What’s That Portion? Investigations Unit 4 5 th Grade Math Alliance Meeting Beverly Woods Elementary

What is the Math in this Unit? What do the students need to know before teaching this unit? What understanding should they develop while studying this unit? Think about how this unit addresses the Common Core standards……..

Investigation 1: Using Percents and Fractions 1.1 Everyday uses of Fractions, Decimals and Percents 1.2 Relating Percents and Fractions 1.3 Finding percents of an area 1.4 Percent equivalents for thirds and sixths 1.5 Assessment: Solving problems with fractions and percents

Everyday Uses of Fractions, Decimals and Percents Keep a chart of Conjectures about Fractions… p.48 Unit Guide Make a list of the everyday uses of fractions, decimals, and percents

Relating Percents and Fractions Play “Guess My Rule”

Finding Percents of an Area

Percent Equivalents for Thirds and Sixths 1.How does an understanding of what 5/6 means, help you figure out the percent equivalent???? 2.Which is greater 5/6 or 3/4? How do you know?

Assessment: Solving Problems with Fractions and Percents How many twentieths is one fourth? 1/4 = ?/20 Eleven of what is one fourth? 1/4 = 11/? What if the denominator were 200? 1/4 = ?/200 What if the numerator were 5? 1/4 = 5/?

Investigation 2: Comparing and Ordering Fractions 2.1 Percent equivalent strips 2.2 Comparing fractions 2.3 Ordering fractions 2.4 Solving problems with fractions and percents 2.5 Solving problems with fractions and percents (continued) 2.6 Assessment: Using fractions and percents

Percent Equivalent Strips Fill in halves, thirds, fourths, fifths, sixths and eighths Look at Math Note on p.59- fractions in simplest form or lowest terms- not reduced fractions

Comparing Fractions Which fractions could you compare on the 4 x 6 rectangles? Suppose you wanted to compare 3/5 and 7/12. Which rectangle would you use? Why? How about 3/8 and 1/3?

Ordering Fractions Play the game “In Between”……….

Solving Problems with Fractions and Percents Can 1/4 be greater than 1/2?

Fractional Parts of a Whole If the yellow hexagon represents one whole, how might you partition the whole into equal parts? Name the fractional parts with unit fractions

Fractional Parts of a Whole One blue rhombus = 1 whole What is the value of the red trapezoid, the green triangle and the yellow hexagon? Show and explain your answer

Identifying Fractional Parts of a Whole What part is red? 16

Create the whole if you know a part… If the blue rhombus is ¼, build the whole. If the red trapezoid is 3/8, build the whole.

Investigation 3: Adding and Subtracting Fractions 3.1 Fractions on clocks 3.2 Using a clock to add fractions 3.3 Assessment: Adding fractions 3.4 Fraction Tracks 3.5 Fraction Tracks (continued) 3.6 The Fraction Track Game 3.7 Addition and Subtraction Problems and games part Addition and Subtraction Problems and games part Addition and Subtraction Problems and games part End-of-Unit Assessment

Fractions on the Clock Play “Roll Around the Clock” Use the clock to add and subtract fractions

The Fraction Track Game Play the game to “1” first, and then use the whole board

Homework….. Please bring some samples of student work that demonstrate mastery, partial mastery, and non-mastery of any of the following pages: SAB pp. 21, 24, 26, 33, 40, 48 or M20

What’s Next???? What worked well/what didn’t?? I still need….. A look at student work samples Multiplication and division of fractions

What’s That Portion? Investigations Unit 4 5 th Grade Math Alliance Meeting Beverly Woods Elementary Session 2

Warm Up Problem How many different fraction models can be used to show 5/4? Draw your models!

Was this one of your model types? Understand a fraction a/b as a multiple of 1/b is the product of 5 x ( ) = 5 x

A Look at Student Work What is 1/5 + 2/3? Show your work……

Common Misconceptions when Multiplying and Dividing Fractions »Multiplication does not always make things bigger »Multiplication is not “just” repeated addition »The meaning of “times” 3 x 4 = 4 x 3. Are they the same? (think about groups)

Common Misconceptions continued Translating multiplication expressions like 5 x 6 could be 5 groups of 6 or 5 taken 6 times We need pictorial representations when it comes to fractions!!- the idea of 1/2 taken 1/4 times makes no sense. 1/2 a group of 1/4 makes more sense. If students can connect multiplication equations to real things, it will help them make sense of problems

More Misconceptions… Students shouldn’t be focused on just the numbers, but make sense of the magnitude of the fractions. Example: 3 1/2 x 3 1/2 The answer can’t be more than 4 x 4 or less than 3 x 3. There is a real connection between multiplication and division of fractions (they are not just opposites) Example: 10 x 1/2 is the same thing as 10 ÷ 2

The meaning of each operation on fractions is the same as the meaning for the operations on whole numbers ― X + ÷ For division of fractions, it is useful to think of the operation as partitioning Critical Area: Fraction Operations

Investigation 4A: Multiplying and Dividing Fractions 4A.1: Multiplying a whole number by a fraction 4A.2: Multiplying whole numbers by fractions and mixed numbers 4A.3: Multiplying fractions or mixed numbers 4A.4: Multiplying fractions by fractions 4A.5: A rule for multiplying fractions 4A.6: Using arrays for multiplying fractions 4A.7: Assessment: Multiplying fractions and multiplying mixed numbers 4A.8: Dividing a whole number by a fraction 4A.9: Dividing a fraction by a whole number 4A.10: Assessment: Dividing with fractions

Multiplying a Whole Number by a Fraction The Big Bicycle Race Use of Fraction Bars And Writing Equations

Multiplying Whole Numbers by Fractions and Mixed Numbers Mitch is riding his bike 90 miles. He’s gone 2/3 of the way. How many miles has he gone?

Multiplying Fractions or Mixed Numbers The bike path is 15 miles long. Hannah bikes 2 ½ times the length of the path. How many miles does she bike? Why is this still considered multiplication? (CC p.42) it is still “groups of”

Multiplying Fractions by Fractions Shading fraction bars ½ of ½ Fill in the table…….

A Rule for Multiplying Fractions The rule is easy….Why don’t we just teach them the rule?

Using Arrays for Multiplying Fractions (paper folding) Notice the labeling!!!! 1/8 1/4 1/2

From Paper Folding to the Open Array

Assessment: Multiplying Fractions and Multiplying Mixed Numbers Do students need to use a representation??? Turn and Talk……….(notice Teacher Note on page CC p67)

Another way of looking at multiplying a whole number times a fraction Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number 3 sets of is the same as 6 sets of

Dividing a Whole Number by a Fraction What does 6 ÷ ½ mean? Notice the STUDENT REASONING!!!!!

Dividing a Fraction by a Whole Number Use of the Array again…. ½ ÷ 3 ?

Assessment: Dividing with Fractions Is multiplication or division of fractions harder? Why do you think so? Turn and talk! ( Note the student dialogue on p.CC81) Check out the Teacher Note CC p82

Homework….. Please bring some student work: An example of mastery, partial mastery and non-mastery of either the multiplication or division assessment.

What’s Next???? What worked well/what didn’t?? I still need….. A look at student work samples More multiplication and division of fractions (and also decimals)