Fraction Ghostbusters.pptx [Read-Only] · Fraction Ghostbusters. ... 3‐5 NUMBER AND OPERATIONS...

transcript

Jason ChamberlainHusband/DadMath Teacher

SJVMP Teacher LeaderMath Vertical Team Lead

Math Coach

San Joaquin Valley Mathematics Projectjchamberlain@caruthers.k12.ca.us

Fraction Ghostbusters

Mental Math Warm‐Up

• One hundred four minus sixty seven = ?

• Twenty seven times twelve = ?

• Two hundred thirty six divided by half = ?

What’s the Plan?

• Discussion: What is at the heart of “I hate fractions”?

• Understand the basics of the progression of fraction sense across grades K‐5

• Believe in the power of “Fractionese” (MP3)• Experience some activities designed to help students make sense of fractions through language and math tools (MP1 & MP5)

*We won’t have time to cover every standard.

Mental Math Warm‐Up

• One hundred four minus sixty seven = 37

• Twenty seven times twelve = 324

• Two hundred thirty six divided by half = 118…or maybe 472?

Why do students say “I hate fractions”?

• 1 minute think/write time

• Timed Pair Share – 30 seconds each

• Whole‐class share

Why do students say “I hate fractions”?

• 1. They don’t understand fractions.• 2. They feel stupid.• 3. They haven’t grasped the concept and/or become fluent at the skill.

• 4. Past experience with teachers that don’t love and/or understand fractions.

What is a fraction?

• As math teachers, we should have a pretty good idea of what a fraction is, right?

• In language any 3rd grader could understand, please define “fraction.”

What is a fraction?

• dictionary.com – 1. Mathematics. a number usually expressed in the form a/b.

• a ratio of algebraic quantities similarly expressed. • 2. Chemistry. (in a volatile mixture) a component whose range of boiling point temperatures

allows it to be separated from other components by fractionation. • 3. a part as distinct from the whole of anything; portion or section: The meeting started with

a fraction of us present.

• merriam‐webster.com ‐ a : a numerical representation (as 3⁄4, 5⁄8, or 3.234) indicating the quotient of two numbers

• b (1) : a piece broken off : fragment (2) : a discrete unit : portion

• mathisfun.com ‐ Part of a whole.

• the bottom number (the denominator) says how many parts the whole is divided into

• the top number (the numerator) says how many parts we have.

3‐5 NUMBER AND OPERATIONS ‐FRACTIONS

K‐2 FRACTION‐RELATED STANDARDS

Kindergarten

• K.G.6 Compose simple shapes to form larger shapes.

First Grade

• 1.G.3 Partition circles and rectangles into two and four equal parts, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal parts creates smaller shares.

Second Grade

• 2.G.3 Partition circles and rectangles into two, three, or four equal parts, describe the sharesusing the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

3‐5 NUMBER AND OPERATIONS ‐FRACTIONS

3‐5 NUMBERS AND OPERATIONS ‐FRACTIONS

Third Grade

• 3.NF.1,2,3• 3.G.2• FRACTIONS are NUMBERS• Fraction units (EQUAL PARTS) make up a WHOLE

• Fraction equivalence• Comparing fractions with the same numerator or denominator

Gr. 3 Act. 1 ‐ Chocolate Sampling

• Milk chocolate or dark chocolate?

Gr. 3 Act. 1 – Chocolate Sampling

• Carefully break into 2 EQUAL PARTS.• How many halves does it take to make a WHOLE Hershey bar?

• On a piece of paper, write “1 EQUAL PART /2 make a WHOLE” (This is called a FRACTION or a PART)

• This may be written as…

• On your blank number line paper (.docx), let’s make a NUMBER LINE to show that a fraction is JUST A NUMBER.

See, it’s just a number!

2/20/2

2 halves make a whole.½ + ½ = 2/2

2/2 = 1

• Could we eat more than 0 and less than ½ of a Hershey bar?

• Break ½ into 2 EQUAL PARTS.• How many EQUAL PARTS of this size does it take to make a WHOLE Hershey bar?

