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## Making Math Magic

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**Fractions, Decimals, and Percents**Are they related??? Making Math Magic**Presented by Making Math Magic“Four Teacher For**Teachers”www.makingmathmagic.comAnn BoothRhonda Allen BurnsTami PickettVonda Stamm M3 MAKING MATH MAGIC**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 Making Math Magic**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 Making Math Magic**We believe……**that the HOW in math instruction is as important as the WHAT, if not more so… Making Math Magic**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? With your talking partner discuss: • Build it! • Draw it! • Write it! Say It! Throughout Making Math Magic**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. Making Math Magic**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! Making Math Magic**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 9.0768% in real life???? Making Math Magic**Let’s concentrate on those numbers as we revisit to**develop understanding. Halves, fourths, eighths Thirds, sixths Tenths Making Math Magic**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%. Making Math Magic**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? Making Math Magic**Use a number line and mark where 50% would belong.**0% 100% Let’s compare the strip model and the number line model. Making Math Magic**Linear Model vs Area Model**0% 50% 100% Making Math Magic Area model using the paper strip Linear model using the paper strip**Let’s look at another model.**Use one of the 4” squares to shade 50% You will also need this Transparency Grid Model Making Math Magic**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? Making Math Magic**Equivalence**How do I write that as a fraction? How do I write that as a decimal? Making Math Magic**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? Making Math Magic**Equivalence**How do I write this as a fraction? How do I write this as a decimal? Making Math Magic**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 Making Math Magic**Let’s look at other area or linear models..**Fraction Circles Fraction Rectangles Cuisenaire Rods Making Math Magic**At your table, each person use a different model to show a**50% (etc.) model.. Fraction Circles Fraction Rectangles Cuisenaire Rods Making Math Magic**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? Making Math Magic**Reverse the process…..**• If 4 represents 50% of a number, what is the number? • 50% of what number is 4? Making Math Magic**Using the number line to solve problems**Some people prefer one number line 0 ? 24 0% 50% 100% Some people prefer two number lines 0% 50% 100% 0 ? 24 Making Math Magic**Using the double number line ….**Some people prefer the two number lines put together 0 ? 24 0% 50% 100% Making Math Magic**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? Making Math Magic**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 Making Math Magic**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 0 4 1 4 2 4 3 4 4 4 Discuss the difference in the labels. Making Math Magic**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% 25% 50% 75% 100% Again, discuss the difference in the labels. Making Math Magic**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. Making Math Magic**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 Making Math Magic**1**4 ? s 10 2½ 10 = = 0.2½ Making Math Magic**1**4 2½ 10 = = 0.2½ = 0.25 Making Math Magic**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? Making Math Magic**Area model**25% of some number is 5, what is the number? Making Math Magic**Area model**75% of some number is 12, what is the number? Making Math Magic**Number line**What is 0.75 of 40? 0 0.25 0.50 0.75 1.00 ?? 0 40 Making Math Magic**Number line**75% of what number is 15? 0 25% 50% 75% 100% 0 15 ?? Making Math Magic**Try these……..**25% of what number is 7? What is 0.5 x 64? ¾ of what number is 21? What per cent of 40 is 30? Making Math Magic**We are debating on doing “eighths” here or moving to**thirds and coming back to eighths later. THOUGHTS????? Making Math Magic**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. Making Math Magic**1**3 Use the paper grid models to shade How many tenths? How many hundredths? Making Math Magic**Tenths**Making Math Magic**cc**• zz Making Math Magic**cc**• zz Making Math Magic