Students are expected to build on their knowledge from the previous year, at a higher level of complexity. The depth of concepts, mathematical procedures and processes will be expanded each year. Elementary school is an important time in your child's academic development. Find out how an individualized approach to learning can build the skills, habits and attitudes your child needs for a solid academic foundation and a lifetime of success. Prerequisite: Math 5

1 × 0 |

0 |

1 × 1 |

1 |

1 × 2 |

2 |

2 × 2 |

4 |

2 × 3 |

6 |

2 × 4 |

8 |

2 × 5 |

10 |

2 × 6 |

12 |

2 × 7 |

14 |

2 × 8 |

16 |

2 × 9 |

18 |

2 × 10 |

20 |

2 × 11 |

22 |

2 × 12 |

24 |

3 × 1 |

3 |

3 × 2 |

6 |

3 × 3 |

9 |

3 × 4 |

12 |

3 × 5 |

15 |

3 × 6 |

18 |

3 × 7 |

21 |

3 × 8 |

24 |

3 × 9 |

27 |

3 × 10 |

30 |

3 × 11 |

33 |

3 × 12 |

36 |

4 × 1 |

4 |

4 × 2 |

8 |

4 × 3 |

12 |

4 × 4 |

16 |

4 × 5 |

20 |

4 × 6 |

24 |

4 × 7 |

28 |

4 × 8 |

32 |

4 × 9 |

36 |

4 × 10 |

40 |

4 × 11 |

44 |

4 × 12 |

48 |

5 × 1 |

5 |

5 × 2 |

10 |

5 × 3 |

15 |

5 × 4 |

20 |

5 × 5 |

25 |

5 × 6 |

30 |

5 × 7 |

35 |

5 × 8 |

40 |

5 × 9 |

45 |

5 × 10 |

50 |

5 × 11 |

55 |

5 × 12 |

60 |

6 × 1 |

6 |

6 × 2 |

12 |

6 × 7 |

42 |

6 × 8 |

48 |

6 × 9 |

54 |

6 × 10 |

60 |

6 × 11 |

66 |

6 × 12 |

72 |

7 × 1 |

7 |

7 × 2 |

14 |

7 × 3 |

21 |

7 × 4 |

28 |

7 × 5 |

35 |

7 × 6 |

42 |

7 × 7 |

49 |

7 × 8 |

56 |

7 × 9 |

63 |

7 × 10 |

70 |

7 × 11 |

77 |

7 × 12 |

84 |

8 × 1 |

8 |

8 × 2 |

16 |

8 × 3 |

24 |

8 × 4 |

32 |

8 × 5 |

40 |

8 × 6 |

48 |

8 × 7 |

56 |

8 × 8 |

64 |

8 × 9 |

72 |

8 × 10 |

80 |

8 × 11 |

88 |

8 × 12 |

96 |

9 × 1 |

9 |

9 × 2 |

18 |

9 × 3 |

27 |

9 × 4 |

36 |

9 × 5 |

45 |

9 × 6 |

54 |

9 × 7 |

63 |

9 × 8 |

72 |

9 × 9 |

81 |

9 × 10 |

90 |

9 × 11 |

99 |

9 × 12 |

108 |

10 × 1 |

10 |

10 × 2 |

20 |

10 × 3 |

30 |

10 × 4 |

40 |

10 × 5 |

50 |

10 × 6 |

60 |

10 × 7 |

70 |

10 × 8 |

80 |

10 × 9 |

90 |

10 × 10 |

100 |

10 × 11 |

110 |

10 × 12 |

120 |

11 × 1 |

11 |

11 × 2 |

22 |

11 × 3 |

33 |

11 × 4 |

44 |

11 × 5 |

55 |

11 × 6 |

66 |

11 × 7 |

77 |

11 × 8 |

88 |

11 × 9 |

99 |

