Effective Feedback and Math Games

Effective Feedback and Math Games

Playing Math Games lets students actively practice math number strategies and provides teachers with the opportunity to observe, listen to and engage with students while keeping a focus on the math learning goal.

Formative Feedback / Assessment For Learning Feedback
The feedback that we give to students while they play math games would be considered Formative Feedback or Assessment For Learning Feedback (Interchangeable terms).  This feedback, based on the evidence we gather from what students say, do and represent, is used to inform teaching and learning with a view to improving learning.(Black & Wiliam, 2009)

Feedback is effective when it helps students move from where they are in their learning to where they desire to be and gives ways to get there. There is a positive impact on the student’s knowledge and skills.

To help us provide feedback to a student in a way that they can receive and use it, consider the following.

Is the feedback:
• Specific (It tells the student exactly what about that particular task, performance, or
event was positive, and what about that task, performance, or event needs some
adjustment, or is an opportunity for growth.)
• Constructive (It doesn't focus on the individual. It focuses on the task, referring to the learning intentions/goals/success criteria and what is needed to be successful)
• Timely (Knowing the best time to provide feedback.  Research has shown that feedback is best received by the learner when it is oral and when it happens while the learning is occurring, Visible Learning Feedback, Hattie and Clarke).

John Almarode - Effective Feedback Matters from The Learning Exchange (1) on Vimeo.

“Effective Feedback Matters” from The Learning Exchange for more information on feedback.

During Math Games or other active learning, we can gather even more evidence of learning when we ask questions.

 Hattie and Clarke provide teachers with examples. (Questioning by Teachers: Visible Learning Feedback, Page 92)
• Tell me/show me what you have learnt so far.
• Tell me what you’re going to do first.
• What do you mean by…..? (Key question, even if the teacher thinks he/she knows what they mean by it)
• Why do you think…?
• Give me an example of what you mean. (Key question as often reveals misconceptions)
• Can you develop on that? Tell me more…
• So why is this one better than that? (Key question if concrete example available)
• How can you change this to make it clearer?

Christine Suurtamm shares some reflections on how valuable teacher feedback and assessment practices can be on promoting student thinking and learning.

This focus on attending to student thinking appears in many ways in the mathematics education world. One area of focus is called professional noticing which can be defined as “(a) attending to children’s strategies, (b) interpreting children’s understandings, and (c) deciding how to respond on the basis of children’s understandings” (Jacobs, Lamb, & Philipp, 2010, p. 169).

Click here for the full article: Classroom Assessment in Mathematics: Paying Attention to Students’ Mathematical Thinking

When we observe, listen and ask students questions while they play math games it strengthens our understanding of where each student is on their learning journey.  We can then use this insight to provide effective feedback as to what those students need to do in order to close the gap between where they are and the desired learning.  These actions make Math Games a valued part of math learning.

Resource Review: The Water Walker

Lillyanna reviews The Water Walker by Joanne Robertson


The Water Walker is an inspirational book that can be shared with students in any grade. This book was written and beautifully illustrated by Joanne Robertson.



This book tells the true story of the journey of an amazing Anishinaabe woman named Josephine Mandamin. We learn about her quest to inspire others to protect the water and understand the importance of taking care of the water.



Photo: www.motherearthwaterwalk.com

Here are some ways you can use this book in your classroom as it has many curriculum connections.

Building A Community and Honouring Identity

There are lots of local connections to this story. The Water Walkers came to visit and pray for the St. Clair River two years ago. A Detroit News story can be found here:


This video is very relevant because it includes interviews with water walkers from Bkejwanong (Walpole Island). Share this video with your class and find Bkejwanong on a map. Did you know that Bkejwanong is a delta and is actually made up of 6 Islands? Water is incredibly important to the people and wildlife living there. Can your class find out why?

A teacher in Thunder Bay is encouraging teachers and students to step up and join the Junior Water Walkers.



Language: Reading, Writing and Oral Communication, Media

The Water Walker can be used as a mentor text for writing as it uses a strong voice that uses authentic, natural language and striking word choice.

