Download Reflection: How can we tell if a number is divisible by 2?

2
Even numbers are divisible by 2
0
2
4
6
8
Odd numbers are not divisible by 2
Multiplication and Division 22
Investigation:
1. Have a pack of playing cards.
2. Select cards and make a number to test for divisibility
by 2 by identifying if it is even.
3. How you know whether the number is divisible by 2?
4. Why does this divisibility test work?
Reflection: How can we tell if a number is divisible by 2?
Problem Solving
Mary had 85 cakes.
2 cakes fit in each box.
Will Mary have any cakes left over?
Multiplication and Division 22
4
4, 8, 12, 16, 20, 24, 28, 32, 36
No odd number is divisible by 4.
Every second even number is divisible by 4.
Even tens digits, ones digits.
Odd tens digits, ones digits.
0
2
4
6
8
Multiplication and Division 22
Investigation:
1. Select cards and make a number to test for divisibility by 4
by identifying if it is even, whether it has an odd tens digit
and ones digits 2 and 6 or an even tens digit and ones digits
4, 8 and zero.
2. How you know whether the number is divisible by 4?
3. Why does this divisibility test work?
Reflection: How can we tell if a number is divisible by 4?
Problem Solving
Mary had 78 cakes.
4 cakes fit in each box.
Will Mary have any cakes left over?
Multiplication and Division 22
8
8, 16, 24, 32, 40, 48, 56, 54, 72, 80, 88, 96, 104
No odd number is divisible by 8.
100 is not divisible by 8
1000 is divisible by 8
Even hundreds digits, two-digit multiples of 8
Odd hundreds digits, two digit multiples of 8,
plus or minus 4.
Multiplication and Division 22
Investigation:
1. Select cards and make a number to test for divisibility by 8 by
identifying if it is even, whether it has an even hundreds digit and
tens and ones digits that are multiples of 8, or an odd hundreds
digit and tens and ones digits that are multiples of 8, plus 4 .
2. How you know whether the number is divisible by 8?
3. Why does this divisibility test work?
Reflection: How can we tell if a number is divisible by 8?
Problem Solving
Mary had 64 cakes.
8 cakes fit in each box.
Will Mary have any cakes left over?
Multiplication and Division 22
3
thousands hundreds tens
ones
10 is not divisible by 3, but 9 is.
100 is not divisible by 3 but 99 is.
1000 is not divisible by 3 but 999 is.
The number one less than each place value is divisible by 3.
If the sum of the digits is divisible by 3, the number is
divisible by 3
258 = 200 + 50 + 8
200 = 99 + 99 + 2
50 = 9 + 9 + 9 + 9 + 9 + 5
2+ 5+ 8=15
8=8
258
Multiplication and Division 22
Investigation:
1. Have a pack of playing cards.
2. Select cards and make a number to test for divisibility by 3 by
identifying whether the digits add to make a multiple of 3.
3. How you know whether the number is divisible by 3?
4. Why does this divisibility test work?
Reflection: How can we tell if a number is divisible by 3?
Problem Solving
Mary had 85 cakes.
3 cakes fit in each box.
Will Mary have any cakes left over?
Multiplication and Division 22
9
thousands hundreds tens ones
10 is not divisible by 9, but 9 is.
100 is not divisible by 9 but 99 is.
1000 is not divisible by 9 but 999 is.
The number one less than each place value is divisible by 3.
If the sum of the digits is divisible by 9, the number is
divisible by 9
468 = 400 + 60 + 8
400 = 99 + 99 + 99 + 99 + 4
60 = 9 + 9 + 9 + 9 + 9 + 9 = 6
4+ 6+ 8=18
8=8
468
Multiplication and Division 22
Investigation:
1. Have a pack of playing cards.
2. Select cards and make a number to test for divisibility by 9 by
identifying whether the digits add to make a multiple of 9.
3. How you know whether the number is divisible by 9?
4. Why does this divisibility test work?
Reflection: How can we tell if a number is divisible by 9?
Problem Solving
Mary had 126 cakes.
9 cakes fit in each box.
Will Mary have any cakes left over?
Multiplication and Division 22
6
2 and 3 are factors of 6.
If a number is divisible by both 2 and by 3,
then it is divisible by 6.
84 is even so is divisible by 2.
8 + 4 = 12 so is divisible by 3.
So 84 is divisible by 6.
364 is even so is divisible by 2.
3 + 6 + 4 = 13 so is not divisible by 3.
So 364 is not divisible by 6.
Multiplication and Division 22
Investigation:
1. Have a pack of playing cards.
2. Select cards and make a number to test for divisibility
by 6 by testing for divisibility by 2 and 3.
3. How you know whether the number is divisible by 6?
4. Why does this divisibility test work?
Reflection: How can we tell if a number is divisible by 6?
Problem Solving
Mary had 84 cakes.
6 cakes fit in each box.
Will Mary have any cakes left over?
Multiplication and Division 22
 10
Numbers with zero ones are divisible by 10,
because we are seeing 10 as '1 ten'.
Multiplication and Division 22
Investigation:
1. Have a pack of playing cards.
2. Select cards and make a number to test for divisibility
by 10 by identifying if it has zero in the ones place.
3. How you know whether the number is divisible by 10?
4. Why does this divisibility test work?
Reflection: How can we tell if a number is divisible by 10?
Problem Solving
Mary had 120 cakes.
10 cakes fit in each box.
Will Mary have any cakes left over?
Multiplication and Division 22
5
Numbers with zero or 5 ones digits are divisible by 5.
Multiplication and Division 22
Investigation:
1. Have a pack of playing cards.
2. Select cards and make a number to test for divisibility by 5
by identifying if it has zero or a 5 in the ones place.
3. How you know whether the number is divisible by 5?
4. Why does this divisibility test work?
Reflection: How can we tell if a number is divisible by 5?
Problem Solving
Mary had 85 cakes.
5 cakes fit in each box.
Will Mary have any cakes left over?
Multiplication and Division 22
Multiplication and Division 22
Investigation:
1. Have a pack of playing cards.
2. Select cards and make a number to test for divisibility by 2, 3, 4,
5, 6, 8, 9 and 10, recording in a table.
3. Look for relationships between numbers that are divisible by
different numbers
Reflection: How can we test for divisibility?
Multiplication and Division 22