Math-4-Parents Fall Workshops

K-4

Central School Tammy Fisch, Math teacher

October 2014

• Discuss math content, language, and teaching methods

that are being used in classrooms today

• Increase understanding of why our children are

learning various strategies

• Explore hands-on math activities using manipulatives

• Discuss games and activities to do at home to support

mathematical thinking

Kindergarten Overview

• Know number names and count to tell numbers of objects.

• Compare groups of objects, up to 10

• Fluently add and subtract within 5

• Add within 10 using objects or drawings

• Decompose numbers to 10 into pairs in more than one way

• Developing understand of addition and subtraction, and strategies for addition and subtraction within 20

• Developing understanding of whole number relationships and place value, including grouping tens and ones

• Developing understanding of linear measurement and measuring lengths as iterating length units

• Reasoning about attributes of, and composing and decomposing geometric shapes

1st Grade Overview

Daily Routines:

Building Number Sense

• Count days of school: 10 frames, place

value bundles

• Calendar

• Quick Images, Rekenreks

Some

students may

know that this

frame has 5! 5 6, 7, 8

Represent

numbers

flexibly

Number Bonds

• Number bonds help students see that numbers

can be "broken" into pieces to make computation

easier.

• Children experience multiple ways to

decompose the same number, rather than

memorizing.

• The part/part/whole mat and concrete practice are

used a LOT! This helps little ones really

understand how addition and subtraction are

related.

•Students can find combinations in a

systematic way by sliding one bead at a

time from one side to the other.

•Notice the part/part/total relationship

shown on the bracelet.

•Students should verbalize each

combination (0 and 3 make 3, 1 and 2

make 3, etc.).

• 1st graders begin learning their basic addition facts and apply that knowledge in a strategy known as "make a ten”.

• This helps make sense of facts that might otherwise be hard to memorize, such as 8 + 4 or 9 + 5.

• Students decompose one of the addends to make a ten from the other. In the example pictured below, the 4 is decomposed (split) into 3 and 1. The 3 is combined with the 7 to make 10, and then the 1 is added for 11.

The Power of 10

Understanding the

Problems

•What is happening in the story?

•Can you tell the story without numbers?

•Visualize/act out the story.

•Draw or use manipulatives to show what

is happening.

Part-Part-Total Models

There are 8 juice boxes on the

table. Some children drank

their juice. Now there are only

5 juice boxes. How many

juice boxes were taken from

the table?

Kate and Nana baked some

cookies. They made 2 heart

cookies and some square

cookies. They baked 8

cookies altogether.

How many square

cookies did they bake?

Let’s take a peek!

2nd Grade Overview

• Extending understanding of base-ten (place value)

• Building fluency with addition and subtraction

• Using standard units of measure

• Describing and analyzing shapes

Developing Place Value

Understanding

Students practice

counting & creating

“bundles” and

then represent numbers

in expanded form.

100 + 100 + 10 + 10 + 10 + 1 + 1 + 1 = 243

200 + 30 + 3 = 243

Stages of Representation

Concrete - Pictorial - Abstract

399 jars of baby food are sitting on the shelf at the

market. Some jars fall off and break. 389 jars are

still on the shelf. How many jars broke?

Read-Draw-Write

1.

2.

Concrete - Pictorial - Abstract

Ben and his dad have sold 60 chocolate chip cookies at the school

bake sale. If they baked 100 cookies, how many cookies do they

still need to sell?

Samantha is helping the teacher organize the pencils in her

classroom for the teacher. She finds 41 yellow pencils and 29

blue pencils. She threw away 12 that were too short. How many

pencils are left in all?

Lisa solves 166 – 48 vertically on her place value chart.

Explain what Lisa did correctly and what she needs to

fix.

The correct answer is not enough.

How you get the answer matters, too!

Hundreds 100’s Tens 10’s Ones 1’s

Use math drawings to

represent additions with

up to two compositions

and relate drawings to a

written method.

As students write

addition problems

vertically and make math

drawings, they are

reminded to be precise

in aligning the digits and

in drawing their dots in

neat

5-groups.

3rd Grade Overview

• Developing understanding of multiplication and division and strategies for multiplication and division within 100

• Developing understanding of the structure of rectangular arrays and of area

• Developing understanding of fractions

• Describing and analyzing two-dimensional shapes

The use of the rectangular bars and the identification of the unknown quantity with a

question mark help students visualize the problem and know what operations to perform—

in short, viewing all problems from an algebraic perspective beginning in early elementary

grade levels.

