virginia birch mfnerc numeracy specialist overview mental math… what is it? grade 1 to 3...
TRANSCRIPT
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Virginia BirchMFNERC Numeracy Specialist
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Overview
• Mental Math… what is it?• Grade 1 to 3 Strategies• Indicators from the Provincial
Report Card
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Mental Math…what is it• Conceptual strategies that enhance
flexible thinking and number sense and number skills (critical numeracy)
• calculating mentally without the use of external memory aids.
• provides a cornerstone for all estimation processes offering a variety of alternate algorithms and non-standard techniques for finding answers
K - Gr 8 Manitoba Curriculum Framework of Outcomes 2013K - Gr 8 Manitoba Curriculum Framework of Outcomes 2013
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• developing mental math skills and recalling math facts automatically
• Facts become automatic for students through repeated exposure and practice.
• When facts are automatic, students are no longer using strategies to retrieve them from memory.
Mental Math…what is it
K - Gr 8 Manitoba Curriculum Framework of Outcomes 2013
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• One of the Math Competencies for the Grade 3 and Grade 7 Math Assessment
• (see report templates)
Mental Math…what is it
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Mental Math:• Should not be timed. Students differ on
the amount of time they need to process concepts.
• Can be done daily approximately five minutes for a daily math routine.
• Can be practiced with math games or learning centers where students can practice the strategies.
• Create a Mental Math Bulletin Board • Create an Estimation Bulletin
Board
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The development of mental math strategies is greatly enhanced by sharing and discussion. Students should be given the freedom to adapt, combine, and invent their own strategies.
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Math Tools you can use…
• Ten Frames• Base 10 Blocks• 100 – Chart• Number Line
• Array Cards• Dominoes• Finger Patterns• Linking cubes
Going from concrete to pictorial to abstract…
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Counting On – Grade 1Concept: Addition
Meaning:Students begin with a number and count on to get the sum. Students should begin to recognize that beginning with the larger of the two addends is generally most efficient.
Example:for 3 + 5think 5 + 1 + 1 + 1 is 8;think 5, 6, 7, 8
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Practising the strategy…
2+7=9+3=3+12=
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Counting Back – Grade 1
Concept: Subtraction
Meaning: Students begin with the minuend and count back to find the difference.
Example: for 6 – 2think 6 – 1 – 1 is 4; think 6, 5, 4
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Practising the Strategy
9-2=10-3=7-1=
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Using One More – Gr 1, 2Concept: Addition
Meaning: Starting from a known fact and adding one more.
Example: for 8 + 5 if you know 8 + 4 is 12 and one more is 13
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Practising the Strategy
5+6=6+7=8+9=
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Using One Less - Gr 1, 2
Concept: Addition
Meaning: Starting from a known fact and taking one away.
Example: for 8 + 6 if you know 8 + 7 is 15 and one less is 14
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Practising the strategy
7+6=9+8=6+5=
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Making 10 – Gr 1, 2
Concept: Addition, Subtraction
Meaning: Students use combinations that add up to ten and can extend this to multiples of ten in later grades.
Example: 4 + ____ is 107 + ____ is 10; so 23 + ____ is 30
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Practising the strategy
28 +___ = 3015 +___=2016 + ___= 40
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Starting from Known Doubles – Gr 1
Concept: Addition, Subtraction
Meaning: Students need to work to know their doubles facts.
Example: 2 + 2 is 4 and 4 – 2 is 2
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Practising the strategy
3+3=__ , so ___-3=___
9+9=__ , so ___-9=___
8+8=__ , so ___-8=___
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Using Addition to Subtract – Gr 1, 2, 3
Concept: SubtractionMeaning: This is a form of part-part-whole representation. Thinking of addition as: part + part = wholeThinking of subtraction as: whole – part = part
Example: for 12 – 5think 5 + ____ = 12so 12 – 5 is 7
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Practising the Strategy
13-7= ? , think 7 +___= 1311-6= ? , think 6 +___=1115-7= ? , think 7+___= 15
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The Zero Property of Addition – Gr 2
Concept: Addition, Subtraction
Meaning: Knowing that adding 0 to an addend does not change its value, and taking 0 from a minuend does not change the value.Example:
0 + 5 = 5;11 – 0 = 11
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Using Doubles – Gr 2, 3Concept: Addition, SubtractionMeaning: Students learn doubles, and use this to extend facts: using doubles doubles plus one (or two) doubles minus one (or two) Example:
for 5 + 7think 6 + 6 is 12;for 5 + 7think 5 + 5 + 2 is 12for 5 + 7 think 7 + 7 – 2 is 12
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Practising the strategy
for 6+ 8,think doubles
for 6 + 8, think double 6 plus two
for 6 + 8, think double 8 minus two
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Building on Known Doubles – Gr 2, 3
Concept: Addition, Subtraction
Meaning: Students learn doubles, and use this to extend facts.
Example: for 7 + 8 think 7 + 7 is 14 so 7 + 8 is 14 + 1 is 15
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Practising the Strategy
3+4=7+6=8+9=
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Adding from Left to Right – Gr 3
Concept: Addition
Meaning: Using place value understanding to add 2-digit numerals.
Example: for 25 + 33think 20 + 30 and 5 + 3 is 50 + 8 or 58
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Practising the Strategy
17+22=26+21=45+34=
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Making 10 – Gr 3
Concept: Addition, Subtraction
Meaning: Students use combinations that add up to ten to calculate other math facts and can extend this to multiples of ten in later grades.