This is a great article from the ETFO Voice magazine about 13-year-old Autumn Peltier, a Water Warrior. It shares her point of view and demonstrates a strong voice. Autumn is a young person with a story and a voice that many students can be inspired by.

The Water Walker can lead to conversations around the boil water advisories on First Nations in Canada

The following can be shared and discussed with your students to initiate conversations and generate questions about water crisis on First Nations.










Science

Looking at the Science Curriculum across the grades, this book would be an excellent conversation starter on stewardship, human impacts on the environment, biodiversity, controlling human impacts on the environment, environmental impacts of a system, and water systems.

It partners very well with the Grade 8 Science Strand of Water Systems:



Social Studies

Investigations may spark Social Studies or Geography inquiry while including Indigenous perspectives. Refer to the revised SSHG curriculum for examples and prompts (found in the brackets).

Strand B. People and Environments

Grade 1: The Local Community

Grade 2: Global Communities

Grade 3: Living and Working in Ontario

Grade 4: Political and Physical Regions of Canada

Grade 5: The Role of Government and Responsible Citizenship

Grade 6: Canada’s Interactions with the Global Community

Grade 7: Physical Patterns in a Changing World

Natural Resources around the World: Use and Sustainability

Grade 8: Global Settlement: Patterns and Sustainability

Global Inequalities: Economic Development and Quality of Life

.Here are some examples inspired by educators.

A teacher in Grade 6 has been able to find global connections to water issues. She talked to her students about water issues in First Nations in Canada and connected them to the issues related to water people in Haiti experience. This was all introduced by a discussion around the UN Declaration of the Rights of the Child which states: All children have the right to clean water.



Mapping Skills:

Students could go to the Water Walker website http://www.motherearthwaterwalk.com/

and map out the walks the Water Walkers have traveled in years past. Students could use Google Street view to see some of the areas the Walkers traveled. They could also use Google to see the First Nations where there are boil water advisories.

Inquiry Questions Directly from the Curriculum

For example, Grade 4 Social Studies:

People and Environments: Political and Physical Regions of Canada B1 and B2
Assess some key ways in which industrial development and the natural environment affect each other.
Investigate some issues and challenges associated with balancing human needs/wants and activities with environmental stewardship.

The Framing Questions for this expectation would allow for some great inquiry:
What impact can human activities have on the natural environment?
What impact can human activities have on the natural environment?
Why is it important to consider the long-term impact of human activities?



Where to Next?
There are so many ways to use this book in your classroom, I could go on for pages and pages about it! If you are using this book in your classroom, please share the great things your students are doing to learn more about the water and what they are doing to take care of our water.

To keep the learning going, investigate the curriculum, for ways to include the Indigenous perspective on other environmental or social issues.

Why Math Games?

Why Math Games?

In Alex Lawson’s book, What To Look For, a selection of math games are provided. The Guides to Effective Instruction also provide Math games.

The intent of math games is to help students to construct an understanding of the mathematical relationship among numbers. The Math Games allow students the opportunity to practice the strategies found on the Addition and Subtraction Continuum and the Multiplication and Division Continuum.

This active math experience will support students’ efficient and fluent recall of the facts which is foundational to their later success in mathematics in higher grades and with real-life applications.

Choosing Math Games: Being Intentional

Assign games for a specific purpose
• Develop a specific strategy
• Become proficient with a strategy
• Recall facts with automaticity

Be mindful of the student’s interest.  When students become bored with a game,
• Revise it to be more challenging
• Switch to a different game

Intentional Groupings
• Pair students who are learning a similar mathematical strategy and are working with the same numbers  (Allows for more math talk)
• Two player games can also be played by teams.  The discussion required “to make a move” promotes math thinking and reasoning

Make Math Games a valued part of the math learning
• Avoid using Math Games as “extras” or “time fillers”
• Use Math Games to promote effective and efficient use of a strategy
• Provide strategic practice time rather than “drills”
• Encourages engagement and community building

Teach the Games
• Model how the game is played “Teacher vs The Class”
• Play the games a few times where the cards can be seen so you can talk about the different strategic actions
• Play as teams first to encourage math talk and strategy talk
• Time to learn each game will vary

Observe and engage in conversations for assessment 
• Asking questions
• Challenge students to justify strategic actions
• Notice and name strategies students are using from the continua
• Encourage efficiency
All of these actions are providing students with “in the moment”,” just right” and “actionable feedback”.

