Welcome to

5th Grade

math Night!

Samantha Clegg and Jacklyn Gelman

Tonight’s Agenda

� Common Core Areas of Focus� Standards of Mathematical Practice� Conceptual Knowledge + Operational

Skills� Algorithms and do some math� Parent Resources

Self Assessment!

� Take a moment to read each of the concepts listed

� Put an X next to the concepts you feel confident about

5th Grade Critical Areas

� Extending division to 2-digit divisors, integrating decimals into the place value system and developing understanding of all operations with decimals to hundredths.

� Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions).

� Developing understanding of volume.

1.

Standards of

Mathematical Practice

1. Make sense of problems and persevere in

solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the

reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in

repeated reasoning.

2.

Procedural vs.

Conceptual

Understanding

Conceptual Understanding:

Way students show thinking

Ability to justify answers

Understand the “why” behind the process

Procedural Knowledge vs. Conceptual Understanding

Procedural Knowledge:

Find answer using a particular method

Steps to find an answer

Memorization of operations without meaning

Knowing how something happens

“Conceptual understanding in mathematics means that students understand which ideas are

key...and that they grasp the heuristic value of those ideas. They are thus better able to use them

strategically to solve problems – especially non-routine problems…”

Grant Wiggins

“

Education is not the learning of facts, but

the training of the mind to think.

- albert Einstein

3.

Multiplication Strategies

Area Model Multiplication and

Partial Products

15 x 13

Multiplication Flow

Area Model for Multiplication

Partial Products

Basic Multiplication

Facts

Traditional Multiplication

(Conceptually)

4.

Division Strategies

Area Model Division

4

345 / 4

Partial Quotients

1, 385 / 34 1, 385 34

Traditional Division

1, 385 / 5 1, 385- 1 0

38- 35

35- 35

5

277Students are not required to talk through problems

like this each time they solve, only to build

understanding in the beginning!

Division Flow

Area Model for Division

Partial Quotients

Traditional Division

Basic Division Facts

Given someone directions to your house or directions to another location?

When you gave those directions, did you provide the shortcuts you take? Or, did you try to keep them on the main roads since they don’t know the area?

The shortcut may be faster! But, sometimes we have to take the long way until we get to know the area. After a few times in the area, then we’re ready for the shortcut.

Have you ever?

Previously math has been seen as a set of

rules and procedures to memorize in order to

calculate quickly and accurately.

Unfortunately, this eliminated the need to

understand the mathematical relationships

that provide the foundation for the rules.

Throughout 3rd and 4th

grade, students have only

experienced situations where

multiplication creates a

larger product.

5.

Multiplication of

Decimals

Multiplication of

Decimals Flow

Whole number x Decimal

larger than 12 x 1.4

Decimal in tenths x decimal in

tenthsEx: 0.3 x 0.4

Whole number x decimal

2 x 0.4

Decimal x decimal

Ex: 1.3 x 1.4Ex: 4.25 x 3.7

Using the base 10 blocks we can

model multiplication with decimals

The Flat = 1 whole

● Build 2 groups of 1● Build 2 groups of 0.2 ● Build 2 groups of 1.2

Standard of Mathematical Practice # 4

Model with Mathematics!

Multiplication of Decimals

Multiplication of Decimals

0.7 x 0.4

0.7 OF 0.4

2.6 x 1.2

Estimation: 3 x 1 = 3

2 6 x 1 22 0 0 4 0 6 0 1 23 1 2.

Multiplication of

Decimals Algorithm Flow

Visual Models Algorithms ● Partial Products● Estimation with

Partial Products

Base Ten Blocks

Whole number x Decimal

larger than 12 x 1.4

Decimal in tenths x decimal in

tenthsEx: 0.3 x 0.4

Whole number x decimal

2 x 0.4

Decimal x decimal

Ex: 1.3 x 1.4Ex: 4.25 x 3.7

6.

Division of Decimals

Division of Decimals Flow

Decimal in tenths divided by

decimal in tenths0.6 / 0.2

Decimal divided by decimal

2.6 / 1.2

Decimal divide by a whole

number2.5 / 3

Division of Decimals

3 352 . 2 - 3 05 - 3 22 - 21 12 - 12

1 1 7 4

We can use the same traditional division algorithm with decimals!

Estimation = 300 / 3 = 100.

Division of Decimals

0.3 35.22

Why is it that when you divide by a decimal, you can simply just move the decimal?

Standard of Mathematical Practice #3 Construct viable arguments and critique the reasoning of others

Division of Decimals

What patterns do you see? Standard of Mathematical Practice #8

Look for and express regularity in repeated reasoning!

Division of Decimals

0.3 35.22

Now that I know I can multiply both numbers by the same multiple of 10 and get the same quotient, I can use that to make my divisor a whole number!

7.

Multiplication of

Fractions

Multiplication of

Fractions Flow

Multiply a fraction by a whole

number

Multiply a fraction by a

fraction

Multiply a whole number by a fraction

Visual Models

Algorithm Visual Models

Algorithm Visual Models

Algorithm

Multiplication of Fractions

¾ x 1 ¾ x 2Think.. 3/4 of 1 whole

Use the commutative property - we can think of this as 1 group of 3/4 !

Multiplication of Fractions

Fill in the grid to show ¾ of �

Multiplication of Fractions

Fill in the grid to show ¾ of �

Multiplication of Fractions

6/20!

Multiplication of Fractions

3 x 2 = 64 5 20

We really just multiplied the

numerators and denominators!

Connecting Representations

A. ⅔ x ½ B. ½ x � C. � x ⅔

Multiplication of

Fractions Flow

Multiply a fraction by a whole

number

Multiply a fraction by a

fraction

Multiply a whole number by a fraction

Visual Models

Algorithm Visual Models

Algorithm Visual Models

Algorithm

8.

Division of Fractions

Division of Fractions

Connecting visual models to the

inverse operation of multiplication

Learn to multiply by the inverse when dividing

fraction.

Dividing unit fractions and whole

numbers using visual models.

Division of Fractions

Unit Fraction Divided by a Whole Number2 students are going to share ½ pound of candy. What is each

student’s share?

Each student will get 1/4 of a pound of candy!

1/2

Division of Fractions

Whole Number Divided by a Unit FractionMrs. Smith has 2 pounds of chocolate. She is going to sell the chocolate in ½

pound packages at the bake sale. How many packages will she make?

½ lb

½ lb

½ lb

½ lbMrs. Smith will have 4 packages to sell.

Division of Fractions

Whole Number Divided by a Unit Fraction

½ lb

½ lb

½ lb

½ lb

¼ In both situations

we really just multiplied by the

reciprocal

12 2 = 14 2 = 4 1

2

12 = 1

4 12 x 2 x 2 = 4

Division of Fractions

Connecting visual models to the

inverse operation of multiplication

Learn to multiply by the inverse when dividing

fraction.

Dividing unit fractions and whole

numbers using visual models.

Parent Resources

� Math Resources and Tutorials

� Located on any of the school websites!

Post Assessment!

� Turn back to the front page.

� Put a check next to the concepts you NOW feel more confident about!

We’d LOVE your Feedback!

Please fill out the google form using the QR code or website.

THANK YOU!!