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Making Subtraction Concepts Meaningful. Rosemary Reuille Irons Senior Lecturer Queensland University of Technology [email protected] or [email protected]. What is a concept?. A concept is the picture in your mind of an idea. - PowerPoint PPT Presentation
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Making SubtractionConcepts Meaningful
Rosemary Reuille IronsSenior LecturerQueensland University of [email protected] or [email protected]
What is a concept?
A concept is the picture in your mind of an idea.
Images built through language experiences help develop concepts?
What steps do we follow to develop operation concepts?
• Child’s Language• Materials Language• Mathematical Language• Symbols
CONCRETE/VISUAL
VERBAL
SYMBOLIC
Student Language oral written
Representations
Eight mice are playing by the cheese. Two mice run away. How many mice are playing now?
CONCRETE/VISUAL
VERBAL
SYMBOLIC
Student Language oral written
Materials Language oral and written
Representations
Concrete/pictorial materials – take away
8
take out 2
8 cover up 2
CONCRETE/VISUAL
VERBAL
SYMBOLIC
Student Language oral written
Materials Language oral and written
Mathematical Language oral and written
Representations
The new mathematical words that are used with the concept
8 5spend 3 leaves 8 5take 3is
8 5subtract 3equals
CONCRETE/VISUAL
VERBAL
SYMBOLIC
Student Language oral written
Materials Language oral and written
Mathematical Language oral and written
Symbolic Language written
Representations
The mathematical abbreviations and formulae.
8 5 3=
Teaching the Subtraction Concept
Subtraction Concept
Finding the missing part.
The missing part could be what is left after a take away.
The missing part could be how many to add on.
The missing part could be the difference in number.
Rosie needs 12 apples. She has picked 7 apples. How many more apples does she need?
Rosie had 12 apples in a bag. She took out 7 apples. How many apples are in the bag now?
Rosie has 12 red apples and 7 green apples. How many fewer green apples does she have?
Take AwayChild’s language
Materials language
Mathematical language
Symbolic language
Missing addendChild’s language
Materials language
Mathematical language
Symbolic language
DifferenceChild’s language
Materials language
Mathematical language
Symbolic language
Child's language
Everyday language – take away
Eight mice are playing? Two mice run away? How many mice are playing now?
Child's language
Everyday language – missing addendThere are 8 mice altogether. How many mice are hiding in the cheese?
Four cars in the carpark. How many more will drive in to make ten cars in the carpark?
Child's language
Everyday language – differenceEight mice are playing in front of the cheese. Two mice are playing in the back. How many more mice are playing in front?
Materials language
Concrete/pictorial materials – take away
spend 2
Materials language
Concrete/pictorial materials – take away
8
take out 2
8 cover up 2
Materials language
Concrete/pictorial materials – missing addend
There are 8 altogether. How many are covered?
Materials language
Concrete/pictorial materials – difference
8 cover up 2How much more is 8 than 2?
Make the number of objects to represent the two groups.
Cover the parts of the groups that are the same to show the difference.
Mathematical languageThe new mathematical words that are used with the concept
subtract
[Try to avoid using the word minus. In mathematics this is best associated with negative numbers.]
Symbol language
The mathematical abbreviations and formulae.
8 5 3=
Rosie needs 12 apples. She has picked 7 apples. How many more apples does she need?
Rosie had 12 apples in a bag. She took out 7 apples. How many apples are in the bag now?
Rosie has 12 red apples and 7 green apples. How many fewer green apples does she have?
What are the features of the stories that make them all subtraction?
For each subtraction situation, the total and number in one part of the total are known. The unknown value is the other part of the total.
For addition, 2 or more parts are known. The unknown value is the total.
Stories provide the opportunity to relate the operations.Make sure that both are introduced when the addition concept is developed.
Relate subtraction to addition
How can you work out the number of covered dots?
6
13 altogether
Build links to addition during the work with missing addend subtraction.
5 +
8=
8 5 =
Teaching the number fact
strategies
The approach to number factsNumber facts are best
learned in clusters. Each cluster is organised
around one strategy – a strategy that can be used to learn facts and then with numbers beyond the facts.
The stages for each cluster
• introduce the strategy
• reinforce the strategy
• practice the facts
• extend to examples beyond the fact range.
Cluster 1: Count on
Count on 1
Count on 2 and for some students,
Count on 3
6
Cluster 2: Use Doubles
Double
Double-add-1
Double-add-2
Cluster 3: Make Ten
Number facts in this cluster have one addend close to 10.
9 + 4 = ____
is the same as
10 + 3 = ____
Teaching the subtraction number
facts
Use the sequence for addition facts to plan the sequence for subtraction facts
Count on factsUse doubles factsMake to 10 or bridge to 10 facts
For each subtraction cluster, encourage students to use the strategy ‘think addition.’
The connection between addition and subtraction is essential.
Begin the links to subtraction when the addition concept is taught.
The stages for each cluster
• introduce the strategy• reinforce the strategy• practice the facts• extend to examples beyond the fact range.
8
Introduce the strategy There were 8 cubes in the cup.I have taken out 2 cubes. How many cubes are still in the cup? What are all of the ways you know?
How can you work out the number of covered dots?
6
8 altogether
Count on/Count back subtraction facts
The addition facts6 + 2 = ___ 2 + 6 = ___
are in the count-on cluster.
The related subtraction facts are8 – 2 = ___ 8 – 6 = ___.
Initially, students might work out 8 – 2 =__ using a count back strategy.
Ask questions such as: How would you work out the answer?
11 - 9 = ___
How could you work out the number that is covered?
2 + = 10
Reinforce the strategy
Use addition to plan the sequenceCount on facts
6 + 2 = __ 8 – 2 = __8 – 6 = __
Doubles facts6 + 7 = __ 13 – 6 = __
13 – 7 = __
Use doubles subtraction facts How can you work out the number of
covered dots?
6
13 altogether
Use addition to plan the sequenceCount on facts
9 + 2 = __ 11 – 2 = __11 – 9 = __
Doubles facts6 + 8 = __ 14 – 6 = __
14 – 8 = __Make to ten facts
6 + 9 = __ 15 – 9 = __15 – 6 = __
Make to 10 subtraction facts How can you work out the number of
covered dots?
6
15 altogether
Consideration of interests does not mean indulging children or abdicating responsibility. It means that children are more likely to find curriculum meaningful and engaging when it relates to and respects their interests.
NAEYC- Developmentally
Appropriate Practice 1997
Learning never ends and as teachers we should approach each day –
the same way as a child does
everything is a new discovery.
Discover something new each day about each child in your learning environment.