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GROUP NORMS AND HOUSEKEEPING Logistics: Phone Calls Rest Rooms Breaks Lunch Punctuality Sharing Group Norms: Participate Listen with an open mind Ask questions Work toward solutions Limit side bars

Fifth Grade Big Idea 2 Day 1 Develop an understanding of and fluency with addition and subtraction of fractions and decimals.

Big Idea 2 Benchmarks

Share 3 donuts between 5 people.

When equally shared, each person gets ⅗ of a donut.

Fractions The idea of breaking a whole into parts, sharing the parts, and providing names for those parts is the fundamental concept in the development of fraction knowledge. There are four ways that fractions are used to represent application situations: part of a whole, part of a set, indicates division, and ratio. Extensive research and observational data demonstrate that few students understand fractions. Therefore major changes must be made in the approach to teaching fractions.

1 st meaning: Part/whole: You take the “whole” and split it into equal parts. Example 1: A baseball game has nine innings. Seven have been played. What fraction of the game has been played? Example 2: This class has 19 students. Eighteen are females. What fraction of the class is female? Three Meanings of a Fraction

QuotientImplies “division” Example 1: Pizza for a group of friends: $12 ÷ 3 people (or $ 12/3 each) Example 2: 3 doughnuts, 5 kids. How much of a doughnut does each kid get? How could they do the above? (Different from part-whole splitting) 2 nd Meaning of a Fraction:

Ratio: Conceptually different and doesn’t imply dividing a whole into parts or division. Example.: 1 week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. Weekend days to school days is 2:5 or 2/5. Weekend to whole week is 2:7 or 2/7. 3 rd Meaning of a Fraction:

Fractions—For these problems, circle the greater number of each pair and tell the strategiy you used. Then: Change 5⅔ to an improper fraction, and Change to a mixed number

When the whole numbers are different, you only have to compare the whole numbers. When the numerator is the same, look at the size of the pieces in the denominator. Strategies to Compare/Order Fraction > >

Use benchmark numbers Compare missing pieces Strategies to Compare/Order Fraction > > Think: 3 is less than half of the denominator so the fraction is less than ½. Think: 6 is more than half of the denominator so the fraction is more than ½. Think: 1/8 is missing to make a whole. Think: 1/5 is missing. Since 1/5 is a larger missing piece than 1/8 then ….

Revisit these fractions. Compare the strategy you used previously with one you used this time. Then: Change 5⅔ to an improper fraction, and Change to a mixed number

Comparing Fractions An article by Go Math co-author Juli Dixon, PhD., “An Example of Depth...”.

MA.5.A.2.1 Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties.

MA.5.A.2.2 Add and subtract fractions and decimals fluently and verify the reasonableness of results, including in problem situations.

Models to Add and Subtract Fractions

Manipulatives for Like and Unlike Denominators

Kathy had 2 yards of ribbon. She gave yard of her ribbon to Matt. How much ribbon did Kathy have left? The oval track at the horse race is mile around, but the horses run for 1 miles during the race. What length of the track will the horses run twice? Fractions Stories…

Real-Life Application of Fractions You need exactly 1-cup of water for the dessert you are making. You can only find the cup, cup and cup measuring cups. How many different ways can you measure out 1- cup of water?

Write stories to support the following: 3/4 + 5/8 4/5 - 1/2 1 1/6 + 2/3 Now it’s your turn to tell the story…

MA.5.A.2.1 FCAT 2.0 Test Spec. Item

Why Show Fractions in Simplest Forms? Less pieces and a clearer visualization of the part whole relationship

There were 80 swimming pools at a local store. If of the pools were sold during one hot summer day, how many pools were left for sale after that day? Jose spent of his money on concert tickets. If he had $ to begin with, how much does he have left? Singapore Model Drawing Examples

Answer: B MA.5.A.2.1 FCAT 2.0 Sample Test Questions

MA.5.A.2.3 Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding.

When asked this question, only 24% of 13- year olds and only 37% of 17-year olds could estimate correctly. Consider this concerning data… Estimate +. a)1b) 2 c) 19d) 21

Consider the highly technical paper plate… What else can you show me?What else can you show me? What should I show you?What should I show you? Can we use this for decimals?Can we use this for decimals?

1/2 + 2/5 2/6 + 3/11 2 1/13 + 6/7 3 4/ /3 1 7/8 - 1/2 Estimate the following:

MA.5.A.2.4 Determine the prime factorization of numbers.

Divisibility Rules

How Do We Know They Are Prime? Composite numbers can be placed into varying types of rectangles Prime numbers cannot Let’s look at that…

Composite Numbers

Prime Numbers

Prime Numbers Eratosthenes’ (ehr-uh-TAHS-thuh-neez) Sieve 276 BC BC Eratosthenes was a Greek mathematician, astronomer, geographer, and librarian at Alexandria, Egypt in 200 B.C. He invented a method for finding prime numbers that is still used today. This method is called Eratosthenes’ Sieve.

Eratosthenes’ Sieve A sieve has holes in it and is used to filter out the juice. Eratosthenes’s sieve filters out numbers to find the prime numbers.

Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

Definition Prime Number – a number that has exactly two factors. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

Let’s use a number grid from 1 to 100 to see how prime numbers were discovered.

Remove the number 1. It is special number because 1 is its only factor.

Leave the number 2 and remove all its multiples.

Leave the number 3 and remove all its multiples.

Leave the number 5 and remove all its multiples.

Leave the number 7 and remove all its multiples.

The PRIME Numbers!

GROWING A FACTOR TREE

Can we grow a tree of the factors of 180? 180 Can you think of one FACTOR PAIR for 180 ? This should be two numbers that multiply together to give the Product 180. You might see that 180 is an EVEN NUMBER and that means that 2 is a factor… 2 x  = 180 ? Or You might notice that 180 has a ZERO in its ONES PLACE which means it is a multiple of 10. SO… 10 x  = 180 Or You might notice that 180 has a ZERO in its ONES PLACE which means it is a multiple of 10. SO… 10 x  = x 18 =

We “grow” this “tree” downwards since that is how we write in English (and we are not sure how big it will be. We could run out of paper if we grew upwards). NOW You have to find FACTOR PAIRS for 10 and 18

x 5 = 10 6 x 3 = 18 Find factors for 10 & 18

ARE WE DONE ??? Since 2 and 3 and 5 are PRIME NUMBERS they do not grow “new branches”. They just grow down alone. Since 6 is NOT a prime number - it is a COMPOSITE NUMBER - it still has factors. Since it is an EVEN NUMBER we see that: 6 = 2 x 

Answer: C FCAT 2.0 Sample Test Question

FCAT 2.0 Test Spec. Item

MA.5.A.6.1 Identify and relate prime and composite numbers, factors and multiples within the context of fractions.