11 × 10 |

110 |

11 × 12 |

132 |

12 × 1 |

12 |

12 × 2 |

24 |

12 × 3 |

36 |

12 × 4 |

48 |

12 × 5 |

60 |

12 × 6 |

72 |

12 × 7 |

84 |

12 × 8 |

96 |

12 × 9 |

108 |

12 × 10 |

120 |

12 × 11 |

132 |

12 × 12 |

144 |

4 ÷ 2 |

2 |

6 ÷ 3 |

2 |

6 ÷ 2 |

3 |

9 ÷ 3 |

3 |

8 ÷ 2 |

4 |

8 ÷ 4 |

2 |

12 ÷ 3 |

4 |

12 ÷ 4 |

3 |

16 ÷ 4 |

4 |

10 ÷ 5 |

2 |

10 ÷ 2 |

5 |

15 ÷ 3 |

5 |

15 ÷ 5 |

3 |

20 ÷ 4 |

5 |

20 ÷ 5 |

4 |

25 ÷ 5 |

5 |

12 ÷ 2 |

6 |

12 ÷ 6 |

2 |

18 ÷ 3 |

6 |

18 ÷ 6 |

3 |

24 ÷ 6 |

4 |

24 ÷ 4 |

6 |

30 ÷ 5 |

6 |

30 ÷ 6 |

5 |

36 ÷ 6 |

6 |

14 ÷ 2 |

7 |

14 ÷ 7 |

2 |

21 ÷ 3 |

7 |

21 ÷ 7 |

3 |

28 ÷ 4 |

7 |

28 ÷ 7 |

4 |

35 ÷ 7 |

5 |

35 ÷ 5 |

7 |

42 ÷ 7 |

6 |

42 ÷ 6 |

7 |

49 ÷ 7 |

7 |

16 ÷ 2 |

8 |

16 ÷ 8 |

2 |

24 ÷ 8 |

3 |

24 ÷ 3 |

8 |

32 ÷ 4 |

8 |

32 ÷ 8 |

4 |

40 ÷ 8 |

5 |

40 ÷ 5 |

8 |

48 ÷ 6 |

8 |

48 ÷ 8 |

6 |

56 ÷ 7 |

8 |

56 ÷ 8 |

7 |

64 ÷ 8 |

8 |

18 ÷ 2 |

9 |

18 ÷ 9 |

2 |

27 ÷ 3 |

9 |

27 ÷ 9 |

3 |

36 ÷ 4 |

9 |

36 ÷ 9 |

4 |

45 ÷ 5 |

9 |

45 ÷ 9 |

5 |

54 ÷ 6 |

9 |

54 ÷ 9 |

6 |

63 ÷ 7 |

9 |

63 ÷ 9 |

7 |

72 ÷ 8 |

9 |

72 ÷ 9 |

8 |

81 ÷ 9 |

9 |

20 ÷ 10 |

2 |

20 ÷ 2 |

10 |

30 ÷ 3 |

10 |

30 ÷ 10 |

3 |

40 ÷ 4 |

10 |

40 ÷ 10 |

4 |

50 ÷ 5 |

10 |

50 ÷ 10 |

5 |

60 ÷ 6 |

10 |

60 ÷ 10 |

6 |

70 ÷ 7 |

10 |

70 ÷ 10 |

7 |

80 ÷ 8 |

10 |

80 ÷ 10 |

8 |

90 ÷ 9 |

10 |

90 ÷ 10 |

9 |

100 ÷ 10 |

10 |

22 ÷ 2 |

11 |

22 ÷ 11 |

2 |

33 ÷ 11 |

3 |

33 ÷ 3 |

11 |

44 ÷ 4 |

11 |

44 ÷ 11 |

4 |

55 ÷ 5 |

11 |

55 ÷ 11 |

5 |

66 ÷ 6 |

11 |

66 ÷ 11 |

6 |

77 ÷ 7 |

11 |

77 ÷ 11 |

7 |

88 ÷ 8 |

11 |

88 ÷ 11 |

8 |

99 ÷ 9 |

11 |

99 ÷ 11 |

9 |

110 ÷ 11 |

10 |

110 ÷ 10 |

11 |

121 ÷ 11 |

11 |

24 ÷ 12 |

2 |

24 ÷ 2 |

12 |

36 ÷ 3 |

12 |

36 ÷ 12 |

3 |

48 ÷ 4 |

12 |

48 ÷ 12 |

4 |

60 ÷ 5 |

12 |

60 ÷ 12 |

5 |

72 ÷ 6 |

12 |

72 ÷ 12 |

6 |

84 ÷ 7 |

12 |

84 ÷ 12 |

7 |

96 ÷ 8 |

12 |

96 ÷ 12 |

8 |

108 ÷ 9 |

12 |

108 ÷ 12 |

9 |

120 ÷ 10 |

12 |

120 ÷ 12 |

10 |

132 ÷ 11 |

12 |

132 ÷ 12 |

11 |

144 ÷ 12 |

12 |

INCORRECT

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Align the place columns correctly...

