When Austin solved his math problem on the number line, he was counting up. He started at a certain number, and he counted up 4 more. When he stopped, he was at a number greater than 20. What three different numbers could he have started at?

How are addition and subtraction related?

What strategy do you use when solving 34 + 2 = and 75 - 2 = ? Explain your thinking.

About the Math

Students need to see that when they count 2 more or 2 less, they are actually adding 2 and taking away 2. At first, students may identify this with counting instead of the relationships between numbers. We want students to see that 7 is two more than 5 and that 8 is two less than 10. These relationships need to be developed through representation of the sets. Dot plates, calculators, part-part whole models can all be used to represent these relationships. Essential vocabulary for this standard includes: addition, subtraction, count on, and count back(online dictionary, HCPSS Vocabulary Cards).

The Illustrative Mathematics task below demonstrates expectation for this standard.

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

1. Counting On with Counters (Van de Walle, K-3, p 41). Give Each child a collection of 10 or 12 small counters that the children line up left to right on their desks. Tell them to count four counters, then push them under their left hand. Then say, "point to your hand. How many are there?" (Four.) "So let's count like this: f-o-u-r (pointing to their hand), five, six, ... Repeat with other numbers under the hand.

Other Teaching Student-Centered Mathematics K-3 Activities include:
Van de Walle, K-3, Activity 2.7 "Real Counting On" page 41
Van de Walle, K-3, Activity 4.1 "One/Two-More-Than Dice" page 100
Van de Walle, K-3, Activity 4.3 "Lotto for +1/+2" page 100

Rich Problems:
Create a set of dot plates with representations of numbers from 1 to 10. Flash a plate up and ask students to show you a set that is two more and/or two less than the number represented. Depending on the level of the students, they can use counters or digit cards to show the number. Counters on an overhead or document camera can also be used as the vehicle for the representation of the number. Give students a four function calculator and ask them to show the number on the calculator. Use prompts such as show me the number that is 2 more than 6.

Journal Prompt:

I subtracted one number from another and got a difference of two. What might the two numbers be?

## Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

(Associated with 1.OA.5, Qtr 1)

(Associated with 1.OA.5, Qtr 1)

(Associated with 1.OA.5, Qtr 1)

(Associated with 1.OA.5, Qtr 1)

Increasing Rigor

Students need to see that when they count 2 more or 2 less, they are actually adding 2 and taking away 2. At first, students may identify this with counting instead of the relationships between numbers. We want students to see that 7 is two more than 5 and that 8 is two less than 10. These relationships need to be developed through representation of the sets. Dot plates, calculators, part-part whole models can all be used to represent these relationships. Essential vocabulary for this standard includes:About the Mathaddition, subtraction, count on,andcount back(online dictionary, HCPSS Vocabulary Cards).The Illustrative Mathematics task below demonstrates expectation for this standard.

## Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

Other Teaching Student-Centered Mathematics K-3 Activities include:Van de Walle

,K-3, Activity 2.7 "Real Counting On" page 41Van de Walle, K-3, Activity 4.1 "One/Two-More-Than Dice" page 100

Van de Walle, K-3, Activity 4.3 "Lotto for +1/+2" page 100

Rich Problems:Create a set of dot plates with representations of numbers from 1 to 10. Flash a plate up and ask students to show you a set that is two more and/or two less than the number represented. Depending on the level of the students, they can use counters or digit cards to show the number. Counters on an overhead or document camera can also be used as the vehicle for the representation of the number. Give students a four function calculator and ask them to show the number on the calculator. Use prompts such as show me the number that is 2 more than 6.

I subtracted one number from another and got a difference of two. What might the two numbers be?Journal Prompt:Print Resources:Brain Compatible Activities

for Mathematics K-1

(9-11)

Math Intervention:

Building Number Power K-2

(100-103)

Number Sense 1-2

(75)

Mastering the Basic Math Facts

in Addition and Subtraction

(31-50)

(1-3, 4, 5, 6, 7, 8)

Web Resources:Games and CentersLessonsStudent ResourcesVideo SegmentsShow One MoreShow One LessOne More on the 10 FrameOne More/One Less Scoop

Online Games

The Counting GameMath Magician

Frogs On a Logs

Counting Back and Counting On

Counting On

How Many More?

How are The Different?

Is it Addition or Subtraction?

Lesson Seeds

Splendid Subtraction Activities

Monster Musical Chairs

The Very Hungry Catepillar

(Michelle Glenn, CLES)

Connecting Children's Literature:Mouse CountBy Ellen Stoll Walsh

## Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.Use and Sharing of HCPSS Website and Resources:Howard County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.