• Write your fraction on another piece of paper.• “1 EQUAL PART /4 make a WHOLE”

2/40/2 2/2

How come 1/2 and 2/4 are in the same place?

• Let’s put ¼ on the NUMBER LINE to show that a fraction is JUST A NUMBER.

See, it’s just a number!

1/4 3/4 4/40/4

4 fourths make a whole.¼ + ¼ + ¼ + ¼ = 4/4

4/4 = 1

• Could we eat more than 0 and less than 1/4 of a Hershey bar?

• Break 1/4 into 3 EQUAL PARTS.• How many EQUAL PARTS of this size does it take to make a WHOLE Hershey bar?

• Write your fraction on another piece of paper.• “1 EQUAL PART /12 make a WHOLE”

1/4 2/40/2 2/2

• Let’s put 1/12 on the NUMBER LINE to show that a fraction is JUST A NUMBER.

3/4 4/40/4

• Sample 1/12 of your Hershey bar• Sample as necessary for energy

Gr. 3 Act. 2 ‐ Coloring Fractions

• Take out one piece of plain white paper.• Color 1/4 of it blue, 1/8 of it green, 1/2 of it red, and 1/8 of it yellow.

Cool Idea ‐ Folding Thirds

• Partitioning into thirds, particularly with circles, can be quite difficult.

• Practice with folding AND estimation drawing.• (.docx)

Gr. 3 Act. 3 –Human Fraction Number Line

• Stand in a circle with plenty of space between you and your neighbor.

• When I say go, walk quickly to get the first fraction card (.docx) you find and work with your team make a human number line.

•GO!

Gr. 3 Act. 4 –Create a Number Line

Gr. 3 Act. 5 –Discover Equivalent Fractions (.docx)

• Fraction equivalence with fraction plates• Paper, card stock, or plastic• Discovery with a study guide

Fourth Grade

• 4.NF.1‐7• 4.MD.5.a• Pre‐requisite: know multiplication facts• Build equivalent fractions; compare fractions with UNLIKE numerators OR denominators

• Add and subtract fractions with LIKE denominators

• Multiply fractions times whole numbers• Fraction 10ths and 100ths as decimals

Gr. 4 Act. 1‐ Fraction Chain

• 1. Using the paper clips, attach cards with numbers 0, 1, 2, 3, and 4 in the correct position.

• 2. Now attach the cards that show 2 EQUAL PARTS make a WHOLE.

• Did you have to change anything?• 3. Now work on the rest of your cards. You’ll notice that there are also some mixed numbers.

Gr. 4 Act. 2 – Closest to 1

• Play against your face partner.• Roll the die twice for each turn.• Using the two numbers you roll in any order, make a fraction closest to 1.

• The student that is closest for each turn gets a point.

• First student to 5 wins.• Change partners.

Gr. 4 Act. 3 – Follow the Leader

• Using the tiles on your desk, work with your group to create a design that is ½ red. Use at least 8 tiles.

• 2 minutes• Are they all the same?• Why not? What’s different?• How did you decide what to do to create your pattern?

• Work with your shoulder partner to complete cards A‐H (packet), in that order.

• Copy each design on a piece of 1‐inch graph paper (packet) so you are ready to present it to the class. Make sure you write the card letter on it.

• Questions for presentation:• What did you do to complete your task card?• Does this fit the directions?• Prove it.

• Extension:• Create your own task cards.• Your designs must use 24 total tiles.• Double check that your instructions work BEFORE you write it on the card.

Gr. 4 Act. 4 – What Fraction?

• What fraction of my design is blue?

Gr. 4 Act. 4 – What Fraction?

• Use pattern blocks to make your design and color it on your pattern block triangle paper (packet).

• Write a question for your neighbors to answer: “What fraction of my design is (color)?”

Gr. 4 Act. 5 – Number Talks

• Which is greater: 5/8 or 3/8? Why?

• Which is greater: 2/3 or 2/8? Why?