Align the place columns correctly...
= 3649

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Align the place columns correctly...

Align the place columns correctly...
= 20,148

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... = 693

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Subract 60 from 560 and 80...
Borrow from the 100's column, 5-- becomes 4--...

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... = 4,568

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Step-by-step (for each place value)...
= 1,568
= 1,068
= 998
= 995

(Yes you could just do 4,568 - 3,573...)

(Yes you could just do 4,568 - 3,573...)

True. Start comparing the place values (ones, tens, hundreds...) from the LEFT-HAND side... (in the hundreds column) 3 is bigger than 9...

0.999

0.90

0.009

1.005

0.88

1.001

0.0095

Compare the place values: ones, tenths, hundredths, thousandths...

1.005, 1.001, 0.999, 0.90, 0.88, 0.0095, 0.009

Can also be written as

1.005 > 1.001 > 0.999 > 0.90 > 0.88 > 0.0095 > 0.009

(comparing the last two, to see more easily, you can change to: 0.0095 > 0.0090)

1.005, 1.001, 0.999, 0.90, 0.88, 0.0095, 0.009

Can also be written as

1.005 > 1.001 > 0.999 > 0.90 > 0.88 > 0.0095 > 0.009

(comparing the last two, to see more easily, you can change to: 0.0095 > 0.0090)

Two hundred twenty thousand and twelve

Five hundred and two thousand four hundred and one

82,444

Julie had the longest time, so she came in last.

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seconds

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Alice finished first: 42.08 seconds

Julie finished last: 45.42 seconds

= 45.42 - 42.08

= 3.34

Julie finished last: 45.42 seconds

= 45.42 - 42.08

= 3.34

0.5 > 0.409

62.37 = 62.370

21.89 < 21.95

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Example: 0.5 has a five in the "tenths" column and a zero in the "ones" column

234.2__1__

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5 or more rounds up...

10,001

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2.5

You can multiply the top (numerator) and bottom (denominator) by the same amount... 11

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$

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25

$

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20 [steps not shown here]

Make a common denominator in order to compare. Use the lowest common multiple (LCM) of 6 & 4: 12...

Make a common denominator (with the lowest common multiple, LCM)

Multiples of 3: 3, 6, 9, 12,__15__, ...

Multiples of 5: 5, 10,__15__, ...

Therefore

Multiples of 3: 3, 6, 9, 12,

Multiples of 5: 5, 10,

Therefore

Prime numbers can only be divided by one and themselves. Composite numbers can be factored into several prime numbers.

These are *multiples* of 22. Multiples multiply, going up higher each time... There are infinite amount of multiples...

(There are only a certain amount of factors... for 22 it's: 1, 2, 11, 22)

(There are only a certain amount of factors... for 22 it's: 1, 2, 11, 22)

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36 is a factor of 36 because you can divide 36 by 36.

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Make the denominator with the lowest common multiple (LCM)...

4 → 8 → 12 → 16 →

5 → 10 → 15 →

4 → 8 → 12 → 16 →

5 → 10 → 15 →

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Make the denominator with the lowest common multiple (LCM)...

3 → 6 → 9 →

2 → 4 → 6 → 8 → 10 →

4 → 8 →

3 → 6 → 9 →

2 → 4 → 6 → 8 → 10 →

4 → 8 →

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You don't need a common denominator for multiplying fractions, look it's easy!

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With multiplication of fractions you can cancel something once on the top and bottom...

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With division of fractions... multiply by the reciprocal of the fraction after the division sign ÷...

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With division of fractions... multiply by the reciprocal of the fraction after the division sign ÷ ... And cancel across division...

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To add fractions, make a __common denominator__... the lowest common multiple (LCM)

In this case the LCM is 20...

In this case the LCM is 20...

Careful, look at each one closely,

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Just method #1 is shown here...

3100 ÷ 999 × 999

= 3100 × 999 ÷ 999

= 3100 × 1

= 3100

= 3100 × 999 ÷ 999

= 3100 × 1

= 3100

Yup, this is how the 'distributive property' works.