Consolidating the learning after Math Games (Very Important!!)
• Have students describe and defend strategic moves
• Provide examples and counter examples to keep focused on the math thinking and learning
• Have students voice what is needed to be successful with the games
• Model successful strategies for all students to see and learn from

Multiple opportunities with Math Games is necessary for students to try out new strategies to become more accurate and efficient on their way to being proficient with number operations.

More information is available from Alex Lawson’s book What to Look For, Pages 153-154.

Math Activity to Teach Repeated Addition: How Long, How Many?

Math Game:  How Long?  How Many?

Math Strand:  Number Sense and Numeration - Multiplication
Math Strategy: Repeated Addition

English:

French:

Materials: 
Cuisenaire rods, one die, How Long? How Many? Recording Sheets ( MK12, one for each player) and pencil

Overview:
This activity can be found in the Alex Lawson’s “What To Look For” book on page 186.
The goal is to cover as many squares as possible on the recording sheet.  Students will roll a die twice, the first roll tells the length of the Cuisenaire rod and the second roll tells how many of these rods are to be used.  The player places the rods on his or her recording sheet to form a rectangle and traces around the outside.  The game encourages modelling of groups by representing the array and writing the total number of squares that the rectangle covers.  For example, four 3-rods would cover 4 x 3 = 12 squares.  The multiplication equation is written inside the array.  This allows students to double check their answers and helps reinforce multiplication facts by connecting them to a visual representation.

How this activity supports student learning?
How Long? How Many? helps students develop early multiplication facts.  This game supports students understanding of unitizing, which is the idea that objects can be simultaneously viewed as individual objects and as a composite units that can be counted.    Throughout the game, students use direct modelling to solve the problems, such as modeling 3 rows of 4, then counting each square.  Moving beyond counting by ones, children may begin to rhythmically count the rows or they may repeatedly count groups on their fingers. This will then lead to more efficient strategies such as skip counting or repeated addition.



Where to next?
Adaptation:  Depending on the needs of your students, new recording sheets can be created by adding or removing rows or columns of squares.

In the Alex Lawson text, What To Look For there are several other games that can be played to support unitizing on page 185 - 189, such as:
• Circles and Stars
• Skip-Counting Race
• Target 75
• Multiplication Change

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

Math Activities to Teach Using Familiar Facts: Multiplication Tic-Tac-Toe

Math Game: Multiplication Tic-Tac-Toe (Le Morpion de Multiplication)
Math Strategy: Using Familiar Facts
Math Strand: Number Sense & Numeration: Multiplication

English:

French:



Overview:
The goal of this activity is for students to recognize factors of products in front of them so they can begin to identify them more quickly. However, we cannot ignore the importance of providing students the opportunity to use models to help develop meaning for the symbols in operations and to lessen their abstraction. Therefore, before introducing this type of activity, students should have had many previous opportunities to use various objects and materials to help them make sense of multiplication.


How this activity supports learning:
Playing games, like “Tic Tac Toe Multiplication” (Le Morpion de Multiplication), is a great way to support the automatic recall of multiplication facts.

By using a game to reinforce the concept, students will be engaged and this will provide the teacher the opportunity to circulate and have a quick look into where students are having success and what challenges they may be encountering. It also helps us to discover what strategies our students are using and where they are on the continuum of learning. Once we can identify what strategies our students are using, we can help determine a more efficient strategy to help improve that individual's proficiency with multiplication.



Where to next?
Remember to include variations of the game to challenge students appropriately and maintain engagement. This will also provide students the opportunity to develop a strong proficiency with a variety of factors and products. As you circulate, join different students games and don’t forget to ask them to explain how they knew their answer. Having students explain their thinking, not only gives us insight into the strategies they used, but also provides a model for others as to different ways to think about the same problem. The more students share ideas and thinking, the more their learning can progress.

Click Here for the French Game Boards

Share your classroom experiences with “Multiplication Tic-Tac-Toe” with us on Instagram and Twitter at @LKelempro #EngageLK!

