½. How many pieces did they eat?

Consolidation:

HW:

Focus on set model and division

Lesson 8

Activation: Draw a rectangle 12 cm by 4 cm. This rectangle represents 2/3 of the whole. What does the whole look like?

Problem: There are 3 fruit bars and 5 friends. How can they divide the fruit bar equally? (Give some groups different numbers of friends, 4 or 6, to get some variety and see the pattern)

Consolidation: The number of objects shared (3) amongst the number set (5) determines the fractional amount (the answer: 3/5).

HW: A basketball team has 12 players. After practice ½ the players want apples, 1/3 of the players want oranges and the rest want pears. How many of each fruit needs to be bought?

Also: text page 347 #3-7

Lesson 9

Activation:

Problem: There are 45 beads in a bracelet. 2/3 are red. How many beads are red?

Consolidation:

Lesson 10

Activation:

Problem: The area of a classroom floor is 120 square metres. The teacher wants to cover ¾ of it. How much carpet does she need?

Consolidation:

Lesson 11

Activation:

Problem: A class is selling 480 tickets for a school concert. Their goal is to sell 2/3 by the end of the first week. They sold 300. Did they reach their goal?

Consolidation:

Lesson 12

Line fractions and decimals

Lesson 13

Reasoning and comparing fractions

Lesson 14

Line/fraction strips (sheet that Brigitte has)

Test

More Questions:

Joe had 8 sections of fence to paint. He painted 2/3 of each section in 1 hour. How many hours did it take him to paint the whole fence?

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