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Make sure to line up all the decimals overtop of eachother...
= 10269.25

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Make sure to line up all the decimals overtop of eachother...
= 23.82

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Make sure to line up all the decimals overtop of eachother (shown above)

You could use placeholder zeros: ... = 37

You could use placeholder zeros: ... = 37

Make sure to line up all the decimals overtop of eachother
You could use placeholder zeros:
= 391, 122.723

As you divide by a smaller factor of ten each time, the decimal place moves one place to the *right*, and the resulting number gets *bigger*.

As you multiply by a smaller factor of ten each time, the decimal place moves one place to the *left*, and the resulting number gets *smaller*.

× 0.1

÷ 0.01

÷ 0.1

× 100

÷ 10

× 10

× 0.1 = ÷ 10

÷ 0.01 = × 100

__For example:__

55 × 0.1 = 5.5

55 ÷ 10 = 5.5

33 ÷ 0.01 = 3300

33 × 100 = 3300

÷ 0.01 = × 100

55 × 0.1 = 5.5

55 ÷ 10 = 5.5

33 ÷ 0.01 = 3300

33 × 100 = 3300

× 10

÷ 0.01

× 0.1

÷ 100

= 15.25

= 152.5

= 15250

= 152500

As you multiply by a smaller factor of ten each time, the decimal place moves one place to the *left*, and the resulting number gets *smaller*.

As you divide by a smaller factor of ten each time, the decimal place moves one place to the*right*, and the resulting number gets *bigger*.

As you divide by a smaller factor of ten each time, the decimal place moves one place to the

First take care of the integers
(25)(2) = 50
Then add the zeros at the end of 2 __0__ __0__...
5 0 __0__ __0__

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Move the decimal by the number of zeros in the number, 1 __0__ __0__, so by 2 zeros. Think: move the decimal to the right to make the number bigger, because you are multiplying by one hundred...
= 525.13

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Count the number of places, behind the decimal,
0.__1__
There is one place behind the decimal,
25.
Move the decimals in the question by the same amount,
2.5

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Count the number of places, behind the decimal,
0.__001__
There are three places behind the decimal,
123456.
Move the decimals in the question by the same amount,
123.456

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Count the number of places, behind the decimal,
0.__001__
There are three places behind the decimal,
200.
Move the decimals in the question by the same amount,
0.200

- Count the total number of decimal places in the numbers (your magic number).
- Multiply normally, as if without decimals
- Once you have the final product, put the decimal at the furthest position to the right
- Move the decimal to the left by the total number of decimal places (your magic number).

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Count the total number of decimal places in 30.__31__ and 5.__00__ = 2 + 2 = 4 decimal places.

Move the decimal 4 places left.

= 151.550̸0̸

= 151.55

Move the decimal 4 places left.

= 151.550̸0̸

= 151.55

- Count the total number of decimal places in the numbers (your magic number).
- Multiply normally, as if without decimals
- Once you have the final product, put the decimal at the furthest position to the right
- Move the decimal to the left by the total number of decimal places (your magic number).

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Count the total number of decimal places

= 1 + 1 = 2 decimal places.

Move the decimal, by the same places as the question, 2 places left.

= 26.52

= 1 + 1 = 2 decimal places.

Move the decimal, by the same places as the question, 2 places left.

= 26.52

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Count the total number of decimal places

= 2 + 1 = 3 decimal places.

= 2 + 1 = 3 decimal places.

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Count the total number of decimal places

= 2 + 2 = 4 decimal places.

= 2 + 2 = 4 decimal places.

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Count the total number of decimal places

= 3 decimal places.

= 3 decimal places.

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Count the total number of decimal places

= 3 decimal places.

= 3 decimal places.

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Count the total number of decimal places

= 1 + 4 = 5 decimal places.

= 1 + 4 = 5 decimal places.

0 . __0__ __0__ __1__

**÷** means move the decimal to the right.

Set up the number by adding more zeros on the end. See how this does not change the number yet, it's still twenty-one point five. Then move the decimal place over in the correct direction, and the correct amount of times. That's it!

The number is__21,500__

Set up the number by adding more zeros on the end. See how this does not change the number yet, it's still twenty-one point five. Then move the decimal place over in the correct direction, and the correct amount of times. That's it!

The number is

11.5 ÷ 0.001 =

22.3 ÷ 0.01 = __2230__

*÷ 0 . *__0__ __1__ means move the decimal **twice**, to the **right**.

Move the decimal place to the **right**, making the number bigger.

