Fractions and Decimals Grades 2-5 MSP Nov. 16 and 18 KCS

Winning the Cereal Prize A brand of cereal has Loony Tunes figurines inside each box. There are six different figurines available to collect. How many boxes of cereal should you buy in order to collect all six figurines? How did you arrive at your answer? How could you "model" or "simulate" this experiment?

Winning the Cereal Prize Here is a dice... how could we model this situation? What would each number dice represent? Model and keep track of how many rolls (boxes) it takes to get each figurine. Repeat the experiment three times. Do your results change? Why? Graph the number of figurines in each box afterwards.

Winning the Cereal Prize What did you find? What math concepts were embedded in the task?

Fractions Grades 2-5

Funky Cookie Task Using 1 of each of the 6 different pattern blocks on your table, create a "Funky" Cookie using these rules: 1. They have to share at least a side 2. You need to use all the different pattern blocks.

Funky Cookie Task After you have made your cookie, can you share it equally among: 2 people 3 people 4 people

Building your own Funky Cookie Can you build a funky cookie that you can share equally among: 2 people? 3 people? Can you make a cookie using 3 different types of pattern blocks? Can you make a cookie using 4 different types of pattern blocks?

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Article Discussion Questions By doing this activity with students, what topics can be discussed or unpacked with your students? What are some questions that you could pose to students to facilitate the discussion of this task? What misconceptions could you see students having with this task? How could you help students address those misconceptions?

Fractions across grade levels List fractions topics that are covered in elementary school. Put grade levels by each of the topics. Put stars by the topics that are "really hard" for students. Put dots by the topics that are "somewhat hard" for students. Put hyphens by the topics that are "somewhat easy" for students.

Need help? Finding parts of a group (set model) (e.g., 1/3 of 24) Splitting a region into equal parts (area model) (e.g., rectangles) Number line models Sharing equally without remainders Sharing equally with remainders Even and odd numbers Splitting (decomposing) shapes into smaller shapes Adding and subtracting fractions with like denominators Adding and subtracting fractions with unlike denominators Probability as a fraction Reading Decimals Converting fractions <--> decimals Adding/subtracting decimals Multiplying decimals

Similarities/Differences Grade K Grade 1 K.N.4 Share fairly (equipartition) collections of up to 10 items between 2 or 4 people, and reassemble.  Common Core Compose 2d shapes out of smaller shapes (6.g) 1.N.4.1  Understand that a region or set must be divided into equal parts of the whole and when reassembled recreates the whole.   Common Core Compose 2d and 3d shapes (listed) and compose shapes from composite shapes (2.g)  Partition (split)  circles and rectangles into 2 and 4 equal shares and use vocabulary (3.g) Similarities/Differences

Similarities/Differences Grade 2 Grade 3 2.N.3  Understand the concept of division as fair shares (equipartitioning).  2.N.3.1  Illustrate division by making equal sized groups using models. 2.N.3.2  Interpret verbally the share as “1/nth of the whole” and the whole as “n times as much" as the share.  2.N.3.3  Understand the relationship between the size of a fair share (of a set or of a single continuous whole) and the number of people sharing (compensatory principle). Common Core Standards  Partition circles/rectangles in 2, 3 or 4 shares and use vocabulary; same size does not mean same shape (3.g) Model fractions concretely using various representations. Compare and order fractions using representations. Model and describe common equivalence within families Understand and use mixed numbers and their equivalent fraction forms. Understand that fractions exists between zero and consecutive whole numbers. Fraction families of focus: (½, 1/4, 1/8) (1/3 & 1/6) Similarities/Differences

Similarities/Differences Grade 4 Grade 5 Everything from 3rd and… Solve problems using models, diagrams, and reasoning about fractions and relationships among fractions. Develop fluency with add/subtracting fractions with like denominators Fraction families of focus: (½, 1/4, 1/8) (1/3, 1/6, 1/12) (1/5, 1/10, 1/100)*** Everything from 4th and… Make reasonable estimates Develop and analyze strategies for adding and subtracting with unlike denom. Estimating sums and differences Judge the reasonableness of solutions. Similarities/Differences

What similarities do you see across grade levels What similarities do you see across grade levels? What gaps exist do you see? Is there one grade level that seems more "top heavy"?

