1. Decimals 1

2. Children should be led to make their own investigations, and to draw upon their own inferences. They should be told as little as possible which can produce unlimited learning potential.
Herbert Spencer
Intellectual Moral and Physical
1864 2

3. McDonald’s Menu…. I’m Lovin It!!
Double Cheeseburger: $ .99
Big Mac Value Meal: $ 4.79
Chicken McNuggetts Meal: $ 3.80
Small Drink: $ .99
McFlurry: $ 1.97
Salad: $ 4.80
2 Cheeseburger Meal: $ 3.70
Ice Cream Cone: $ .87

4. Order Up! Least Expensive to Most Expensive
Ice Cream Cone
Double Cheeseburger:
Small Soft Drink:
McFlurry:
2 Cheeseburger Meal:
Chicken McNuggetts Meal:
Big Mac Value Meal:
Chicken Salad:

5. What Do I Mean Compare Decimals?
When we compare we use terms such as:
Less than <
Greater than >
Equal to =
Comparing decimals is similar to comparing whole numbers.
45<47
150>105
When we compare decimals we use place value or a number line.

6. Place Value Ones Tens Tenths Hundreds Thousands Hundredths Thousandths
1,000
100 10 1
0.1
0.01
0.001
0.0001
Tens
Ones
Tenths
Hundreds
Thousands
Hundredths
Thousandths
Ten-thousandths

7. Compare Sara’s score with Danny’s score. Sara 42.1 Danny 42.5 Ross
Diving Results
Compare Sara’s score with Danny’s score.
Line Up Decimal Points
Sara:
Danny:
Start at the left and find the first place where the digits differ. Compare the digits
1 < 5
42.1 < 42.5
This means Sara’s score was lower than Danny’s score.
Sara
42.1
Danny
42.5
Ross
42.0
Bethany
40.7
Jacob
46.1

8. Let’s Try Using A Number Line
Sara
42.1
Danny
42.5
Ross
42.0
Bethany
40.7
Jacob
46.1 42 43
42.0
42.1
42.5
Numbers to the right are greater than numbers to the left. Since 42.5 is to the right of 42.1 we have:
42.5 > 42.1

9. Equivalent Decimals
Decimals that name the same number are called equivalent decimals.
0.60 and 0.6
Are these the same???

10. =
0.6
0.60

11. Annexing Zeros
This means placing a zero to the right of the last digit in a decimal.
0.6
Although we added a zero, the value of the decimal did not change!!
Annexing or adding zeros is useful when ordering a group of decimals.
0.60

12. Ordering Decimals
We can order decimals from least to greatest or we can order from greatest to least.
Let’s try an example:
Order 15, 14.95, 15.8, and from least to greatest

13. 15, 14.95, 15.8, 15.01 First, line up the decimal points 15 14.95 15.8

14. 15, 14.95, 15.8, 15.01
Next, annex zeros so that each number has the same number of decimal places
15.00
14.95
15.80
15.01
Finally, use place value to compare the decimals. Always start from the left!!
14.95, 15, 15.01, 15.8

15. One More Example Order these numbers from greatest to least
35.06, 35.7, 35.5,
35.060
35.700
35.500
35.849
35.06
35.7
35.5
35.849
35.06, 35.5, 35.7,

16. Rounding Decimal Numbers
Sometimes close enough is good enough!

17. Molly has $16 in her pocket
She buys:
3 $1.89 each
3 $2.19 each
3 Large French $ $1.79 each
Does she have enough money?

18. About how much will it cost to fill up?
Gas costs $1.79 per gallon
I’m running on empty and I have a 20 gallon tank on my truck……
About how much will it cost to fill up?

19. You have one hour to take a 50 question test.
About how much time can you spend on each question?
Close enough is good enough!

20. The Rounding Poem Find your number Look right next door
4 or less, just ignore
5 or more add one more!

21. Rounding Whole Numbers
Round 474 to the closest hundred.
500
474
Find your number
Look right next door
Four or less, just ignore
Five or more, add one more

22. Round 474 to the closest 10’s
474
470
Just ignore

23. Try These
4,215
394 27
127,591
638

24. What about decimal numbers
The same rules (and poem) apply!
Round to the closest hundredths
4.167
Find your number
Look right next door
Five or more, add one more
4.17

25. Remember
If you are asked to round to the nearest tenth…….your answer stops at the tenth place!
Example: Round to the closest tenth would be 42.7

26. Special Case! Rounding a 9
Round to the closes hundredths
Since there is a “9” in the hundredths place consider the tenth and hundredths together – 19 – do you leave it at 19 or move it to 20?

27. Round 4.95 to the closest tenth
Since there is a “9” in the tenth spot consider the ones and tenths together…… should you leave it at 49 or move it to 50?
4.95 rounded to the nearest tenth is 5.0

28. Try these
Round to hundredths
Round to tenths:
4.56
4.6
18.784
18.78
5.32
5.3
9.46
9.456
10.00
0.98
1.0
9.997

29. Addition and Subtraction

30. What Does Addition Look Like?
Model using base ten blocks and an open number line.
Show 2 different representations of the mathematical thinking as you evaluate each expression. 13

31. What Does Subtraction Look Like?
Model using base ten blocks and an open number line.
97 − 58
9.7 − 5.08
Show 2 different representation of solutions for each expression.
9.7

32. Reflect Describe the strategies you used to solve addition problems.
Describe the strategies you used to solve subtraction problems.
a) How is adding whole numbers and decimal numbers similar?
b) Different?
a) How is subtracting whole numbers and decimal numbers similar?

33. Developing Conceptual Understanding
The veterinarian told Camilla that the weight of her puppy increased by 3.5 lb in the last month. If the puppy weighs 15.6 lb now, what was its weight a month ago?
Solve this problem in 2 different ways.
Show your work.
Compare your solutions.
How are they similar? different?

34. Alternative Algorithms
Partial-Sums Addition
Traditional Addition
1 1
3.48
+5.83
9.31
1 1
348
+583
931
348
+ 583
800
120 11
931
34.8
+ 58.3
80.0
12.0
1.1
93.1

35. Alternative Algorithms
Adding-Up Subtraction
724 –
345
7.24 –
3.45

36. Practice
439.56
439.56
439.56
417.66
439.56 –
439.56 –
451.46
451.46

37. Sharing Strategies
1. What strategies do you use to add and subtract whole numbers mentally?
2. What strategies do you use to add and subtract decimal numbers mentally?
257 − 39
25.7 – 3.9

38. Mental Math for Addition
Adding On
= 236
= 276
= 279
Compensation
= 536
536 – 3 = 533
Constant Sum
Take 2 from 153 and add 2 to 598
= 751
So,
= 751

39. Mental Math for Subtraction
Partial Subtraction
387 – 146
387 – 100 = 287
287 – 40 = 247
247 – 6 = 241
Compensation
547 – 296
547 – 300 = 247
= 251 So
547 – 296 = 251
Constant Difference
598 – 153
Add 7 to 153 to make it 160.
So, add 7 to 598.
605 – 160 = 445
Check:
= 598

40. Apply These Strategies
Joan is wondering whether the class’ hot lunch sales were above or below the actual cost of the lunches, $ Here are the numbers she is using.
Calculate using different mental math strategies: –