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May 2013

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How to help students with multiplication tables?

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I have two games on my site, plus links to many.

(easy hangman)
(difficult)

The ideas in this decimals lesson are taken from
Math Mammoth Decimals 1 book ($4.00 download). Only a few examples of each problem type are shown.

Comparing decimals
Free decimals lesson plan from HomeschoolMath.net

Which is more, 0.4 or 0.16? A student with a common misconception will answer 0.16, thinking of the decimal digits (digits after the decimal point) as "plain numbers." I show the truth of the matter using place value charts--a powerful tool to compare decimals and to combat this misconception.

Review. Which is greater, 4506 or 4606? How do you know?
Which is greater, 4512 or 4562? How can you tell?
Which is greater, 4603 or 4478? How can you tell?

Challenge. How well can you do on comparing decimal numbers?

5.6	5.2	5.02	5.2	4.1	4.03	0.16	0.017

0.09	0.1	0.4	0.13	4.7	4.70	1.09	1.9

Decimals are compared in exactly the same way as other numbers: by comparing the different
place values from left to right. To help in that, you can write the two numbers into the place
value tables on top of each other. Then compare the different place values in the two numbers
from left to right, starting from the biggest place value.

7.3

7.03

	7	.3
	7	.0	3
T	O	te	hu

3.01

3.1

	3	.0	1
	3	.1
T	O	te	hu

The two numbers have the same amount of ones. The first number has more tenths than the second, so the first number is bigger.

Now the two numbers have the same amount of ones. The second number has more tenths than the first, so 3.1 is bigger.

0.16

0.05

	0	.1	6
	0	.0	5
T	O	te	hu

0.16

0.5

	0	.1	6
	0	.5
T	O	te	hu

The two numbers have the same amount of ones. The first number has more tenths than the second, so the first number is bigger.

The two numbers have the same amount of ones. The second number has more hundredths than the first, so is bigger.

2.3

2.30

	2	.3
	2	.3	0
T	O	te	hu

2.32

2.39

	2	.3	2
	2	.3	9
T	O	te	hu

These have the same amount of ones (two), tenths, (three), and hundredths (zero). The numbers are equal.

The numbers have the same amount of ones (two) and tenths (three), but the second one has more hundredths So the second is bigger.

Tip: It is easier to compare if the numbers have the same amount of decimals. You can tag a zero (or zeros) to the end of the number with less decimals.

Which is bigger, 0.2 or 0.15 ? Tag a zero to the end of 0.2 to get... Which is bigger, 0.20 or 0.15 ?

Example problem types

1. a)

Which is greater,
0.3 or 0.21?

b) Draw a number line from 0.5 till 0.6 with tick marks at every hundredth, and find the numbers 0.55 and 0.6 on it. Which is greater?

2. a) Mark the numbers 5.2 and 5.02 on the following number line.

[available in the ebook]

b) Write the following numbers in order. Remember: It is easier to compare if the numbers have the same amount of decimals. You can also use the number line above to help.

[available in the ebook]

3. a) Write these numbers from smallest to greatest: 1.4 1.34 1.44 1.5 1.3 1.30 1.28 1.49

b) Draw a number line from 1.2 till 1.5 with tick marks at every hundredth. Mark the numbers from a) on it, and check your work.

4. Compare. Use the place value tables if you need to.

9.1

9.09

		.
		.
T	O	te	hu

12.08

12.70

		.
		.
T	O	te	hu

0.96

0.79

		.
		.
T	O	te	hu

6.10

6.9



T	O	te	hu

0.5

0.05



T	O	te	hu

5.67

5.7



T	O	te	hu

5. Compare.

17.7		7.17

7.07		0.77

0.77		0.7

62.08		62.09

1.01		1.09

7.60		7.55

70.00		70.07

14.7		14.17

108.09		188.9

6. a) Write decimal numbers under the tick marks of the number line in the middle. Under the two other ones, write fractions.

b) Which is the closest tenth to

1

3

? To

2

3

To 1

1

3

To 2

1

3

c) One of the fractions

1

4

2

4

, or

3

4

, is exactly a certain amount of tenths.

Which? How many tenths?

d) Compare. Do NOT look at the number lines above at first but think of the facts you found in b). After completing the work, check your answers with the number lines.

[available in the ebook]

7. Write the numbers in order from smallest to greatest.
[available in the ebook]

8. Give an example of two decimal numbers where
a) the number with more decimal digits is smaller than the other
b) the number with more decimal digits is bigger than the other
c) the number with more decimal digits is equal to the other

The ideas in this decimals lesson are taken from
Math Mammoth Decimals 1 book ($4.00 download). Only a few examples of each problem type are shown.

New! Times Tales is now on DVD!

The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.

Comparing decimals Free decimals lesson plan from HomeschoolMath.net

Example problem types

Comparing decimals
Free decimals lesson plan from HomeschoolMath.net