Embed Size (px)
Citation preview
Filling in Knowledge Gaps: Critical
Lessons Across Grade Levels Cassy Turner
singaporemathsource.com
Twitter Bio: Passionate about Singapore Math,
Teacher Trainer/Coach, Treasure Hunter, Learner,
Answer to the ultimate question? 42.
Slides at:
bitly.com/sdehandouts
Grade 1
Number Bonds & part-whole
relationships
part
part
whole
2
?
10
22
78
?
3B Mental
Math
4A Four Operations of Whole Numbers
4B Decimals
12.20 ÷ 4 = ?
12 20 hundredths
3.05
4 12.20
12
0.20
0.20
0
Number
Bond
Method
Long
Division
Method
1
49 + 32 = ?
31
50 + 31 = ?
11
49 min. + 32 min. = ?
21
1 hr. 21 min.
4
12 oz. + 9 oz. = ?
5
1 lb 5 oz
3 2
3
3
3+
3
3+
3
3+
2
3
3 2
3
9
3
2
3
19 + 3 =
Grade 1 - Addition and Subtraction:
Numbers to 100
onestens
onestens
3+
19
9
1019
+ 3
2
1
2
18 - 4 = ?
onestens
18 - 4 = 10 + 4
= 14
22 - 3 = ?
onestens
onestens
3-22
12
10 22
- 3
9
1
1
12
48 + 20 = ?
onestens
68 + 5 = ?
onestens
48 - 20 = ?
onestens
65 - 8 = ?
onestens
Development of Place Value
Grade 1 Numbers to 100
Ones and tens
Grade 2 Numbers to 1000
Grade 3 Numbers to 10,000
Grade 4 Numbers to 100,000 (Primary Mathematics - U.S. and Math in Focus)
Numbers to the millions (Primary Mathematics - Standards)
Grade 5 Numbers to the millions (Primary Mathematics - U.S.)
Numbers to 10,000,000 (Math in Focus)
Numbers to the billions (Primary Mathematics - Standards)
Pi-project.com
Make the number 477.
Add a ten.
What number do we have?
Add a ten.
What number do we have?
Add a ten.
What number do we have?
Make the number 1435.
Subtract one hundred.
What number do we have?
Subtract one hundred.
What number do we have?
Subtract one hundred.
What number do we have?
Subtract one hundred.
What number do we have?
Subtract one hundred.
What number do we have?
My number has 2 hundreds and 4 tens and 15
ones.
My number has 6 ten thousands, 15 thousands
and 12 tens.
Development of Addition and Subtraction
Grade 1
Mentally and with strategies with 100
Grade 2
Vertical algorithm within 1000 (Main lessons)
Grade 3
Vertical algorithm within 10,000
Bar modeling
Grades 4 - 6
Review and apply algorithm to larger numbers
Regrouping/Renaming
onestens24 + 37
110 10
1
11
1 1 1
1 1 1
1
101010
Regrouping/Renaming
onestens24 + 37
110 10
101010
10
24
+ 371
1
6
Regrouping/Renaming
onestens31 - 16
110 10 10
1
1
1
1
1
1
1
1
1
1
Regrouping/Renaming
onestens31 - 16
110 10
31
- 161
1
1
1
1
1
1
1
1
1
4000
- 278
4000 - 278
onestens
1
1
1
1
1
1
1
1
1
1
10
hundreds
100
1000 100
10
10
10
10100
thousands
10001000
1000
100
100
100
100
100
100
100
10
10
10
10
10
4000
- 278
4000 - 278
onestens
1
1
1
1
1
1
1
1
1
1
10
hundreds
100
1000 100
10
10
10100
thousands
1000
1000
100
100
100
100
100
100
10
10
10
10
10
4000
- 278
3 9 9 10
Development of Multiplication & DivisionGrade 1
Use repeated addition for multiplication with 40
Use sharing and grouping to divide
Grade 2
Understand multiplication and division as related
operations
Learn multiplication and division facts for 2, 3, 4, 5
and 10
Grade 3 Multiply a 2- or 3-digit number by a 1-digit number
Division algorithm, including remainders
Learn multiplication and division facts for 6 7, 8 and 9.
Development of Fractions
Grade 1
Halves and fourths
Grade 2
Name and illustrate fractions as parts of a whole to twelfths.
Order unit fractions
Grade 3
Compare fractions by numerators and denominators
Find equivalent fractions and simplest form of a fraction
Grade 4
Add and subtract like and related fractions
Convert between mixed numbers and improper fractions
Multiply a fraction by a whole number
2nd Grade
Development of Bar Modeling
Grade 2
Examples in materials to explain fractions
Grade 3
Introduces part-whole and comparison models for four
operations
Explain equivalent fractions
Grade 4
Two step word problems for four operations
Two step word problems involving fractions and decimals
Grade 5
Multi-step word problems for four operations
Multi-step word problems with average rate and percentage
Use manipulatives
Jamie has 6 apples.
Kara has 8 apples.
They have ? apples altogether.