―drawing a picture‖ usually this entails drawing objects, animals, or counters. It is not very

efficient when you move to larger numbers. When you use bar modeling, students learn to

represent these objects with rectangles that enable them to see the number relationships,

rather than focusing on the objects of the problems. Rectangles are used because they are

easy to draw, divide, represent larger numbers, and display proportional relationships.

Tape Diagrams or Bar Models

There are 21 fish in a bowl. Fifteen are from a

student. The rest are from the school. How

many are from the school.

Grant buys 345 fruit bars. Ken buys 230 more

fruit bars than Grant. How many fruit bars does

Ken buy?

Read-Draw-Write

Red, orange, and blue scarves are on sale for $4 each. Nina buys 2 scarves of each color. She also buys a hat that costs $4. How much does she spend altogether?

Arrays

7 x 5 = ( 5 x 4 ) + ( 5 x 3 ) 35 = 20 + 15

Commutative Property of Multiplication states that changing the order of factors does not change the product. Four groups of 2 is the same as two groups of 4, but one is more efficient. Students begin to apply this property when solving multiplication problems.

2 x 4 = 4 x 2

4 + 4 = 2 + 2 + 2 + 2

Distributive Property of Multiplication states that the product of a number is equal to the sum of the individual products and the number. I can use the distributive property to solve multiplication problems I don’t know more efficiently.

8 x 8 = ?

(8 x 4) + (8 x 4) = ?

32 + 32 = 64

4 sixes

2 sixes

2 sixes

4 x 6 4 groups of 6

2 sixes + 2 sixes = 4 sixes

2 x 6

4 x 6

2 x 6

( 2 x 6 ) + ( 2 x 6 ) = 24

Number Bonds

Area of Figures The tile floor in Brandon’s living room has a rug on it as shown below. How many square tiles are on the floor, including the tiles under the rug?

4th Grade Overview

(1) Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends;

(2) Developing an understanding of fraction equivalence,

addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers;

(3) Understanding that geometric figures can be analyzed

and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

Jennifer texted 5,849 times in January. In February , she texted

1,263 more times than she did in January. What was the total

number of text messages that Jennifer sent in the two months

combined? Explain how you would check the reasonableness of

your answer.

Word Problems & Tape Diagrams

X and ÷ by 10

1‖

1‖ 1‖ 1‖

“ ___ times as many”

A rectangle is 1 inch wide. It is 3 times

as long as it is wide. Use square tiles to

find its length.

The basketball team is selling t-shirts for $9 each. On Monday, they sell 4 t-

shirts. On Tuesday, they sell 5 times as many t-shirts as on Monday. How

much money did the team earn altogether on Monday and Tuesday?

Multiplication Models

•Students learn to decompose numbers into base ten units in order to find

products of single-digit by multi-digit numbers.

•Students use the distributive property and multiply using number disks to

model.

•Students bridge partial products to the recording of multiplication via the

standard algorithm.

Division Models

• Students represent division with single-digit divisors using arrays

and the area model, followed by the place value disks.

• The standard division algorithm is taught using students’

knowledge of place value, decomposing unit by unit.

Why Does the Algorithm Work?

Emma takes 57 stickers from her collection and divides them

up equally between 4 of her friends. How many stickers will

each friend receive? Emma puts the remaining stickers back

in her collection. How many stickers will Emma return to her

collection?

Algorithm – step by step

• Supporting work habits instead of work – What is the question asking? – What information do we need to solve? – What is a reasonable answer? Why? – What steps do we need in order to solve the problem?

• Don’t provide too much support. Homework is an important assessment tool for the teacher.

• Provide tools to help your child solve problems.

• Focus more on the why and how than simply getting the correct answer.

Providing Support at Home

• Count everything!

• Play games

• Talk about math

• Talk about our thinking

• Explain why something works

• Explore new ideas and make generalizations

• Take a risk, It’s OK to make a mistake and struggle!

How can we bring math

into our children’s worlds?

It’s the questions that

drive mathematics.

• Encourage them to explain their thinking.

• By expressing wonder and amazement at what they are figuring out!

• “Can you show me how you got that answer?”

• “How do you know? Can you show me?”

• “Interesting, can you prove it?”

• “Do you think it will always work?”

• “What do you think it would look like if we put it on paper?”

Educate Yourself

Math Module Parent Letters

Play, Play , Play!

Math Resources

Central School homepage Support Services Math AIS

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