Making Math Magic Are they related??? Presented by Making Math Magic “Four Teacher For Teachers”...

Making Math Magic

Are they related???

Presented by Making Math Magic

“Four Teacher For Teachers”

www.makingmathmagic.comAnn Booth

Rhonda Allen BurnsTami Pickett

Vonda Stamm

M3 MAKING MATH MAGIC

Making Math Magic

•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

We believe……

In short….Students can be more successful when

they have plenty of opportunities to:

•Build it! Concrete•Draw it! Mental Image•Write it! Symbolic

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SAY IT! throughout

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that the HOW in math instructionis as importantas the WHAT, if not more so…

We believe……

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

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

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!

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Say It!Throughout

With your talking partner discuss:

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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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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How long has it been since you had to deal with 9.0768% in real life????

Are there some fractions, decimals, per cents that are more prevalent in real life?

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Halves, fourths, eighthsThirds, sixthsTenths

Let’s concentrate on those numbers as we revisit to develop understanding.

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Write down (or draw) some things that you know about 50%.

Pre-assessment

We are going to start with percents and we are going to start with 50%.

WHY?????

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•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?

Shade 50% of your paper strip.

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0% 100%

Use a number line and mark where 50% would belong.

Let’s compare the strip model and the number line model.

Linear Model vs Area ModelArea model using the paper strip

Linear model using the paper strip

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50% 50%

0% 50% 100%

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Let’s look at another model.Use one of the 4” squares to shade 50%

You will also need this Transparency Grid Model

EquivalenceIf 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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EquivalenceHow do I write that as a fraction?

How do I write that as a decimal?

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EquivalenceIf 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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EquivalenceHow do I write this as a fraction?

How do I write this as a decimal?

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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.

50100

12

510

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Let’s look at other area or linear models..

Fraction CirclesFraction RectanglesCuisenaire Rods

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At your table, each person use a different model to show a 50% (etc.) model..

Fraction CirclesFraction RectanglesCuisenaire Rods

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Use either a paper circle or a paper square to fold and shade 50%.

If you have 6 beans, how can youplace them on your model to be “fair”?

What is 50% of 6?

Introducing the discrete or set model

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If 4 represents 50% of a number, what is the number?

50% of what number is 4?

Reverse the process…..

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Some people prefer two number lines

Using the number line to solve problems

Some people prefer one number line

0% 50% 100%

0 ? 24

0% 50% 100%

0 ? 24

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Some people prefer the two number lines put together

Using the double number line ….

0% 50% 100%

0 ? 24

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Choose a model to show and solve:

1. 50% of what number is 18?

2.What is 0.5 of 32?

3.What fraction of 30 is 15?

4. Twenty-one is 0.50 of what number?

Practicing with the models

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•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?

Moving on to Fourths……

one-fourth one-fourth one-fourth one-fourth

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Fourths……

one-fourth one-fourth one-fourth one-fourth

04

14

24

34

44

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.

Discuss the difference in the labels.

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Fourths……

25% 25% 25% 25%

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%”.

Again, discuss the difference in the labels.

0% 25% 50% 75% 100%

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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.

Fourths….

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Let’s look at another model.Use one of the 4” squares to shade25% or one-fourth. You will also need

this Transparency Grid Model

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14

? s 10 = 0.2½2½10

=

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14

= = 0.2½ = 0.25 2½10

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Area modelLet’s do some math…..

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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Area model25% of some number is 5, what is the number?

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Area model75% of some number is 12, what is the number?

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What is 0.75 of 40?

Number line

0 0.25 0.50 0.75 1.00

0 40 ??

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75% of what number is 15?

Number line

0 25% 50% 75% 100%

0 15 ??

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1. 25% of what number is 7?

2. What is 0.5 x 64?

3. ¾ of what number is 21?

4. What per cent of 40 is 30?

Try these……..

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We are debating on doing “eighths” here or moving to thirds and coming back to

eighths later.

THOUGHTS?????

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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.

Thirds……..

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Use the paper grid models to shade 13

How many tenths? How many hundredths?

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Tenths

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