Math Continuum: Addition and Subtraction - Session 1

The session, Math Continuum: Addition and Subtraction - Session 1, was presented online on Tuesday, November 5th.  This online session was presented by Heather Wark (Lakehead University), Samantha VanHooft, and Alicia Schenck (LKDSB Instructional Coaches).  

The continua referenced are:

- Addition and Subtraction Continuum by Dr. Alex Lawson, Lakehead University

Children should learn their number facts. However, they would benefit from learning these facts by using an increasingly sophisticated series of strategies rather than by jumping directly to memorization.
- (Lawson, 2016, p. 4)

Strategies help students find an answer even if they forget what was memorized. Discussing math fact strategies focuses attention on number sense, operations, patterns, properties, and other critical number concepts.
- (O’Connell & SanGiovanni, 2011, p. 5)

Strategies Include:
- Counting 3x
- Counting on/back
- Counting on from larger #

- Direct modelling vs. Tracking  

Join us for the next sessions that will dig into the strategies:

Thursday, November 7  3:45	Multiplication & Division 2 Online location: https://zoom.us/j/762357173
Tuesday, November 12 3:45	Addition & Subtraction 2 Online location:  https://zoom.us/j/323581620
Thursday, November 14 3:45	Multiplication & Division 3 Online location:  https://zoom.us/j/308551586
Tuesday, November 19 3:45	Addition & Subtraction 3 Online location:  https://zoom.us/j/522244692

Math Activity to Teach Counting On: Piggy Bank Wars

Math Game: Piggy Bank Wars

Strand: Number Sense and Numeration, Addition
Math Strategy: Counting On

Video French:

Video English: 

Materials: 
• 1 deck of cards with 10, J, Q and K removed
• counters
• 2 cups
• 2 players

Overview: 
In this twist on the classic War game, students work to find the difference in value between the two cards that are drawn. They are deepening their understanding of the part whole relationship and developing the counting on strategy, as they count on of from the lower card until they reach the value of the higher card. Students use counters to represent the difference.
How this Supports Student Learning: 
Students are able to practice the counting on strategy in this game. Through this activity they construct their understanding of part whole relationships as they recognize the higher value card being the “whole”, the lower card being one “part” and the difference being another “part”. This game supports students in moving from counting all, or counting backwards into counting on.

Reflection & Consolidation
Which questions might you ask students to help connect their learning and consolidate their understanding?

Where to next?
For students that require more practice to master the counting on strategy activities like Salute, Riddles with Tiles and Dots and Number Dice provide excellent opportunities to strengthen this strategy. Once the student has mastered this strategy they are ready to begin playing games that promote the use of the 5 and 10 anchor, like Go Fish to Ten, Steal the Bundle and Make 10 Concentration.

Math Activity to Teach Using Known Facts / Familiar Facts: Salute

Math Activity: Salute

Strand: Number Sense and Numeration, Addition & Multiplication
Math Strategy: using known facts; using familiar facts

English:

French:

Materials: 
• 1 deck of cards with 10, J, Q and K removed
• A math tool to help solve the problem (rekenrek, counters or square tiles)
• 3 players

Overview: 
In this game students work to find the “missing part” or value of the card on their head. Students take turns being the “sum finder”, adding up the value of the two cards and shouting out the sum. Each student needs to use the part they see (the value of the card on the other players forehead) and the whole to determine the value of the card on their forehead. After each turn the players rotate their roles by one so that each player has a chance to be the sum finder or to find the missing part.
How this Supports Student Learning:
Students are able to practice a variety of math strategies through this game. Students can find the missing part by counting on, making ten, using doubles or familiar facts. In this game, each player could be practising a different strategy. Having a math tool nearby will support students in solving the problem.

Where to next?
For students that are developing their ability to join numbers, removing all cards greater than 5 may be helpful. As students become comfortable finding the missing part you can increase the complexity of the game by adding higher value cards, eventually including 10 - K, and assigning a value to each card. Alternately you can refer to each card as a decimal tenths. For example if player 1 draws a 7 and player 2 draws a 4 the sum finder would call out “1 and 1 tenth”. In order for the “part finders” to win the round they must refer to their card as a tenth (I.e.7/10 or 2/10 in this case).

Where to Next: Moving from "Counting 3 Times" to "Counting On"

Student Work Sample Video: Where to Next For This Student?

Strategy Being Used: Counting Three Times

Counting Three Times - Explanation Video

More 'Counting Three Times' info in the blog post.

In the student work video, the student created a model to represent a balanced equation. When she composed each side of the balanced equation she counted each part individually and then recounted all cubes, starting at one, to find the total. This is called counting three times.

She modelled both numbers in the equation using cubes. She counted out 3 black cubes to represent the 3, and 6 yellow cubes to represent 6.

Where To Next: Consider the Continuum from 'What to Look For' by Alex Lawson

Where to Next? Counting On 

Looking at the continuum on page 4 of the What To Look For text by Alex Lawson, we can see that a possible next step should be counting on. This would be a more efficient strategy for the student as she would not have to count one "part" of the equation. A student using this strategy select one of the numbers and would count up from it. For example; start at 3 and count on 6.

'Counting On' - Explanation Video

More 'Counting On' info in the blog post.

Activities to Get You There:

When developing questions to support your students using the strategy of counting on keep one of the numbers small, to encourage success. A great activity to get started with reinforcing counting on is Dots and Numbers Dice, found on page 163 of the What To Look For text. Other activities include Real Counting On, Hide the Counters, Missing Part Cards, Piggy Bank Wars, Riddles with Tiles, Salute and Snakes and Ladders

Math Strategy: What is 'Counting On'?

What is Counting On?

Math Strategy: Instead of counting all when combining two values the student begins counting at one of the given numbers and continues to count on until they have counted as many as the second number.
Math Strand: Number Sense and Numeration



Overview: 

 Counting On is a mental math strategy to use for addition. Students could be encouraged to start using this strategy once they are joining two numbers and Counting Three Times (add link). Counting On is being able to "hold" a quantity in their head and then add on to it. Students start with one of the addends and count on by ones until the second addend is reached. Once the student has grasped counting on then the next step would be to focus on efficiency with this strategy which leads into counting on from the larger amount and identifying that Counting On is only effective if your adding 1, 2, 3, 4 to a number (no higher amount).

How this supports student learning:
Being able to start counting at any number is important because it shows how well a student understands numerical order. For example, when a student adds 7+5, some students have to rote count to 7 and then begin counting on. Also, the Counting On strategy reinforces the commutative property of addition where a pair of numbers can be switched around without changing the result, for example, 5+7=7+5. This strategy puts them on the road to more efficient strategies.



Where to next?
You can reinforce the Counting On strategy by using a variety of manipulatives such as dominoes, linking cubes, ten frames, and number lines. Counting On activities can be found in the texts, "Number Talks" by Sherry Parish and "What to Look For" by Alex Lawson, specifically on page 162. (Copies of this book will be available in all schools shortly.)

Share your classroom experiences with Counting On with us on Instagram and Twitter at @LKelempro #EngageLK!