Changing the Whole http://math.rice.edu/~lanius/Patterns/

Equivalent Fractions Find equivalent fractions for: 1/2 2/3 3/7

Equivalent Fractions How did you do to find equivalent fractions? •How can you prove that they are equivalent? –With manipulatives? –With an area model (circle or rectangle) –With an equation? –With words?

Comparing Fractions •Two pizzas are on the counter. The pepperoni pizza is cut into 5 slices. The cheese pizza is cut into 8 slices. •If you take two pieces from the pepperoni pizza and four pieces from the cheese pizza, which pizza has more left? •How do you know?

•What did you to solve the task? Comparing Fractions •What did you to solve the task? •Can you prove your answer with: –A circular shaped pizza –A rectangular shaped pizza –Individual pieces of pizza -A number line  –Cross multiplication (butterfly) –Finding equivalent fractions with common denominators

Comparing Fractions: Student Work For each work sample: What do you notice? What do students' understand? What misconceptions do students have? What grade would you give?

Chocolate Chip Pancakes There are 30 chocolate chips to be distributed among 6 chocolate chip pancakes. How many chocolate chips will be in each pancake? How do you know? How could we model or simulate this situation?

Thursday Night  

Chocolate Chip Pancakes Here is a dice.... Keep track of how many chocolate chips end up in each pancake. Repeat 3 times. Do your results vary? Why?

Sharing Fractions Ideas/Resources What did you bring?

Fractions, Decimals, Percents •Represent each decimal grid as a: –Fraction (in simplest form) –Decimal –Percent

Discussing the Grid Activity •Easiest…. • •Hardest… •What did you need to know to be successful?

Problem #2 •Problem #2 34/80 is the fraction since there are 80 squares and 34 are shaded 34/80 is equal to 0.425 and 42.5% T: “how did you get your answer?” N: “used the calculator and did 34 divided by 80.” T: “anyone do this another way?” Deanna: “multiplying both the numerator and denominator by 10 means the fraction is equal to 340/800 and then divide both by 8. You get 42.5/100 or 0.425 or 42.5 percent. What do these strategies show about both students? How have they used the diagram to support their answer?

Connecting Percents to the Grid •Teacher asks: “Is each of the 80 squares going to be more than, less than or equal to 1%?” •Students shout: “all.” •Teacher asks for explanation •Rashid: “We have 100% to shade across 80 squares, so if each square gets 1% there is still 20% leftover.” •Teacher: “So how much of that 20% does each of the 80 squares get?” •Bonnie: “I think ¼ of a percent since 20 is ¼ of 80.” •Teacher: “So how much percent of the whole grid is in one square?” •Bonnie: “1 and ¼ or 1.25% percent.” What do these students know? How have they connected the diagram to the mathematical concepts?

Sam •Teacher: “So what was Natalie’s answer as a percentage?” •Sam: “42.5 percent.” •Teacher: “How much percent is in one square?” •Sam: “1.25 percent.” •Teacher: “So if 34 boxes are squared what percent is shaded?” •Sam (uses overhead calculator): 34 * 1.25 = 42.5 •Sam: “42.5 percent”

Fraction Track Pick a fraction card from the deck Move a chip or a few chips the equivalent value of the card For example: If you pick 1/2, you can either move: the chip on the 1/2 line a distance of 1/2 OR the chip on the 1/4 line a distance of 2/4 OR the chip on the 1/8 line a distance of ___ eighths? Play the entire game....keep a tally of how many "moves" it takes to move all of your beans.