Example: for 8 + 5think 8 + 2 + 3 is10 + 3 or 13
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Practising the strategy
8+7=7+9=5+7=
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Compensation – Gr 3Concept: Addition, Subtraction
Meaning: Using other known math facts and compensating. For example, adding 2 to an addend and taking 2 away from the sum.
Example: for 25 + 33think 25 + 35 – 2 is 60 – 2 or 58
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Practising the strategy
47+22= 18+15=39+17=
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Commutative Property – Gr 3
Concept: Addition
Meaning: Switching the order of the two numbers being added will not affect the sum.
Example: 4 + 3 is the same as3 + 4
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Compatible Numbers – Gr 3, 4
Concept: Addition, Subtraction
Meaning: Compatible numbers are friendly numbers (often associated with compatible numbers to 5 or 10).
Example: for 4 + 3 students may think 4 + 1 is 5 and 2 more makes 7
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Practising the Strategy
4+7=9+8=7+8=
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Array – Gr 3Concept: Multiplication, DivisionMeaning: Using an ordered arrangement to show multiplication or division (similar to area).Example: for 3 x 4 think
for 12 ÷3 think
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Practising the strategy
5x5=3x4=4x2=
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Commutative Property – Gr 3
Concept: Multiplication
Meaning: Switching the order or the two numbers being multiplied will not affect the product.
Example: 4 x 5 is the same as5 x 4
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Skip Counting – Gr 3Concept: Multiplication
Meaning: Using the concept of multiplication as a series of equal grouping to determine a product.
Example: for 4 x 2 think 2, 4, 6, 8 so 4 x 2 is 8
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Practising the Strategy
2x5=3x4=5x4=
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Zero Property of Multiplication– Gr 4
Concept: Multiplication
Meaning: Multiplying a factor by zero will always result in zero.
Example: 30 x 0 is 00 x 15 is 0
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Multiplicative Identity– Gr 4
Concept: Multiplication
Meaning: Multiplying a factor by one will not change its value.Dividing a dividend by one will not change its value.
Example: 1 x 12 is 1221 ÷ 1 is 21
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Skip-Counting from a Known Fact– Gr 4, 5
Concept: Multiplication, Division
Meaning: Similar to the counting on strategy for addition. Using a known fact and skip counting forward or backward to determine the answer.Example: for 3 x 8
think 3 x 5 is 15 and skip count by threes 15, 18, 21, 24
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4 x 7 =6 x 8=8 x 7=9 x 8=
Practising the Strategy
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Doubling or Halving– Gr 4, 5
Concept: Multiplication, Division
Meaning: Using known facts and doubling or halving them to determine the answer.
Example: for 7 x 4, think the double of 7 x 2 is 28for 48 ÷ 6,
think the double of 24 ÷ 6 is 8
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8 x 4 =think double 8 x 2 = ___
32 ÷ 4 =think double 16 ÷ 4 = ____
Practising the Strategy
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Using the Pattern for 9s- Gr 4
Concept: Multiplication, Division
Meaning: Knowing the first digit of the answer is one less than the non-nine factor and the sum of the product’s digits is nine.
Example: for 7 x 9 think one less than 7 is 6 and 6 plus 3 is nine, so 7 x 9 is 63
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4 x 9 = 365 x 9 = 456 x 9 = 547 x 9 = 638 x 9 = 72
Practising the Strategy
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Repeated Doubling– Gr 4, 5
Concept: Multiplication
Meaning: Continually doubling to get to an answer.
Example: for 3 x 8, think 3 x 2 is 6, 6 x 2 is 12, 12 x 2 is 24
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To find 8 X 8, first find 2 X 8, then double, then double again.
2 X 8 = 16
4 X 8 is double 2 X 816 + 16 = 32 so,4 X 8 = 32
8 X 8 is double 4 X 832 + 32 = 64 so,8 X 8 = 64
Practising the Strategy
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Using multiplication to divide - Gr 4
Concept: DivisionMeaning: This is a form of part-part-whole representation. Thinking of addition as: part x part = wholeThinking of subtraction as: whole ÷ part = partExample: for 35 ÷ 7
think 7 x ____ = 35• so 35 ÷ 7 is 5
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36 ÷ 6 =Think 6 x ___ = 36 42 ÷ 7 = Think 7 x ___ = 42
Practising the Strategy
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Distributive property – Gr 4, 5
Concept: MultiplicationMeaning: In arithmetic or algebra, when you distribute a factor across the brackets: a x (b + c) = a x b + a x c (a + b) x (c + d) = ac + ad + bc + bd
Example: for 2 x 154think 2 x 100 plus 2 x 50 plus 2 x 4
is 200 + 100 + 8 or 308
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Place a straw between two columns.
What does it now show?
a x (b + c) = a x b + a x c
Record it as 3 x 7 = 3 x 2 + 3 x 5
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13 x 12 = (10 + 3) x (10 + 2)= (10 x 10) + (10 x 2) + (3 x 10) + (3 x 2)
(a + b) x (c + d) = ac + ad + bc + bd
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How do you assess for mental math strategies?
• Use checklists• Observe strategies students are
using through games• Make anecdotal notes while
conversing with a student • Collect student sample work
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Indicators from the Provincial Report Card (Gr 1 to 8)
• Determines an answer using multiple mental math strategies
• Applies mental math strategies that are efficient, accurate, and flexible
• Makes a reasonable estimate of value or quantity using benchmarks and referents.
• Uses estimation to make mathematical judgments in daily life.
Provincial Report Card Document Pg. 43