FRACTIONS( PATTERN BLOCKS)2004

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Slide 1:

FRACTIONS Grade 8 Grade 7 Grade 5 Grade 6 Grade 4 Created by: Enzo Timoteo EFT Consulting Ltd. for Alberta Learning E-mail: timoteoe@ecsd.net

Slide 2:

FRACTIONS: WITH FRACTION BLOCKS = + =

Slide 3:

Table of Content: Add and Subtract fractions (using one hexagon) 2.Multiply and Divide fractions (using one hexagon) 3. Add and Subtract fractions ( using a double hexagon) 4. Multiply and Divide fractions (using a double hexagon) 5. Extension ( using triple hexagons, etc… 6. Blackline masters

Slide 4:

Grade 8: Add, Subtract,Multiply and Divide fractions Concretely, Pictorially and Symbolically. [ E, PS, V ]

Slide 5:

CONCRETE PICTORIAL SYMBOLIC UNDERSTANDING Modes(Styles) of Learning

Slide 6:

BLOCKS Hexagon Rhombus Triangle Trapezoid

Slide 7:

One whole The yellow hexagon , double and triple hexagon are templates for all operations of fractions and representing the whole. One whole One whole

Slide 8:

Equivalent Fractions:

Slide 9:

ADD and SUBTRACT FRACTIONS:

Slide 10:

+ Hint: To ADD fractions with pattern blocks, you MUST be sure that all blocks are of the same color ( just like finding the lowest common Denominator ).

Slide 11:

+ Hint: To ADD fractions with pattern blocks, you MUST be sure that all blocks are of the same color ( just like finding the lowest common Denominator ).

Slide 12:

+ Hint: To ADD fractions with pattern blocks, you MUST be sure that all blocks are of the same color ( just like finding the lowest common Denominator ).

Slide 13:

Hint: To ADD fractions with pattern blocks, you MUST be sure that all blocks are of the same color ( just like finding the lowest common Denominator ). + +

Slide 14:

Hint: To ADD fractions with pattern blocks, you MUST be sure that all blocks are of the same color ( just like finding the lowest common Denominator ). + +

Slide 15:

Subtraction: - Hint: Subtraction means to take away.

Slide 16:

- Hint: To SUBTRACT fractions with pattern blocks, you MUST be sure that all blocks are of the same color ( just like finding the lowest common Denominator ).

Slide 17:

+ - Hint: To ADD or SUBTRACT fractions with pattern blocks, you MUST be sure that all blocks are of the same color ( just like finding the lowest common Denominator ).

Slide 18:

+ - Hint: To ADD or SUBTRACT fractions with pattern blocks, you MUST be sure that all blocks are of the same color ( just like finding the lowest common Denominator ).

Slide 19:

+ + -

Slide 20:

In all operations of fractions the word “ Group ” is used. This means , For example: 4 of3= or 4 X 3= means 4 groups of 3 . That is: 3+3+3+3=12

Slide 21:

MULTIPLY and DIVIDE FRACTIONS:

Slide 22:

HINT : Identify which block is a half , then take one one-half of the whole.

Slide 23:

HINT : Identify which block is one-third , then take one one-third of the whole.

Slide 24:

HINT : Identify which block is one-third , then take two wholes and replace with one-thirds. HINT : Take one-third of the two wholes

Slide 25:

HINT : Identify which block is one-sixth , then put one-sixth in each of the 3 wholes. 1 2

Slide 26:

HINT : When multiplying fraction by another fraction, it is very important that the blocks are of equal group. For example, one-third can be made equivalent to two-sixths ,etc…. Hint: Take one-half of two-sixths

Slide 27:

Hint: Take two-thirds of one-half. 1 1 Hint: You are left with two-sixths of the whole or one -third.

Slide 28:

Hint: Take two-thirds of one and one-half. 1 1 1 1

Slide 29:

Hint: Take one-half and divided into three equal parts. Hint: Take the reciprocal of the divisor and multiply. Hint: There is 1 one sixth of the whole .

Slide 30:

Hint: Take four-thirds and divided into two equal parts. Hint: Take the reciprocal of the divisor and multiply. 2 1 Hint: There is 1 two-thirds of the whole.

Slide 31:

Hint: How many groups of one-half is in two-thirds of a whole? Hint: There are 1 half and a third of a half. Hint: Take the reciprocal of the divisor and multiply. DIVIDE : Fraction by a Fraction:

Slide 32:

Hint: How many groups of one-third in five-sixth? Hint: There are 2 and half thirds in five-sixths. Hint: Take the reciprocal of the divisor and multiply.

Slide 33:

Hint: How many groups of one and five-sixth is in one half? Hint: There are 3 and two-thirds halves in one and five-sixth. Hint: Take the reciprocal of the divisor and multiply.