Math Activity to Teach Skip Counting: Skip Counting Race

Math Game: Skip Counting Race

Strand: Number Sense and Numeration 
Strategy: Skip Counting 



 Materials:
One 6-sided die with the numbers 2, 2, 3, 3, 4 and 5 (use stickers over the existing numbers)
BLM MK13: Skip Counting Race game board

Overview:
The students (or teacher) determines the number that the students will skip count by, prior to beginning the game. Students roll the die and skip count by the agreed upon number, based on the number rolled. For example; if a student is skip counting by 2 and rolls a 3 they must skip count 3 times (2, 4, 6). The first student to reach 60 wins. 

How This Supports Students Learning: 
This game provides students with the opportunity to develop efficiency by using the skip counting strategy. Students that are able to skip counting can use this strategy when solving multiplication problems. They are also strengthening their understanding of unitizing; recognizing that each time they skip count the value represents a given quantity or set of numbers.

In this game, students begin by skip counting with a friendly number once they master this skill they can move on to another number. Teachers may want students to begin with 5 or 2, moving forward to 3 or ’s. 

For students that are struggling with skip counting, they may rely on counting rhythmically by 1’s, emphasizing every time they have added a unit (1, 2, 3, 4). It may also be helpful to provide the student with an extra copy of the game board and have them use two different colours to record their counting (colour 2 squares red, two squares blue, etc.). 

 

Where To Next:
Once students have developed efficiency with the skip counting strategy, they are able to move towards using repeated addition and doubling strategies. As students are introduced to the repeated addition strategy it may be useful for them to first skip count and then to record their addition sentence above this, in order to make the connection between the two strategies visible.

Additional games to reinforce the concept of skip counting from the What to Look For text by Alex Lawson include Target 75 (page 188) and Array Pattern Flashes (page 194).

  

Math Activity to Teach Using Familiar Facts: Triplets

Math Game: Triplets 

Strand: Number Sense and Numeration, Addition & Multiplication
Math Strategy: Using Familiar Facts

Materials: 
• Triplets deck addition (BLM16 and BLM17)
• Triplets deck multiplication (BLM19 and BLM20)
(These are located in the Guides to Effective Instruction, Vol. 5)

Overview:
Using the addition or multiplication cards provided in the GEIM Volume 5, students can play independently, in groups, or with the whole class. Students will have to match their answer card with the matching fact cards for each set. An example of a triplet would be the three cards: 3+5, 5+3, and 8; or 3 x 6, 6 x 3, and 18. In addition to sorting and matching the cards, you can also play a variation called « Go Fish », where students need 3 cards to make the set.

How this Supports Student Learning: 
This game provides students an opportunity to strengthen their understanding of « commutative » property, which stems from the idea of moving stuff around. Addition and multiplication have the property of commutativity.  When numbers are added or multiplied, the operation can occur with the values in any order and the same answer will be obtained: 3 + 2 = 5, 2 + 3 = 5; 4 x 6 = 24, 6 x 4 = 24. Subtraction and division are not commutative.

Where to next?
Some students immediately see the connection between the commutative property of addition and multiplication.  For others, this is something that has to be seen, felt and experienced many times before they believe it. That's okay! This activity provides an opportunity for the learners who need to see the connections to have that time. This property allows students to work with numbers flexibly, as they adjust numbers to make them easier to work with.  One option to support students in grasping this concept would be to build arrays for multiplication and represent amounts with manipulatives when adding. Placing the values in the part-whole model would also support students to grasp this property.

Addition: Ten Frame activities in the Guide to Effective Instruction: Number Sense and Numeration K-3 support this thinking (i.e., Ten in the Nest, Ten Frame Cards, etc).

Multiplication: The game Boxed Out could support this thinking.

Math Activity to Teach Using Familiar Facts: Boxed Out

Game: Boxed Out
Math Strand: Number Sense and Numeration
Math Strategy: Using Familiar Facts

English Video:

French Video:

Purpose:
To create grid arrays for basic multiplication facts.

