strand 3: number · 2018. 9. 3. · simplifying . algebraic fractions.” chief examiners’...
TRANSCRIPT
Strand 3: Number
• Half a cup of tea• Quarter of an hour• Three quarters full
Fractions are Easy!
00000 =2 4 of ?3 5
Point to Ponder!
Chief Examiners’ Reports
LC HL - 2000
"Candidates answering showed weaknesses in the following specific areas: handling fractions"
Chief Examiners’ Reports
LC HL - 2000
"Candidates answering showed weaknesses in the following specific areas: handling fractions"
Chief Examiners’ Reports
LC HL - 2005
“Incorrect cancelling in algebraic fractions.”
Chief Examiners’ Reports
LC HL - 2005
“Incorrect cancelling in algebraic fractions.”
Chief Examiners’ Reports
LC HL - 2005
“Incorrect cancelling in algebraic fractions.”LC FL - 2005
“Fractions again caused problems for many.” “..it would appear that fractions are not well understood.”
Chief Examiners’ Reports
LC FL - 2005
“Fractions again caused problems for many.” “..it would appear that fractions are not well understood.”
Chief Examiners’ Reports
LC FL - 2005
“Fractions again caused problems for many.” “..it would appear that fractions are not well understood.”
JC OL - 2006
“Common errors were: mishandling either fraction or square root; adding before multiplying.”
Chief Examiners’ Reports
JC OL - 2006
“Common errors were: mishandling either fraction or square root; adding before multiplying.”
Chief Examiners’ Reports
JC OL - 2006
“Common errors were: mishandling either fraction or square root; adding before multiplying.”
JC HL - 2006
“Areas of weakness in candidate performance:simplifying algebraic fractions.”
Chief Examiners’ Reports
JC HL - 2006
“Areas of weakness in candidate performance:simplifying algebraic fractions.”
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Cara has 4 pizzas for her party.3She decides that a serving will be of a pizza.5
2 2Will she get 6 or 6 servings from the 4 pizzas?3 5
Unifix Cubes
Cara has 4 pizzas for her party.3She decides that a serving will be of a pizza.5
2 2Will she get 6 or 6 servings from the 4 pizzas?3 5
Unifix Cubes
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Fraction Strips & Fraction Circles
Spoken Symbols
ManipulativeModels
Real Life Situations
Written Symbols
Pictures
Lesh’s Translation Model
Prior knowledge
Overview of Fractions
Diagnostic Test
Prior knowledge
Overview of Fractions
00000
3Which of these rectangles has shaded in? 4
Is it more than one rectangle?
A. B. C. D.
Answer:
Diagnostic Test
00000
What fraction of the fraction circle is marked ‘f’?
a
bc
d
e
f
Diagnostic Test
Answer:
00000
(a) (b) (c) (d)
(a) (b) (c) (d)
The shaded part of this diagram could represent the numbers:1 5 15 2 12 8 4
Identify the unit in each case by drawing:
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Ordering
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Equivalence
Ordering
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Add Subtract
Equivalence
Ordering
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Multiply & Divide
Add Subtract
Equivalence
Ordering
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Decimals
Multiply & Divide
Add Subtract
Equivalence
Ordering
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Percentages
Decimals
Multiply & Divide
Add Subtract
Equivalence
Ordering
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Ratio
Percentages
Decimals
Multiply & Divide
Add Subtract
Equivalence
Ordering
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
Ratio
Percentages
Decimals
Multiply & Divide
Add Subtract
Equivalence
Ordering
Partitioning
Diagnostic Test
Concepts
Operations
Connections
Prior knowledge
Overview of Fractions
AlgebraStrand 4
• Partitioning
• Ordering
• Equivalence
Reasons for rules ~Checking tools
Concepts
00000
3Is always the same?4
Concepts
00000
3Is always the same?4
Only if the unit is the same.
Concepts
00000
3Is always the same?4
Only if the unit is the same.
Concepts
00000
3Is always the same?4
Only if the unit is the same.
