Courtesy of Dr. Carrie Cutler

NCTM ConferenceApril 2014

Common Core kinder and 1st Domain: Operations & Algebraic Thinking

K.OA.3 Decompose numbers less than or equal to 10 into

pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

1.OA.6 Add and subtract within 20, demonstrating fluency for

addition and subtraction within 10 by decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9).

Leading to 3rd

3.OA.9 Identify arithmetic patterns

(including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

From the research…

Traditional flash cards or timed tests have not been proven as effective instructional strategies for developing fluency.

Rather, numerous experiences with breaking apart actual sets of objects and developing relationships between numbers help children internalize parts of number and develop efficient strategies for fact retrieval.

Burns. About Teaching Mathematics (2000). Fosnot & Dolk. Young Mathematicians at Work. (2001). Richardson. Assessing Math Concepts (2002). Van de Walle & Lovin (2006). Teaching Student Centered Mathematics

K-3.

Partition a Number

The seven partitions of the number 5:5 + 04+13+2

3+1+12+2+1

2+1+1+11+1+1+1+1

Break-Apart Partners

Term popularized by Fuson and Zantsky (2000)

Pairs of numbers “hiding” inside a number

Break-apart partners for 5 4 and 1 2 and 3

How do we build students’ number sense?

Lots of exploration!

Concrete Pictorial Abstract

Don’t rush to introduce the number sentence or purely symbolic representations for number.

How do we build students’ number sense?

For very young children, focus on

only a single number for the entire activity.

A note about notation

Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.

Break-Apart Stick

Craft stick separates the line of counters into break apart partners.

Break-Apart Baggies

Draw line down middle of ziplock bag.

Place counters inside.

Record the break-apart partners.

Part-Part-Whole Linking Cubes

Part-Part-Whole Plates

Three-section paper platePick a card. Put the corresponding number of counters in the large section of the plate. Explore different ways to move the counters from the large section to the two smaller sections. This shows how the number may be decomposed. It is not unreasonable to expect students to find six or more ways to break apart a number. After lots of exploration, have older children record the break apart partner on paper .

Part-Part-Whole Paper Plates Recording Sheet

Name ___________________________________

A. I picked the number ________________I can think of this number as …

___________ and ___________

___________ and ___________.

___________ and ___________

___________ and ___________.

Part-Part-Whole Paper Plates Recording Sheet

Name McGregor

A. I picked the number 8 I can think of this number as …

5 and 3

4 and 4

6 and 2

1 and 7

Part-Part-Whole Hearts (or any symmetrical figure)

Domino Parking Lot

Place dominoes face down on the table. Students take turns drawing a domino, adding the number of dots on both sides of the domino and placing it in the correct “parking spot” on the mat.

Each person takes ten turns. At the end of ten turns, the person with the tallest stack on any parking spot is the winner.

In and Out

Draw a large circle on paper. Drop manipulatives on the paper. Some may fall in the circle and some out of the circle. Students record how many are in and how many are out.

Bears in a Cave

Each pair of students needs a bowl with 10 bears in it. The bowl is the cave. Player A covers his eyes while Player B turns the cup over and hides bears under the cup. Player A uncovers his eyes and counts how many bears are "out" of the cave. He then determines how many bears must be in the cave. Player B checks the amount by revealing the bears in the cave.

I Wish I Had …I Have… I wish I had …

Hold out a bar of connecting cubes, a dot strip or a dot plate showing 6 or less. Say, “I wish I had six.” Students respond with the part that is needed.

Ten FramesTen Frames

Ten Frame FlashVARIATIONS

Say the number of spaces on the card instead of the number of dots

Say one more or two more than the number of dots

Say the ten fact

Double War with Ten Frames

Both players turn up two ten-frame cards. The winner is the one with the larger total number. Children can use many different number relationships to determine the winner without actually finding the total number of dots.

Difference War

Count out 50 counters. Players each turn over one card as in

War. The player with the greater number of dots wins as many counters from the pile as the difference between the two cards. The players keep their cards. The game is over when the counter pile runs out. The player with the most counters wins.

More and Less Extended

Show a set number of counters. Ask what is 2 more or 1 less, etc. Add a filled ten-frame and repeat the questions. Add more filled ten-frames or take some away.

All Red Number Game

Play with a partner. Each player has ten counters. Turn all of the counters over so that the yellow side is showing. Each player rolls the die and turns over that number of counters to the RED side. Continue until each person has all of their RED sides showing. Then start the game over again.

Recording a number sentence is optional.

3 and 2 3 and 0

Dots and Numbers Memory Turn all cards over on table. Match the numbers card to the correct dot

card.

Snappo

If he can't, he lays his card face up on the table. Players keep taking turns, flipping cards, trying to make 10. A new card that is turned over can be matched with any card to make 10. Any player recognizing a pair that makes 10 can call “Snappo” and take the set. Game ends when there are no matches left. The player who captured the most cards wins.

Play with a partner. Deal Uno cards. Players lay cards face down. Player A flips top card over. Player B flips his card over. If he can make 10, he captures both cards and says "Snappo!"

Go Fish for Sums of Ten

Rules of Go Fish game except players ask one another for the missing addend to complete their sum of ten.

Use playing cards with face cards removed or Uno cards.

The Disappearing Train

With a partner build a train 20 cubes long. One partner rolls the die and removes exactly that number of cubes from the train until there are no cubes left. The other partner keeps a record of how many rolls of the die it takes to make the train disappear. He/she writes a number sentence to show what happens after each roll. Switch rolls and repeat the activity several times.

How Many Ways Number Bracelets

After children have explored the concept

using lots of concrete…

somewhat more abstract but still concept-strong…

Build it in Parts

5 3

2

Number Bonds

Teaching Number Bonds

1. Teach how numbers “go together.” 2. Create addition stories. 3. Create subtraction stories. 5

3

2

3 2

1

+

+

-

-

=

=

=

=

Number Bond Stories

Sentence Frame

There are ______ birds. ________ of the birds are _______ and _______ of the birds are _______.

Symbols-only Practice

7 + 9 8 + 5

6 1 2 3

6 + 10 = 16 10 + 3 = 13

Practice

9 + 6 26 + 8

10 + 5 = 15

Choose a Few for Practice

38 + 7 197 + 6

298 + 4 2,394 + 29

3,495 + 38