Slide 34:

, Hint: How many groups of three and half is in one-half ? Hint: There are 7 trapezoids (halves) in three and one-half. Hint: Take the reciprocal of the divisor and multiply. 1 1

Slide 35:

, Hint: How many groups of one-third is in three and two-thirds? Hint: There are 11 one-third blocks in 3 and two-thirds of a whole. Hint: Take the reciprocal of the divisor and multiply. 1 1

Slide 36:

, Hint: How many groups of one-half is in two and one-sixth? Hint: There are four and one-third of a whole. . Hint: Take the reciprocal of the divisor and multiply. 1 3

Slide 37:

ADD and SUBTRACT FRACTIONS:

Slide 38:

Identifying the Blocks Fraction Blocks:

Slide 39:

Double Hexagon Hexagon Chevron Trapezoid Rhombus Triangle

Slide 40:

+ = Hint: ALLWAYS have the same color blocks in order to ADD and/or SUBTRACT !!! ( Note : it is like finding lowest common denominator )

Slide 41:

+ = Hint: ALLWAYS have the same color blocks in order to ADD and/or SUBTRACT !!! ( Note : it is like finding lowest common denominator )

Slide 42:

+ =

Slide 43:

+ =

Slide 44:

+ =

Slide 45:

+ + =

Slide 46:

- = Hint : Subtract means to take away . ( note : provided that the blocks are of the same color )

Slide 47:

- = Hint : Subtract means to take away. ( note : provided that the blocks are of the same color )

Slide 48:

- =

Slide 49:

- =

Slide 50:

- =

Slide 51:

- =

Slide 52:

+ - =

Slide 53:

MULTIPLY and DIVIDE FRACTIONS:

Slide 54:

Double Hexagon Hexagon Chevron Trapezoid Rhombus Triangle

Slide 55:

Hint: There are two halves in one whole. Hint: Take 1-half of one whole.

Slide 56:

Hint: There are two whole one’s. Hint: Take one half of the two whole one’s.

Slide 57:

Hint: There are 6 thirds ? Hint: Take one-third of the two whole one’s. Remember we must create 3 equal parts.

Slide 58:

Hint: Five-sixth of two whole ones.

Slide 59:

Three groups of one- thirds.

Slide 60:

One-half of two-thirds. 1 3

Slide 61:

Can you take one-quarter of two-sixth ? No! Can you take one-quarter of four-twelve’s ? Yes!

Slide 62:

Can you see that two-thirds of three-quarters will not work! Can you see that two-thirds of four- sixth will not work!

Slide 63:

Take one-third of fifteen-twelve’s.

Slide 64:

Take one-quarter of twenty-twelve’s.

Slide 65:

Take two-thirds of twenty-one twelve’s. 7 6

Slide 66:

Division of Fractions

Slide 67:

Double Hexagon Hexagon Chevron Trapezoid Rhombus Triangle

Slide 68:

Hint: You can say that one-half is divided into two equal parts. When dividing: Take the reciprocal and multiply Hint: Take 1 one-half of a half.

Slide 69:

Hint: You can say that one-quarter is divided into three equal parts. When dividing: Take the reciprocal and multiply 1 1 Hint: Now, take one-third of three- twelve’s.

Slide 70:

Hint: How many groups of one-half is in two-thirds of a whole? Hint: There are 1 half and one-third of a half in two-thirds of a whole. When dividing: Take the reciprocal and multiply Divide: fraction by a fraction;

Slide 71:

Hint: How many quarters are there in a half? Hint: There are two quarters in a half. When dividing: Take the reciprocal and multiply 2 1

Slide 72:

, Hint: How many groups of one-half is in one-quarter of a whole? Hint: There is one-half of a half in one-quarter of a whole. When dividing: Take the reciprocal and multiply 1 2

Slide 73:

, Hint: How many groups of one-quarter is in a sixth of a whole? Hint: There is two-thirds of one- quarter in a sixth. When dividing: Take the reciprocal and multiply 2 3

Slide 74:

, Hint: How many groups of one-half is in two-thirds of a whole? Hint: There is 1-half and third of a half. When dividing: Take the reciprocal and multiply

Slide 75:

, Hint: How many groups of one-sixth is in one half of a whole? Hint: There is 3-sixths in one-half. 3 1 When dividing: Take the reciprocal and multiply

Slide 76:

, Hint: How many groups of one half is in one and two-thirds of a whole? Hint: There is 3 and a third halves in one and two-thirds. When dividing: Take the reciprocal and multiply

Slide 77:

, Hint: How many groups of one quarter is in one and three-quarters of a whole? Hint: There are 7 quarters in one and three-quarters. When dividing: Take the reciprocal and multiply 1 1

Slide 78:

, Hint: How many groups of one-half is in one and one-sixth of a whole? Hint: There are 2 and a third halves in one and one-sixth. When dividing: Take the reciprocal and multiply 7 3

Slide 79:

Extension!

Slide 80:

Triple Hexagon

Slide 81:

+ =

Slide 82:

+ =

Slide 83:

+ - =

Slide 84:

, Hint: Take two-thirds of one-sixth of the whole

Slide 85:

, Hint: Take one-third of fifteen-eighteens of the whole.

Slide 86:

, Hint: Take one-half of four-thirds of the whole.

Slide 87:

, Hint: Take two-thirds of twenty-one eighteens of the whole.

Slide 88:

, Hint: Take one-third and divided into three equal parts of the whole.

Slide 89:

, Hint: What part of one eighteenth in one-sixth of a whole. Hint: There are 3 parts of one-eighteenth in one-sixth of a whole.

Slide 90:

, Hint: What part of one–ninth is in two-thirds of a whole. Hint: There are 6 one-ninth in two-thirds of a whole.