Download Reflection: How can we multiply and divide by 2?

Multiplying by 2 - additively
Multiplying by 2 – multiplicatively
Multiplication and Division 10
Patterns and Algebra 15 18
Skip counting is
repeatedly adding 2
$2
$4
$6
$8
$10
$12
$14
$2
$4
$8
$16
$32
$64
$108
Repeatedly
multiplying by 2
Multiplication and Division 10
Patterns and Algebra 15 18
2x7=
5 + 2
2 x 5 = 10
2x2=4
10 + 4 = 14
x 2 = double
Distributive propertydistribute multiplication over
addition
2 x 7 = 14
Multiplication and Division 10
Patterns and Algebra 15 18
2 x 40 = 2 x 4 x 10 = 8 x 10 = 80
2 x 300 = 2 x 3 x 100 = 6 x 100 = 600
2 x 40 = 2 x 4 x 10 = 8 x 10 = 80
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Select cards to make a number to multiply by 2, for example,
or
2. Multiply the number by 2 using the distributive property, for example,
Problem Solving
The teacher made 2 teams of 8 children.
How many children altogether?
Problem Solving
The school had 2 classes of 28 children.
How many children altogether?
3. Record the product, for example, 2 x 7 = 14
2 x 47 = 94.
4. If you multiplied a single-digit number by 2, learn the multiple of 2
(table).
5. Explain to a friend how you used the distributive property to multiply
the number by 2.
Reflection: How can we use the distributive
property to multiply by 2?
Multiplication and Division 10
Patterns and Algebra 15 18
Dividing by 2 - additively
Dividing by 2 – multiplicatively
Multiplication and Division 10
Patterns and Algebra 15 18
16 ÷ 2 =
10 + 6
10 ÷ 2 = 5
6÷2=3
5+3=8
Partition and divide by 2
16 ÷ 2 = 8
1 of 16 =
2
10 + 6
÷ 2 = halve
÷2=
1 of 10 = 5
2
1
2 of 6 = 3
5+3=8
Partition and halve
1 of 16 = 8
2
Multiplication and Division 10
Patterns and Algebra 15 18
15 ÷ 2 =
10 + 5
4+1
10 ÷ 2 = 5
4÷2=2
5+2=7
Partition and divide by 2
15 ÷ 2 = 7r1
1 of 15 =
2
10 + 5
÷ 2 = halve
÷2=
4+1
1
of 10 = 5
2
1
2 of 4 = 2
5+2=7
15 ÷ 2 =
14 + 1
14 ÷ 2 = 7
15 + 2 = 7r1
Partition and halve
1 of 15 = 7r1
2
Multiplication and Division 10
Patterns and Algebra 15 18
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
Select cards to make a number to divide by 2 / halve, for example,
or
or
or
Divide your number by 2 by partitioning it into multiples of 2 that you do
know, for example,
Record the quotient.
Explain to a friend how you divided by 2 / halved.
Reflection: How can we divide by 2 / halve?
Problem Solving
The school divided 56 children into 2 classes.
How many children in each class?
Problem Solving
16 children are divided into 2 teams.
How many in each team?
Multiplication and Division 10
Patterns and Algebra 15 18
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Use a calculator to multiply numbers by 2.
2. Check using the distributive property.
3. Explain your strategy to a friend.
Reflection: How can we use the distributive
property to multiply by 2?
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Use a calculator to divide numbers by 2 / halve.
2. Check by partitioning into multiples of 2 that you know.
3. Explain your strategy to a friend.
Reflection: How can we divide by 2 / halve?
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Sit with a friend.
2. Each of you has 2 cards.
3. Places your cards face down and record each number’s product when
multiplied by 2, on paper next to the card, for example,
16
12
4. Take turns to tell your friend what number you think is on each card,
explaining using multiplication, by saying ‘I think the number on the card
is 8 because 2 times 8 equals 16’.
5. If correct, you take the card.
Reflection: How can we use the distributive property to multiply by 2?
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Sit with a friend.
2. Each of you has 2 cards.
3. Places your cards face down and record each number’s product when
multiplied by 2 on paper next to the card, for example,
16
12
4. Take turns to tell your friend what number you think is on each card,
explaining using division, by saying ‘I think the number on the card is 8
because 16 divided by 2 equals 8’.
5. If correct, you take the card.
Reflection: How can we divide by 2 / halve?
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Sit with a friend.
2. Lay out 5 cards in a row.
3. Take turns to secretly select cards and to name a number that, when
divided by 2, gives that number as the quotient.
4. If you friend works out the quotient, they keep the card.
5. For example, you may secretly select 6 and say, ‘When I divide 12 by 2,
the quotient is this number’.
6. For example, you may secretly select 4 and 6 to make 46, and say,
‘When I divide 92 by 2, the quotient is this number’.
Reflection: How can we multiply and divide by 2?
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1.
2.
3.
4.
5.
Sit with a friend.
Lay out 5 cards in a row.
Take turns to secretly select cards.
Describe the number after it has been multiplied by 2.
For example, you may secretly select 8 and say, ‘When my number is
multiplied by 2, the product is 16’.
6. For example, you may secretly select 4 and 6 to make 46 and say,
‘When my number is multiplied by 2, the product is 92’.
Reflection: How can we multiply and divide by 2?
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Select a card to make single-digit numbers to multiply by 2.
2. Record the multiplication number sentence.
3. Use the commutative property to record another
multiplication sentence.
4. Use the inverse relationship between multiplication and
division to record 2 division number sentences.
5. For example, flip 6 and record 6 x 2 = 12 and 2 x 6 = 12. Then
record 12 ÷ 2 = 6 and 12 ÷ 6 = 2.
Reflection: How can we multiply and divide by 2?
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Have a multiplication by single-digit numbers array and use it to recall
multiples of 2 (tables!) through properties and relationships.
2. For example, 2 x 7 could be represented using 2 sheets of card as, for
example,
Reflection: How can we multiply and divide by 2?
Multiplication and Division 10
Patterns and Algebra 15 18
Investigation:
1. Flip cards one at a time and name the product when the number is multiplied by 2.
2. If you know the product when multiplied by 2 efficiently (quite quickly, without skip
count), place the card in the ‘know’ pile.
3. If you do not know the product when multiplied by 2 efficiently, place the card in the
‘learn’ pile.
4. Once you have 2 cards with different numbers in the ‘learn’ pile, stop flipping cards.
5. Look at the numbers that you cannot yet multiply by 2, and use multiplicative place
value to assist you to efficiently multiply the number by 2.
6. If you cannot think of any strategies yourself, ask your classmates in either a
structured sharing session, or while investigating multiplying and dividing by 2.
7. Record the multiplication facts, and related division facts, for example,
6 x 2 = 12 2 x 6 = 12 12 ÷ 2 = 6 12 ÷ 6 = 2
Reflection: How can we multiply and divide by 2?
Multiplication and Division 10
Patterns and Algebra 15 18