Move the decimal**5** times: 0 . __0__ __0__ __0__ __0__ __1__

Move the decimal

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Convert the decimals first: move both 2 spaces...
Then, long division... (make sure to place the decimal directly above)

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Convert the decimals first: move both 2 spaces...
Then, long division... (make sure to place the decimal directly above)

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Convert the decimals first: move both 4 spaces...
Then, long division...

22 ≈ 20

113 ≈ 100

562 ≈ 1,000

1,200 ≈ 1,000

19,201 ≈ 20,000

132,092 ≈ 100,000

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The curriculum says 105 should round to 100, the nearest largest place value.

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A little bit more than 200 ÷ 4 = 50

...which is a bit more than 50

...which is ≈ 55

...which is a bit more than 50

...which is ≈ 55

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Use PEMDAS/BEDMAS...

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Use PEMDAS/BEDMAS...

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Use PEMDAS/BEDMAS...

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Fraction | Percent |

50 % | |

75 % | |

10% |

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%

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Fraction | Percent |

50 % | |

75 % | |

40 % | |

10% |

Decimal | Percent |

0.3 | 30% |

0.25 | 25% |

5% | |

0.01 | 1% |

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Decimal | Percent |

0.3 | 30% |

0.25 | 25% |

0.05 | 5% |

0.01 | 1% |

0:90 or 90 seconds is actually longer than 1:00 or 1 minute, which is only 60 seconds.

990 m

9,000 m

99 m

0.99 m

9 km

0.099 km

0.99 km

0.0099 km

Make sure the number of kilometers is always a factor of 1,000 **lower** than the number of meters.

9 km = 9,000 m

0.9 km = 900 m

(The 'km' moves down one place value, so the 'm' moves down one place value as well)

9 km = 9,000 m

0.9 km = 900 m

(The 'km' moves down one place value, so the 'm' moves down one place value as well)

Pair A: | 1,000 m | 1 km |

Pair B: | 100 cm | 1 m |

Pair C: | 10 mm | 1 cm |

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km

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Move the decimal by three, to the left.

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km

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Move the decimal by three, to the left.

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m

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Move the decimal by three, to the right.

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m

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Move the decimal by three, to the right.

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cm

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Move the decimal by one place, to the left.

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mm

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Move the decimal by one, to the right.

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m

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Move the decimal by two, to the left.

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km

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You can do it all at once, or split it into steps like this,
12,585.0 mm = _____________ cm
Move the decimal by one, to the left.
12,58.50 cm = _____________ m
Move the decimal by two, to the left.
12.5850 m = _____________ km
Move the decimal by three, to the left.
= 0.012585 km

There are __1,000__ mm in 1 m.

1,000 mm

1,000 mL

1,000 mg

1 L

1 m

1 g

None of them

1,000 mL = 1 L

1,000 mg = 1 g

1,000 mm - 1 m

1,000 mg = 1 g

1,000 mm - 1 m

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grams

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To go from kilograms (kg) to grams (g) to milligrams (mg):
or the other way around, from milligrams (mg) to grams (g) to kilograms (kg)...
Move the decimal place 3 times to the right when multiply 1000.

There are __1,000__ m in 1 km.

2 km

5 kg

200 m

2,000 m

500 g

5,000 g

2 km = 2,000 m

5 kg = 5,000 g

5 kg = 5,000 g

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kilometers

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When you divide by 1000, move the decimal __3__ spaces to the __left__.

Grams (g) | Kilograms (kg) |

220 | 0.22 |

0.5 | |

12,500 | 12.5 |

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grams

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Milliliters (mL) | Liters (L) |

4 | 0.004 |

34 | |

2344 | 2.344 |

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L

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cm

Add each of the four side lengths to get the perimeter of the rhombus.

Add the 4 side lengths...

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cm

Each side of a square is equal.

Divide: 25 ÷ 4 = ...
Each side is 6.25 cm.

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cm

Each side of a square is equal.

The perimeter of one square is 4 × 4.5cm = 18 cm.

If the total perimeter is 80 cm, then the perimeter of the other square must be: Since the sides are all equal, divide 62 cm by 4... Each side is 15.5 cm.

If the total perimeter is 80 cm, then the perimeter of the other square must be: Since the sides are all equal, divide 62 cm by 4... Each side is 15.5 cm.

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cm

Each side of a square is equal.

The perimeter of one square is 4 × 11 cm = 44 cm.

If the total perimeter is 80 cm, then the perimeter of the other square must be: Since the sides are all equal, divide 38 cm by 4...