Task Instruction
· This game is played in partners. Two children share a blank grid.
· The first partner rolls two number dice.
· The numbers that come up are the numbers the child uses to make an array on the grid.
· They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible.
· After the player draws the array on the grid, she writes in the number sentence that describes the grid. Students record the multiplication fact in two places: once on their side of the calculation board and the other time inside the rectangular array.  By writing and recording we hope that this repetition will enhance their memory of these facts to reach the eventual goal of automatic recall. 
· The second player then rolls the dice, draws the number grid and records their number sentence.
· As more and more arrays occupy the game board fewer arrangements are possible.  When a student cannot create an array they may roll up to three times in a row hoping to roll a multiplication fact that will fit.  When they are BOXED OUT the game is finished.

Alternative Goals: Students could try collectively to occupy as much of the game board as possible.


How This Activity Supports Learning?
From the Guide to Effective Instruction in Mathematics Grades 4 to 6 Multiplication
http://www.eworkshop.on.ca/edu/resources/guides/NSN_vol_3_Multiplication.pdf
Page 15-16

Learning Multiplication Facts:
A knowledge of basic multiplication facts supports students in understanding multiplication concepts, and in carrying out more complex computations with multi-digit multiplication. Students who do not have quick recall of facts often get bogged down and become frustrated when solving a problem. It is important to note that recall of multiplication facts does not necessarily indicate an understanding of multiplication concepts. For example, a student may have memorized the fact 5 × 6 = 30 but cannot create their own multiplication problem requiring the multiplication of five times six.
The use of models and thinking strategies helps students to develop knowledge of basic facts in a meaningful way.

Where to Next?
Creating arrays of larger numbers to model partial products.

Consider the following problem.
“Amy’s uncle has a large stamp collection. Her uncle displayed all his stamps from Australia on a large sheet of paper. Amy noticed that there were 8 rows of stamps with 12 stamps in each row. How many Australian stamps are there?”

To solve this problem, students might arrange square tiles in an array, and use various strategies to determine the number of tiles. For example, they might count the tiles individually, skip count groups of tiles, add 8 twelve times, or add 12 eight times. Students might also observe that the array can be split into two parts: an 8 × 10 part and an 8 × 2 part. In doing so, they decompose 8 × 12 into two multiplication expressions that are easier to solve, and then add the partial products to determine the product for
8 × 12
8 × 10 = 80
8 ×   2 = 16
80+16 = 96

The BOXED OUT game board can be found on the LKDSB portal https://portal.lkdsb.net/BoardDepartments/prog-elem/math/_layouts/15/WopiFrame2.aspx?sourcedoc=/BoardDepartments/prog-elem/math/Number%20Sense%20and%20Numeration/JUNIOR/MULTIPLICATION%20and%20DIVISION/Boxed%20Out%20Multiplication%20Game.docx&action=default

The French instructions and board game of L'Empêchement, can be found here.


Printing these game boards out on 11 X 17 card-stock and then laminating them is helpful to provide many opportunities for students to reinforcing these facts.  Playing this game at home will also provide an enjoyable way for parents and guardians to support their children. 

Math Activity to Teach Doubling: Concentrating on Doubles

Game: Concentrating on Doubles
Strand: Number Sense and Numeration, Addition and beginning Multiplication
Math strategy: Doubling

Materials: 
Concentrating on Doubles cards ( BLM8 GEIM vol 5) 1 or 2 sets for each pair

Overview: 
Students can play in pairs or small groups. Similar to 'memory' or other concentration games, students place all of the cards face down and spread out on a desk or floor. Each player takes a turn, by turning up two cards at a time. The goal of the game is to match the doubles number expression with the correct sum card. If a match is found, the player keeps the cards. If a match is not found, then the cards are turned over in the same place, and it is the next player's turn. The player with the most matches wins.
*a variation on this would be to have students play individually with a timer to see how many matches he/she can find in a set amount of time.

How this supports Student Learning: 
This game provides opportunities for students to strengthen their doubles facts. Students are often able to learn certain number facts, such as doubles (e.g., 3+3 , 5+5) before others, and will use these known facts to derive answers for unknown facts (3+4 is related to 3+3 and 5+6 is related to 5+5). 
There are only ten double facts.  Students can practice learning facts by playing games such as concentrating on doubles, which will lead them to the learn the two times tables. The two times tables should be linked to student's prior knowledge about the addition of doubles.