Concepts
3 5Which is bigger: or ?7 7
2 2Which is bigger: or ?3 5
5 3Which is bi
5 1 becau
gger:
se there are
or ?9 7
more 7 7
1 1 2 23 5 3 5
5 1 3 1 5 3 and 9 2 7 2 9 7
> ⇒ >
> < ⇒ >
Concepts
3 5Which is bigger: or ?7 7
2 2Which is bigger: or ?3 5
5 3Which is bi
5 1 becau
gger:
se there are
or ?9 7
more 7 7
1 1 2 23 5 3 5
5 1 3 1 5 3 and 9 2 7 2 9 7
> ⇒ >
> < ⇒ >
Concepts
3 5Which is bigger: or ?7 7
2 2Which is bigger: or ?3 5
5 3Which is bi
5 1 becau
gger:
se there are
or ?9 7
more 7 7
1 1 2 23 5 3 5
5 1 3 1 5 3 and 9 2 7 2 9 7
> ⇒ >
> < ⇒ >
Concepts
3 5Which is bigger: or ?7 7
2 2Which is bigger: or ?3 5
5 3Which is bi
5 1 becau
gger:
se there are
or ?9 7
more 7 7
1 1 2 23 5 3 5
5 1 3 1 5 3 and 9 2 7 2 9 7
> ⇒ >
> < ⇒ >
Concepts
3 5Which is bigger: or ?7 7
2 2Which is bigger: or ?3 5
5 3Which is bi
5 1 becau
gger:
se there are
or ?9 7
more 7 7
1 1 2 23 5 3 5
5 1 3 1 5 3 and 9 2 7 2 9 7
> ⇒ >
> < ⇒ >
Concepts
3 5Which is bigger: or ?7 7
2 2Which is bigger: or ?3 5
5 3Which is bi
5 1 becau
gger:
se there are
or ?9 7
more 7 7
1 1 2 23 5 3 5
5 1 3 1 5 3 and 9 2 7 2 9 7
> ⇒ >
> < ⇒ >
Concepts
Concepts
3 2Which is bigger: or ?5 3
=
=
> ⇒ >
3 6 1If we double , we get 15 5 52 4 1If we double , we get 13 3 3
1 1 2 3 .3 5 3 5
Whole Number Multiplication
Whole Number Multiplication
Liz wants to give each of her 3 friends 4 bars of chocolate. How would you work out how many bars she needs?
Whole Number Multiplication
Liz wants to give each of her 3 friends 4 bars of chocolate. How would you work out how many bars she needs?
Whole Number Multiplication
Liz wants to give each of her 3 friends 4 bars of chocolate. How would you work out how many bars she needs?
Whole Number Multiplication
Liz wants to give each of her 3 friends 4 bars of chocolate. How would you work out how many bars she needs?
Whole Number Multiplication
Liz wants to give each of her 3 friends 4 bars of chocolate. How would you work out how many bars she needs?
• 3 multiplied by 4 or 3 times 4
Whole Number Multiplication
Liz wants to give each of her 3 friends 4 bars of chocolate. How would you work out how many bars she needs?
• 3 multiplied by 4 or 3 times 4
• 4 + 4 + 4 (Repeated Addition)
Whole Number Multiplication
Liz wants to give each of her 3 friends 4 bars of chocolate. How would you work out how many bars she needs?
• 3 multiplied by 4 or 3 times 4
• 4 + 4 + 4 (Repeated Addition)
• 3 groups of 4
Whole Number Multiplication
Multiplying a Whole Number by a Fraction
Barry is having 4 of his friends over to his house for pizza. 2He is going to give them of a pizza each.3
How is this like the last problem? Draw a picture to model this situation.
(a)(b)
(c) 2If you have “4 groups of ", how many ‘one thirds’ do you have?3
Multiplying a Whole Number by a Fraction
Barry is having 4 of his friends over to his house for pizza. 2He is going to give them of a pizza each.3
How is this like the last problem? Draw a picture to model this situation.
(a)(b)
(c) 2If you have “4 groups of ", how many ‘one thirds’ do you have?3
Multiplying a Whole Number by a Fraction
Barry is having 4 of his friends over to his house for pizza. 2He is going to give them of a pizza each.3
How is this like the last problem? Draw a picture to model this situation.
(a)(b)
(c) 2If you have “4 groups of ", how many ‘one thirds’ do you have?3
Multiplying a Whole Number by a Fraction
Barry is having 4 of his friends over to his house for pizza. 2He is going to give them of a pizza each.3
How is this like the last problem? Draw a picture to model this situation.
(a)(b)
(c) 2If you have “4 groups of ", how many ‘one thirds’ do you have?3
Multiplying a Whole Number by a Fraction
Barry is having 4 of his friends over to his house for pizza. 2He is going to give them of a pizza each.3
How is this like the last problem? Draw a picture to model this situation.
(a)(b)
(c) 2If you have “4 groups of ", how many ‘one thirds’ do you have?3
Picture/Words
Multiplication sentence
...groups of...
Repeated addition
Poster/ White Boards
00000If I multiply what incorrect answer do you think I might get?
Pair Work
×243
00000
Pair Work
4 2 8 1 3 3How come 4 2 24 ?1 3 3
× = + =
and
00000
Fraction x Fraction
2Cara has of her rectangular birthday cake left 5
over from her party. 3She ate of the leftover cake.4
How much of the full cake was this?