If the total perimeter is 80 cm, then the perimeter of the other square must be: Since the sides are all equal, divide 38 cm by 4...

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cm

Use the formula for the area of a triangle and compare the bases and heights

You know the area of a triangle is:
The area of triangle 1:
The area of triangle 2:
Since the areas are equal...

You know the area of a triangle is:
Use guess & check to find the answer choice that has __twice the area__... eventually check D)

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cm^{2}

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Chop off the end at the dotted line and place it in the nook on the right-hand side to make a rectangle with the dimensions:
width = 10

height = 6 Then calculate the area of this rectangle,

height = 6 Then calculate the area of this rectangle,

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cm

Hint Unavailable

You have the area and height in the formula:

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cm^{2}

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See that this shape is made of two triangles plus one rectangle. The triangles and rectangle have:
height = 5 cm
Calculate the base lengths of the triangles.
Now that you have all the dimensions, calculate the area of each shape
Add the area of each shape together to get the total area.

Area of a square is the length times width. The length is the same as the width in a square. First:
Second:

This is the correct conversion.

meters^{2} | centimeters^{2} |

0.5 m^{2} | _________ |

1 m^{2} | 10,000 cm^{2} |

2 m^{2} | 20,000 cm^{2} |

3 m^{2} | 30,000 cm^{2} |

4 m^{2} | _________ |

See the pattern, increasing by the same amount each time...

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cm^{2}

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Area = Length × Width

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m^{2}

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Know that the place value difference between m^{2} and cm^{2} is 4 places...

Convert to meters... move the decimal 4 places left. Or, convert the lengths to meters first, and then calculate the area:

Convert to meters... move the decimal 4 places left. Or, convert the lengths to meters first, and then calculate the area:

- 10 cm --> 0.1 m
- 20 cm --> 0.2 m

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units^{2}

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Calculate the area of each pair of similar faces. There are 3 pairs...
Now add all 6 faces, or 3 pairs of faces,

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units^{2}

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Calculate the area of each pair of similar faces. There are 3 pairs. It doesn't matter if you chose your length, height, and depth differently.
Now add all 6 faces, or 3 pairs of faces,

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units

Hint Unavailable

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units^{3}

Hint Unavailable

You can choose any combination for length, width, height
Your multiplication will be in steps, like this
Then multiply the last,

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units^{3}

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units

Hint Unavailable

At this point, you are able to solve using guess and check, using a calculator, keep plugging in numbers, until eventually you find:
Therefore the height 'h' is 4 units

Obtuse is greater than 90˚

True

Obtuse triangles only have 1 obtuse angle.

A right angle is exactly 90˚

True. And an acute triangle with all angles equal is called an equilateral.

Measure the biggest angle first, if greater than 90˚ it is obtuse...

(If equal to 90˚ it is right, and if less than 90˚ it is acute)

(If equal to 90˚ it is right, and if less than 90˚ it is acute)

An isosceles triangle has 2 equal side lengths.

True

None of the side lengths are equal in a scalene triangle.

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With the use of tick marks. The same number of tick marks indicates the side lengths are the same. For example, equilateral would have three single tick marks, isosceles triangle would have two single tick marks and a double, and a scalene triangle would have on of each of: single tick mark, double tick mark, and triple tick mark.

Congruent means same __size and same shape__.

(The rest are similar shapes, with the same shape but different size).

(The rest are similar shapes, with the same shape but different size).

Polygons:

- Closed shape
- All sides are straight lines
- 2-dimensional

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Any two of the following with same sides and angles: equilateral triangle, square, pentagon, hexagon, ...

Regular polygons have all side lengths and angles equal.

Regular polygons have all side lengths and angles equal.

All are 4-sided:

- Quadrilateral
- Rectangle
- Rhombus
- Square
- Trapezoid
- Parallelogram
- Kite

- Square (all sides equal, all right angles)
- Quadrilateral (4 sides)
- Rectangle (all right angles)
- Polygon (closed, 2D, straight sides)
- Rhombus (all sides equal)
- Parallelogram (2 parallel sides)
- Kite (two different pairs of equal, adjacent sides)
- Trapezoid (at least one pair of parallel sides)

This is the general order...
Google 'em!

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degrees

Hint Unavailable

An octagon has 8 sides...

Complete the pattern ... 540˚, 720˚, 900˚,__1080˚__, ...

