2. Fractions, Decimals, and Percents
Are they related???
Making Math Magic

3. Presented by Making Math Magic “Four Teacher For Teachers” www
Presented by Making Math Magic “Four Teacher For Teachers” Ann Booth Rhonda Allen Burns Tami Pickett Vonda Stamm
M3 MAKING MATH MAGIC

4. We believe…… that all students can and should learn math!
that if children like math and feel successful at math - they will learn math!
there are 3 basic stages that children need to go
through when learning math:
–Stage 1: Using Manipulatives
–Stage 2: Developing a Mental Image
–Stage 3: Using Symbols
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5. Build it! Concrete Draw it! Mental Image Write it! Symbolic
In short….
Students can be more successful when they have plenty of opportunities to:
Build it! Concrete
Draw it! Mental Image
Write it! Symbolic
SAY IT! throughout
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6. that the HOW in math instruction is as important as the WHAT,
We believe……
that the HOW in math instruction
is as important
as the WHAT,
if not more so…
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7. Review the Standards for Mathematical Practice:
Make sense of problems and
persevere in solving them
Reason abstractly and quantitatively
(contextualize and decontextualize)
Construct viable arguments and
critique the reasoning of others

8. Standards for Mathematical Practice:
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in
repeated reasoning

9. With your talking partner discuss:
If we pay particular attention to the learning stages mentioned earlier, which Standards for Math Practice would/could be naturally addressed?
Build it!
Draw it!
Write it!
Say It!
Throughout
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10. Big Rocks:
Understand the relationship between the names (fraction, decimal, percent)
Move freely between the “part”, the “name”, and the “whole”
Explore Benchmark numbers to understand size/location, and comparisons.
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11. Why do middle school and high school students still struggle with fractions, decimals, and per cents?
Our goal is to help students that struggle make sense of rational numbers!
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12. Are there some fractions, decimals, per cents that are more prevalent in real life?
How long has it been since you had to deal with % in real life????
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13. Halves, fourths, eighths Thirds, sixths Tenths
Let’s concentrate on those numbers as we revisit to develop understanding.
Halves, fourths, eighths
Thirds, sixths
Tenths
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14. Write down (or draw) some things that you know
We are going to start with percents and we are going to start with 50%.
WHY?????
Pre-assessment
Write down (or draw) some things that you know
about 50%.
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16. Shade 50% of your paper strip.
Compare your 50% with your talking partner.
Did you agree?
How do you know you are correct?
If I wanted to describe what I shaded with a common fraction, what fraction did I shade?
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17. Use a number line and mark where 50% would belong.
0% %
Let’s compare the strip model and the number line model.
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18. Linear Model vs Area Model
Area model using the paper strip Linear model using the paper strip
50%
0% % %
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19. Let’s look at another model. Use one of the 4” squares to shade 50%
You will also need this Transparency Grid Model
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20. Equivalence
If this entire square represents my unit (my 1), what is the name for each of my inside pieces?
What is my shaded part called?
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21. Equivalence How do I write that as a fraction?
How do I write that as a decimal?
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22. Equivalence
If this entire square represents my unit (my 1), what is the name for each piece?
What would be the name for my shaded part?
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23. Equivalence How do I write this as a fraction?
How do I write this as a decimal?
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24. Let’s look at all of the ways we have represented our 50%:
50%, , , 0.5, , and 0.50
These are all equivalent and can be used interchangeably. 1 2 5 10 50
100
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25. Let’s look at other area or linear models..
Fraction Circles
Fraction Rectangles
Cuisenaire Rods
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26. At your table, each person use a different model to show a 50% (etc
At your table, each person use a different model to show a 50% (etc.) model..
Fraction Circles
Fraction Rectangles
Cuisenaire Rods
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27. Introducing the discrete or set model
Use either a paper circle or a paper square to fold and shade 50%.
If you have 6 beans, how can you
place them on your model to be “fair”?
What is 50% of 6?
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28. Reverse the process…..
If 4 represents 50% of a number, what is the number?
50% of what number is 4?
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29. Using the number line to solve problems
Some people prefer one number line ?
0% % %
Some people prefer two number lines
0% % % ?
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30. Using the double number line ….
Some people prefer the two number lines put together ?
0% % %
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31. Practicing with the models
Choose a model to show and solve:
50% of what number is 18?
What is 0.5 of 32?
What fraction of 30 is 15?
Twenty-one is 0.50 of what number?
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32. Moving on to Fourths…… Why would we do fourths next?
Start back with folding the strips.
Have the students use an 8.5 paper strip and find half. Ask them to leave this folded and fold in half again. Have them predict how many parts they will have.
How should we label these if I want to use fractions?
one-fourth
one-fourth
one-fourth
one-fourth
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33. Fourths……
Use one of the 8.5” number lines to label fourths . They can used their folded strip as a reference or they can fold the number line.
one-fourth
one-fourth
one-fourth
one-fourth 4 1 4 2 4 3 4 4
Discuss the difference in the labels.
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34. Fourths……
Ask them to use other paper strips and number lines to label using percents.
You may have to lead them to the discovery of “If the whole strip is 100%, then one section is 25%”.
25%
25%
25%
25%
0% % % % %
Again, discuss the difference in the labels.
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35. Fourths….
Because students may struggle with finding half of 0.5, we are going to use the 4” square and the grid model before we ask them to do the decimal version of the number line.
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36. Let’s look at another model. Use one of the 4” squares to shade
25% or one-fourth.
You will also need this Transparency Grid Model
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37. 1 4
? s 10 2½ 10 =
= 0.2½
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38. 1 4 2½ 10 =
= 0.2½
= 0.25
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39. Let’s do some math…..
Area model
Find an area model for fourths or fold one of the circles or squares into fourths.
What is ¼ of 12?
What is ¾ of 12?
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40. 25% of some number is 5, what is the number?
Area model
25% of some number is 5, what is the number?
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41. 75% of some number is 12, what is the number?
Area model
75% of some number is 12, what is the number?
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42. Number line
What is 0.75 of 40? ??
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43. 75% of what number is 15? Number line 0 25% 50% 75% 100% 0 15 ??
% % % % ??
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44. Try these…….. 25% of what number is 7? What is 0.5 x 64?
What per cent of 40 is 30?
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45. We are debating on doing “eighths” here or moving to thirds and coming back to eighths later.
THOUGHTS?????
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46. Thirds……..
Because of the fractions involved in thirds when they are written as a decimal and as a percent, we decided to approach them using the grid model first.
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47. Use the paper grid models to shade1 3
Use the paper grid models to shade
How many tenths?
How many hundredths?
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48. Tenths
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