Fourth GradeAn Overview of the Second Half

Presented by:

Anthony Forcinito, Math Specialist

Lauren Dunlap, Fourth Grade Teacher

Chatsworth Avenue School

March 3, 2017

Today’s Agenda

What fourth graders need to know

What fourth graders will be doing

What you can do to help your fourth grader

What Fourth GradersNeed to Know

Number, Operations, & Algebraic Thinking

Generalize place value understanding for whole numbers

Add and subtract within 1,000,000

Multiply and divide whole numbers Multiplication: up to 4-digit by 1-digit, and 2-digit by 2 digit numbers

Division: up to 4-digit dividends and 1-digit divisors

Solve multi-step word problems involving the four operations

Number & Operations – Fractions Extend understanding of fraction equivalence and ordering

using visual fraction models

Compare fractions with different numerators and different denominators

Add and subtract fractions and mixed numbers with like

denominators (e.g., 2

8+ 5

8= 7

8)

Multiply fractions by whole numbers (e.g., 5 x 1

4= 5

4)

Understand decimal notation for fractions (tenths and hundredths)

Geometry

Understand concepts of angle and measure angles

Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines

Classify 2-dimensional shapes

Recognize and draw lines of symmetry

Game #1: Connect 4

How to Play Where’s the Math?• Begin by randomly placing the two paperclips

on any two numbers on the number strip.For each round:• Select the number you wish to capture.• Move one of the paperclips on the number

strip to capture the desired number.• Cover the captured product on the game

board with your counter.• Continue until one player has connected 4

squares horizontally, vertically, or diagonally.

• Automaticity with multiplication facts

• Missing factor problems

• Relationship between multiplication and division

• Strategy & planning• Perseverance

What Fourth GradersWill Be Doing

Geometry – Learning the Vocabularypoint

line segment

rayline

parallel lines

perpendicular lines

A

C

B

D

E

I

G

H

K

J

EG II HJ

F

intersecting linesL

M

EG II HJ

Geometry – Measuring Angles

110˚ ?

…with a protractor …without a protractor

110˚

Geometry – Measuring Angles

z = 180 - 90 - 66 = 24

x = 24

y = 180 - 24 = 156

With someone at your table…

Find x, y, and z

Geometry – Shapes and Symmetry

• Identify and classify triangles

• Identify and classify quadrilaterals

• Identify and draw symmetrical shapes

Equivalent Fractions

2

3

8

12

• Students use area models and multiplication/division to create equivalent fractions

2

3=

2 𝑥 4

3 𝑥 4=

8

12

8

12≠2

3𝑥 4 =

Area Model

8

3

Equivalent Fractions• Fractions are also plotted on the number line to find equivalencies

2

3=

Number Line 4

12

0 11

3

2

3

8

12

Tape Diagram

2 𝑥 4

3 𝑥 4=

8

12

Comparing Fractions• Compare fractions with a different numerator but the same

denominator; e.g., 1/8 is smaller than 3/8, because 1 of a certain unit must be smaller than 3 of that same unit

• Compare fractions with the same numerator but a differentdenominator; e.g., 3/8 is smaller than 3/5 because splitting the same whole into eight equal parts would yield smaller parts

Comparing Fractions – Area Models

2

3

3

4

3

4=

9

12

2

3=

8

12

<

Adding Fractions

32

5+ 2

4

5= 3 + 2 +

2

5+4

5= 5 +

6

5= 6

1

5

I can add the parts in any order without changing the sum.

1

5

5

5

Subtracting Fractions

Game #2: Capture Fractions

How to Play Where’s the Math?• Divide the deck into equal-sized piles, one

for each player.• In each round, each player turns over the

top card in his/her pile. The players then figure out which fraction is larger. They may use fractions strips, a number line, or a verbal explanation to prove their thinking.

• The player with the larger fraction puts both cards at the bottom of his/her pile.

• The person with the most cards wins.

• Fractions as numbers• Equivalent fractions• Comparing fractions• Fraction on a number

line

Decimals – An Introduction

5

10

1

10

2

10

3

10

4

10

0

10

6

10

7

10

8

10

9

10

10

10

0.10.0 0.2 0.40.3 0.5 0.70.6 0.8 0.9 1.0

3 tenths = 3

10= 0.3

Decimals

Hundreds Tens Ones Tenths Hundredths

÷ 10 ÷ 10x 10x 10

Symmetry about the ones place

Memorization

Committing the results of operations to memory so that thinking is unnecessary

Isolated problems practiced one after another

Emphasis is on answer recall

Automaticity

Relies on thinking about relationships among facts

Answer produced within a few seconds

Eventually leads to memorization, but with much more meaning

What is Automaticity?

Adapted from: Twomey Fosnot, Catherine & Dolk, Maarten (2001). Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Portsmouth, NH: Heinemann.

What is Automaticity?

9 x 3

I know 10 x 3 is 30, so 9 x 3 must be 3 less

than 30... 27!9 x 3

10 x 3

What is Automaticity?

9 x 3

I know 5 x 3 is 15, and 4 x 3 is 12, so 9 x 3 is

15 plus 12… 27!9 x 3

5 x 3

4 x 3

What You Can Do to Help

Your Fourth Grader

Things You Can Do at Home

Find the math in ordinary activities (cooking, gardening, shopping, home design)

Ask questions strategically Can you tell me how you know that? Can you prove your thinking to me? Is there another way to solve that

problem?

Play board and card games Play some of our school games…

Game #3: Decimals In Between

How to Play Where’s the Math?• Place the cards labeled 0, ½, and 1 on the

table, with space in between each.• Deal 6 decimal cards to each player.• Players take turns placing a card so that it

touches another card in one of these ways:--to the right of 0 --on either side of ½ --to the left of 1 --on top of any equivalent

• Cards must be placed in increasing order, from left to right. A card may not be placed between two cards that are touching.

• Decimal notation• Place value to the

hundredths place• Fraction/decimal

equivalence

Try These Apps!

Addition and Multiplication

Number Bubbles

Try These Apps!

Math Drills

Math Module Parent Letters

Helpful Resources

My Web Page

Reflection

What is one thing that you can commit to doing at home to support the work

being done here at school?

My contact information:aforcinito@mamkschools.org

Please fill out a feedback form on your way out.

Thank You!

Questions?