1. Fractions and decimals
4.NF.3.5, 3.6, & 3.7

2. Learning Goals for Notebooks/Date & Rate
Our Learning goals
By the end of this unit, I will be able to:
Express a fraction with the denominator 10 as an equivalent fraction with the denominator 100.
Add two fractions with the denominators 10 and 100 (e.g. 4/ /100)
Write fractions with the denominators 10 and 100 as decimals.
Compare two decimals to hundredths using the symbols >, =, and <.
Model my understanding of decimals (place value, addition, & comparing) using tenths/hundredths grids and number lines.

3. What we already know
fraction numerator denominator equivalent fraction tenths hundredths visual model number line compare (>, <, =)

4. How are fractions and decimals related?
Journal prompt for 4.NF.3.5
(2-column notes)

5. Let’s practice modeling fractions using tenths and hundredths grids!
What we already know
Use visual models (tenths & hundredths grids) and number lines to represent fractions with denominators 10 and 100.
Let’s practice modeling fractions using tenths and hundredths grids!

6. What we already know
Use visual models (tenths & hundredths grids) and number lines to represent fractions with denominators 10 and 100.
If a fraction with denominator 10 and a fraction with denominator 100 occupy the same point on a number line, they are equivalent.
Let’s practice modeling fractions with denominators 10 and 100 using number lines!

7. Let’s practice using visual models!
What we already know
Express a fraction with denominator 10 as an equivalent fraction with denominator 100 (e.g. 3/10 = 30/100)
3/10 = ___/100
7/10 = ___/100
20/100 = ___/10
50/100 = ___/10
Let’s practice using visual models!

8. What we already know 4/10 + 3/10 24/100 + 33/100 6/10 + 1/10
Add two fractions with the same denominators (10 or 100).
4/10 + 3/10
24/ /100
6/10 + 1/10
51/ /100
2/10 + 7/10
80/ /100
Let’s practice!

9. Add two fractions with the denominators 10 and 100.
New learning goal
Add two fractions with the denominators 10 and 100.
Math Talk: How could you use what you already know
to find the sum of 4/ /100?
LearnZillion Video
Let’s practice!
Task Cards
MFAS Tasks (4)

10. How does your knowledge of multiples help you find equivalent fractions with denominators of 10 or 100?

11. How can understanding
“3/10 is equivalent to 30/100” help when adding and fractions? Give an example of how this can be used.

12. How does your knowledge of place value help you prove that 4/10 + 5/100 = 45/100?

13. Is there another possibility?
Write a fraction addition number sentence where one addend has a denominator of 10 and the other addend has a denominator of 100 and the sum of 90/100.
Is there another possibility?

14. Do 6/10 and 60/100 occupy the same point on a number line
Do 6/10 and 60/100 occupy the same point on a number line? Justify why or why not.

15. How are fractions and decimals related?
Journal prompt for 4.NF.3.5
(Revise and add to previous response)

16. How can I represent a fraction as a decimal?
Journal prompt for 4.NF.3.6

17. Learning Goals for Notebooks/Date & Rate
Our Learning goals
By the end of this unit, I will be able to:
Express a fraction with the denominator 10 as an equivalent fraction with the denominator 100.
Add two fractions with the denominators 10 and 100 (e.g. 4/ /100)
Write fractions with the denominators 10 and 100 as decimals.
Compare two decimals to hundredths using the symbols >, =, and <.
Model my understanding of decimals (place value, addition, & comparing) using tenths/hundredths grids and number lines.

18. New learning goal
Write fractions with the denominators 10 and 100 as decimals.
Model my understanding of decimals (place value, addition, & comparing) using tenths/hundredths grids and number lines.
BrainPop Decimals

19. What do I need to know about decimals?
5 in the hundredths column has a value of “five hundredths”
Fraction: 5/100
Decimal: 0.05
1 in the tenths column has a value of “one tenth”
Fraction: 1/10
Decimal: 0.1
The decimal point separates the whole number amount from the part of the number that is less than one.

20. Decimal models
Decimals are an extension of our whole number base ten system.
Decimals and fractions both represent parts of a whole.
The fraction and decimal sound the same when we say them out loud. 
6/10
60/100

35. How can I represent a fraction as a decimal?
Journal prompt for 4.NF.3.6
(Revise and add to previous prompt)

43. Practice activities
“Decimal Match” (DD 1.3/mix-n-match)- Match decimal to model.
“Place Value Partners” (DD 1.2/shoulder partners)- Students build a decimal number using place value clues.
Given model, name decimal
Given decimal, shade model.
Given number line, name decimal.
Given decimal, place on number line,
Words to decimals
“Decimals Read Around” (DD 2.2/quiz-quiz-trade)- Decimals to words
Digits in decimals– values? Which place value column? (write decimal riddles)
Equivalent decimals-

44. JOURNALs What is the relationship between decimals and fractions?
Is it easier to convert a fraction to a decimal when the denominator is a multiple of 10? An even number? An odd number?
Rewrite this number sentence using decimals : 40/ /100 = 42/100,
Write three decimals that are in between ¼ and ¾? How do you know your answer is correct?
Name two decimals that occupy the same point on a number line?
How can you write the decimal 0.53 as the sum of two fractions? (examples include same denominator 50/ /100, changing addends 49/ /100, or different denominators 5/10 + 3/100)

45. How can I represent a fraction as a decimal?
Journal prompt for 4.NF.3.6
(Revise and add to previous prompt)

46. What we already know
Compare two decimals to hundredths using the symbols >, =, and <.
Model my understanding of decimals (place value, addition, & comparing) using tenths/hundredths grids and number lines.

47. How can I compare two or more decimals?
Journal prompt for 4.NF.3.7

48. Compare and order decimals
Create a model and compare.
Use a number line to compare.
Use music!
Ordering and Comparing Decimals
To order them I look left to right,
Find the first place that’s not alike.
Line up the decimal points vertically.
Look left to right—horizontally.
Where the greatest place that’s different,
The greater number will become apparent!

49. How can I compare two or more decimals?
Journal prompt for 4.NF.3.7
(Revise and add to previous prompt)