Focus on proportionality
Jamie has 6 apples.
Kara has 8 apples.
They have ? apples altogether
6 8
?
They have 14 apples altogether.
?
86
Comparison models
Sam scored 9 points in the basketball game.
Keisha scored 6 points. How many more
points did Sam score than Keisha?
Sam
Keisha
Move toward abstract models
Sam scored 9 points in the basketball game.
Keisha scored 6 points. How many more points
did Sam score than Keisha?
Sam
Keisha
?6
99
?6
A refrigerator costs $1739. An oven is $850 cheaper
than the refrigerator. Mrs. Coles buys both the
refrigerator and the oven. How much does she pay?
Step 1:
How much for the oven?
Step 2:
How much altogether?
fridge
oven?
$1739
$850?
$1739 – $850 = $889
The oven cost $889
$1739 + $889 = $2628
Mrs. Coles paid $2628 for the
oven and refrigerator.
Development of Multiplication & DivisionGrade 2 Understand multiplication and division as related
operations
Learn multiplication and division facts for 2, 3, 4, 5 and
10
Grade 3
Multiply a 2- or 3-digit number by a 1-digit
number
Division algorithm, including remainders
Learn multiplication and division facts for 6 7, 8
and 9.
36 x 3
30 6
(30 x 3) + (6 x 3)
36
X 31890
108
30 x 3 = 90
6 x 3 = 18
36
X 3
108
1
onestenshundreds
10 10
10
10
10 10
10
10
10
1
11
11
1
1
11
11
1
1
11
11
1
onestenshundreds
10 10
10
10
10 10
10
10
10
1
11
11
1
1
11
11
1
1
11
11
1
10
onestenshundreds
10 10
10
10
10 10
10
10
10
1
1
1
11
11
1
10
100
53 ÷ 2= ?
tens
2
2 53
-4
1
10 10 101010
111
onestens111
111
11
11
53 ÷ 2= ?
tens ones
2
2 53
-4
1 3
10
10
10
10
1
onestens
11
11
11
1
1
11
11
6
-1 21
R 1
Divide (Does)
Multiply (McDonalds)
Subtract (Serve)
Bring down (Burgers)
Division Algorithmtens ones
2
2 53
-4
13
6 R 1
-121
Development of Fractions
Grade 2
Name and illustrate fractions as parts of a whole to twelfths.
Order unit fractions
Grade 3
Compare fractions by numerators and denominators
Find equivalent fractions and simplest form of a
fraction
Grade 4
Add and subtract like and related fractions
Convert between mixed numbers and improper fractions
Multiply a fraction by a whole number
Grade 3 –
Comparing
Fractions
Equivalent Fractions
Development of Area & Perimeter
Grade 3
• Square units
Grade 4
• Area, perimeter, unknown sides of rectangles
• Composite shapes
• Units of volume
Multiplication
Grade 4
Multiply with 10,000 by a 2-digit number
Find factors and multiples with 100
Use divisibility rules for 2, 3, 5, 6, 9 and 10
Use Order of Operations to solve expressions
with and without parentheses (Standards)
Grade 5 Divide numbers to 10,000 by a 2-digit divisor
Use Order of Operations to solve expressions
with and without parentheses (U.S.)
Development of Fractions Grades 4 - 6
Grade 4
Add and subtract like and related fractions
Convert between mixed numbers and improper
fractions
Multiply a fraction by a whole number
Grade 5
Multiply a fraction by a fraction
Divide a fraction by a whole number
Divide a whole number by a fraction (Standards)
Grade 6
Divide a whole number by a fraction (U.S.
3 2
3
3
3+
3
3+
3
3+
2
3
3 2
3
9
3
2
3
Grade 4
Mixed numbers/improper fractions
3
3+3
3+3
3+2
3=
8
3
3
3
3
3
2
3
Grade 4
Multiply a
fraction
by a
whole
number
Fraction of
a set
Development of Area & Perimeter
Grade 3
• Square units
Grade 4
• Area, perimeter, unknown sides of rectangles
• Composite shapes
• Units of volume
Development of Decimals
Grade 3
Add and subtract money within $100
Multiply & divide money
Grade 4
Understand, locate on a number line and compare
tenths, hundredths, thousandths
Apply four operations up to 2 decimal places
Convert fractions to decimals
Grade 5
Apply four operations up to 3 decimal places
Development of Fractions Grades 4 - 6
Grade 4
Add and subtract like and related fractions
Convert between mixed numbers and improper
fractions
Multiply a fraction by a whole number
Grade 5
Multiply a fraction by a fraction
Divide a fraction by a whole number
Divide a whole number by a fraction (Standards)
Grade 6
Divide a whole number by a fraction (U.S.
Grade 5
Area of a triangle
Grade 5
Equivalent ratios/Ratio of 3 quantities
Grade 5
Percentage - Decimal and fraction
equivalents
Grade 5
Percentage of a quantity
Grade 5
Angles
Grade 5
Average/ Rate
Slides: bitly.com/sdehandouts
Password: math rocks
Thanks for coming!