= 1080˚

Complete the pattern ... 540˚, 720˚, 900˚,

= 1080˚

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degrees

There are 8 equivalent angles and 8 equivalent sides in an octagon.

An octagon has 8 sides so divide the sum of the angles, 1080˚, by 8...

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One word, a shape.

A pentagon. See the first obtuse angle (greater than 90˚) is the pentagon with 108˚ for each angle. One up from a square with each angle at 90˚.

See that each has a first difference of 180˚...

See that,

See that,

- 3 sides is 1 × 180˚
- 4 sides is 2 × 180˚
- 5 sides is 3 × 180˚
- 6 sides is 4 ×
- ...

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degrees

A dodecagon has 10 equal sides and 10 equal interior angles

10 sides, so n = 10...

Determine the pattern rule quickly: +5.5

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Term numbers start at 1

60 is the 4^{th} term in the pattern, so the term number is 4.

Determine the pattern rule first: +9. Then find the 5th term.
5th term is 45.

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Number of Tickets | Cost |

1 | $18.00 |

3 | $23.00 |

5 | $28.00 |

7 | $33.00 |

9 | |

$43.00 |

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Follow the pattern

Find the pattern rule for the number of tickets, and the pattern rule for the cost.

Number of tickets: +2

Cost: +5. The missing numbers are 11 tickets, and $38.00

Number of tickets: +2

Cost: +5. The missing numbers are 11 tickets, and $38.00

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Start with 3, and then use the pattern rule of 10 up to 53...
The term number is 6.

x | y |

1 | 2 |

2 | __ |

3 | __ |

4 | __ |

5 | __ |

x | y |

1 | 2 |

2 | 6 |

3 | 14 |

4 | 30 |

5 | 62 |

Find out what it multiplies by each time: × 4.
The pattern rule is multiply by 4...

Do a quick check by simplifying some of the ones that look funny, try d)...

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Use guess and check

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Use guess and check

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Use guess and check

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Use guess and check

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Use guess and check

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Use guess and check

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Use guess and check

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Use guess and check

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Use guess and check

Solve with guess and check... 1, 2, 3, 4, 5, 6!

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Use guess and check

With guess and check...

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Use guess and check

With guess and check...
Or with more advanced rearrangement (Not required)...

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Use guess and check

With guess and check...
Or with more advanced rearrangement (Not required)...

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Use guess and check

With guess and check...
Or with more advanced rearrangement (Not required)...

True

"Three less than a number" means subtract (take away) 3 from your number, n.

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= 7 ×

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7 × ___ = 35

35 = 7 × ___

35 = 7 × ___

Yes these are all the same. They all mean multiply 2 × *n*.

n =

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Use guess and check, or division

n =

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Use guess and check, or division

n =

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Use guess and check, multiplication, or division

Multiplying by 10 makes the number bigger.
Move the decimal place 1 to the right (because there is 1 zero in 10).

r =

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Use guess and check, multiplication, or division

Multiplying by 100 makes the number bigger.
Move the decimal place 2 places to the right (because there are 2 zeros in 100).

n =

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Use guess and check, multiplication, or division

You can see that the number got bigger by a factor of 10, so the decimal must have been multiplied by __10__.

n =

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Use guess and check, multiplication, or division

Multiply the numbers together
See it works,

n =

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Use guess and check, multiplication, or division

The variable (n) should be a factor of 10 lower than 22.22, so move the decimal place once to the left.

n =

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Use guess and check, multiplication, or division

Multiplying by 100 moves the decimal place 2 to the right, which gave us the bigger number, 1.234

So the number had to be 2 decimal places__smaller__ → move the decimal 2 to the left.

So the number had to be 2 decimal places

n =

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Use guess and check, multiplication, or division

The number got smaller, so it was multiplied by a decimal.
The decimal place moved 3 times, so the number was 0.0001

n =

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(Also accept 0.5)

P =

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cm

Hint Unavailable

W =

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cm

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The width is 10cm!

Also accept answers with different arrangements:

- 5.99n + 8
- (5.99)(n) + 8
- 8 + n(5.99)
- 8 + n × 5.99
- 8 + 5.99(n)
- ...

The 'overall' trend is increasing.

World population is increasing constantly.

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Changing the scale of the axis on the left (y-axis) can make the graph appear smaller, or larger.

Loading and rendering MathJax, please wait...

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