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Making Math Magic Fractions, Decimals, and PercentsAre they related???Presented by Making Math MagicFour Teacher For Teachers

www.makingmathmagic.comAnn BoothRhonda Allen BurnsTami PickettVonda Stamm

M3 MAKING MATH MAGIC

Making Math Magicthat 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 ManipulativesStage 2: Developing a Mental ImageStage 3: Using SymbolsWe believe

In short.Students can be more successful when they have plenty of opportunities to:Build it! ConcreteDraw it! Mental ImageWrite it! Symbolic

Making Math MagicSAY IT! throughout

Making Math Magicthat 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 themReason abstractly and quantitatively (contextualize and decontextualize)Construct viable arguments and critique the reasoning of others Standards for Mathematical Practice:

Model with mathematicsUse appropriate tools strategicallyAttend to precisionLook for and make use of structureLook 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!

Making Math Magic

Say It!ThroughoutWith your talking partner discuss:Big Rocks:Understand the relationship between the names (fraction, decimal, percent)Move freely between the part, the name, and the wholeExplore Benchmark numbers to understand size/location, and comparisons.Making Math Magic

Making Math MagicWhy 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!Making Math MagicHow 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?Making Math MagicHalves, fourths, eighthsThirds, sixthsTenths

Lets concentrate on those numbers as we revisit to develop understanding.Making Math MagicWrite down (or draw) some things that you know about 50%.Pre-assessmentWe are going to start with percents and we are going to start with 50%.WHY?????

Making Math MagicCompare 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.Making Math Magic 0% 100%Use a number line and mark where 50% would belong.Lets 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

Making Math Magic 50%50% 0% 50% 100%Making Math MagicLets look at another model.

Use one of the 4 squares to shade 50%You will also need this Transparency Grid ModelEquivalenceIf this entire square represents my unit (my 1), what is the name for each of my inside pieces? What is my shaded part called?Making Math MagicEquivalenceHow do I write that as a fraction?How do I write that as a decimal?Making Math MagicEquivalenceIf this entire square represents my unit (my 1), what is the name for each piece? What would be the name for my shaded part?Making Math MagicEquivalenceHow do I write this as a fraction?How do I write this as a decimal?Making Math MagicMaking Math MagicLets 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. 5010012510Making Math MagicLets look at other area or linear models..

Fraction CirclesFraction RectanglesCuisenaire RodsMaking Math MagicAt your table, each person use a different model to show a 50% (etc.) model..

Fraction CirclesFraction RectanglesCuisenaire RodsMaking Math MagicUse 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 modelMaking Math MagicIf 4 represents 50% of a number, what is the number?

50% of what number is 4?

Reverse the process..Making Math MagicSome people prefer two number lines Using the number line to solve problemsSome people prefer one number line 0% 50% 100% 0 ? 24 0% 50% 100% 0 ? 24Making Math MagicSome people prefer the two number lines put together Using the double number line . 0% 50% 100% 0 ? 24Making Math MagicChoose 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?

Practicing with the modelsMaking Math MagicWhy 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 Fourthsone-fourthone-fourthone-fourthone-fourthMaking Math MagicFourthsone-fourthone-fourthone-fourthone-fourth0414243444Use 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.Making Math MagicFourths25%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%Making Math MagicBecause 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.Making Math MagicLets look at another model.

Use one of the 4 squares to shade25% or one-fourth.You will also need this Transparency Grid ModelMaking Math Magic14 ? s 10= 0.2210= Making Math Magic14== 0.2= 0.25 210Making Math MagicArea modelLets do some math..Find an area model for fourths or fold one of the circles or squares into fourths.What is of 12?What is of 12?Making Math MagicArea model25% of some number is 5, what is the number?Making Math MagicArea model75% of some number is 12, what is the number?Making Math MagicWhat is 0.75 of 40?Number line 0 0.25 0.50 0.75 1.00 0 40 ??Making Math Magic75% of what number is 15?Number line 0 25% 50% 75% 100% 0 15 ??Making Math Magic 25% of what number is 7?

What is 0.5 x 64?

of what number is 21?

What per cent of 40 is 30? Try these..Making Math MagicWe are debating on doing eighths here or moving to thirds and coming back to eighths later.

THOUGHTS?????Making Math MagicBecause 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..Making Math MagicUse the paper grid models to shade 13

How many tenths?How many hundredths?Making Math MagicTenthsMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math MagiczzccMaking Math Magiczzcc