• A couple of times a week; progressively more difficult

Gr. 4 Act. 6 – Show Your Fractions

• Take 3 colored fraction strips.• Cut each strip into equal parts that are

1/8 of the whole.• How many equal parts does it take to make the whole?

• On your desk, show your shoulder partner 1/8. Using “Fractionese”, explain why it is 1/8.

• Have students show other amounts and explain.

Gr. 4 Act. 7 – Fraction Relays (packet)

• Form relay teams of 3.• There are 4 different races.• For each race, find which fraction of the race each teammate will run. You can only hand off the baton at the specified marks, but you do not all need to run equal distances.

• Find as many options you can for each race and decide which will be best for your team.

Fifth Grade• 5.NF.1‐7• 5.NBT.1‐4• 5.MD.2• Add and subtract fractions with UNLIKE denominators

• Multiply fractions by fractions• Divide whole numbers by fractions OR fractions by whole numbers

• Estimation and reasonableness of X and ÷• Fraction 10ths, 100ths, and 1,000ths as decimals

Gr. 5 Act. 1 – Lasagna Feast

• We had lasagna last week for dinner at my house.

• My family ate 1/2 of the pan for dinner.

• My son ate 1/3 of the pan for breakfast.

• How much did we eat all together?

• Maybe we need some background information.

• Would you agree that 9 + 7 = 10?• Would you agree that 3 apples + 5 oranges = 8 apples?

• What’s the problem here?• We need common units!

• Now back to our lasagna feast. If we cut the whole dish into 2 equal parts, my family ate 1 of those parts.

• If we cut whole dish into 3 equal parts, my son ate 1 of those parts.

• Adding those together is like adding apples and oranges!!!

• We need some common units, so let’s slice this thing 2 ways. First in 1/2.The family ate this part.

Now let’s cut it the other way into 3 equal parts.

If the whole lasagna were still there, how many equal parts would there be?

• Those 6 equal parts are the common units!

• The family ate 3/6 or 1/2.

• My son ate 2/6 or 1/3.• How much did we eat all together?

• This is a great hands‐on activity with brownies.

Gr. 5 Act. 2 – Running the Track

• Today we are going to run on the track at P.E..• The track is 3/4 of a mile long.• We are going to run 2/3 of the track today.• Estimate: more or less than 1 mile?• How much of a mile will we run today? Prove your solution with a model.

• How many laps will we need to complete to run 2 miles next Friday?

Gr. 5 Act. 3 – Ice Cream Party (packet)

• Connects 4th grade whole number X fraction to 5th grade fraction X fraction

• Estimation is KEY for multiplication and division sense

• Show area models

Gr. 5 Act. 4 – Cupcake Chef

• You have a recipe for 30 cupcakes (.docx), but you only need 10. You are going to give the leftover ingredients to 2 of your friends so they can cook their own little batch.

• Re‐write the recipe for 10 cupcakes.

How can teacher‐leaders help?

• Spread the word among your grade‐level colleagues.• Form a team for school/district vertical articulation.• Follow‐up, follow‐up, follow‐up.• Stress common use of fraction (and decimal) vocabulary: equal parts, whole, equivalent, “fractions are numbers”

• Don’t underestimate the power of estimation.• Understanding concepts is important for learning, but don’t forget the PRACTICE. Fluency builds confidence!

Jason Chamberlain

• jchamberlain@caruthers.k12.ca.us

DisclaimerThe National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring equitable mathematics learning of the highest quality for all students. NCTM’s Institutes, an official professional development offering of the National Council of Teachers of Mathematics, supports the improvement of pre-K-6 mathematics education by serving as a resource for teachers so as to provide more and better mathematics for all students. It is a forum for the exchange of mathematics ideas, activities, and pedagogical strategies, and for sharing and interpreting research. The Institutes presented by the Council present a variety of viewpoints. The views expressed or implied in the Institutes, unless otherwise noted, should not be interpreted as official positions of the Council.

Fraction Ghostbusters.pptx [Read-Only] · Fraction Ghostbusters. ... 3‐5 NUMBER AND OPERATIONS...

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