Where to next?: 
This strategy is particularly helpful because students who know their two times table well can relate these facts to the three times table. If 2 x 4 is 8, then 3 x 4 is 8 plus one more group of 4.

They will see connections to everyday items when they think about doubles:

When students know the double facts (two times tables), they can apply this knowledge to the four times table by simply doubling the product.


Another way to help students learn doubles is by models. This helps students make connections between the models, the symbols, and the words. The emphasis is on understanding the concept and accessing the strategies for computations with multiplication.





Games to support where to next: 
Over-Easy Doubles GEIM Vol.5, pg. 73 (BLM10)
Snappy Doubles GEIM Vol.5, pg. 75 (BLM12)
Find a Friendly Neighbour GEIM Vol. 5, pg 75  (BLM13)
Spinning for Near-doubles GEIM Vol.5 pg 76 (BLM14)

Math Activity to Teach Doubling: Last One to School

Math Game: Last One to School
Strand:  Number Sense and Numeration - Multiplication
Strategy:  Doubling

This game is from the Number Sense and Numeration Guide to Effective Instruction K-3

Materials
• Last One to School game sheet (BLM11)
• 10 counters per player
• 1 ten-sided number cube (or a spinner on BLM4)
-recording sheet or whiteboard with dry erase marker

Overview: 
Students spin and record the double of that number removing a counter from the gameboard with that double.

How this supports student learning: 
Learning their doubles is the pre-cursor to multiplying by 2.  A strong knowledge of doubles will help support decomposing other facts into partial products and doubling these.  For example; to help solve 6 X 4 a student may use their knowledge that double 6 is 12 (2 X 6 = 12) and then double 12 is 24 to get the answer to 6 X 4=24  because 6 X 4 can be decomposed to 6 X 2 + 6 X 2.

Instructions:
Work with a partner. Each player takes 10 counters and places one inside each house on his or her side of the game sheet.

Once the counters have been placed, player 1 rolls the number cube (or spins) and says what the number would be when doubled. If that number house has a counter in it, the counter is moved to the centre of the game sheet in the “Last One to School” box.

If a player rolls a number that has previously been rolled and the house is empty, that player misses his or her turn.

Player 2 then rolls the number cube (or spins), doubles the number rolled, takes the counter from that numbered house, and places it in the centre of the game board. The game continues until one player has successfully moved all his or her counters from the houses and sent all the students off to school.

Where to Next?
Once students are in grade 2 the multiplication symbol is introduced.  Students can also record the multiplication fact which reflects the same addition fact.  E.g. 6 + 6 = 12  and 6 X 2 = 12
Playing a variety of games with doubling will help solidify this essential skill to develop multiplicative thinking.

Math Activity to Teach Subitizing: Fill the Tower

Math Activity: Fill the Tower

Strand: Number Sense and Numeration - Addition and Subtraction Continuum

Math Strategy: Subitizing

Fill the Tower:

Fill the Tower - Use square tiles or linking cubes, take turns building towers on a game board (MK5).  The towers are constructed by adding the number of tiles or cubes that have been rolled on the die. Play close attention to building the towers to the correct height.  The game ends when one player successfully fills all the towers on his or her gameboard.

How this Supports Learning:

These games promote components of counting and the strategy of subitizing.   There are three components of counting that children must learn in order to count accurately: one-to-one pointing (pointing at or touching each object that is being counted only once), the correct counting sequence (the sequence of number words you use to count 1,2,3,4,5,…), and coordinating (assigning a count to each object as you point at or touch it).  As children learn to count accurately, they may have difficulty with any one, or all of these components.  Counting accurately requires a great deal of time and many opportunities to count and to count for a purpose.

Overview of Games to support these strategies:  What to Look For, pages 158-161

Where to next?

Once students have developed confidence with counting and subitizing they should move towards using the counting on strategy,  which is when the student hold one of the numbers from an equation in their heads and continues to count on until they have counted as many as the second number.  Games and activities to promote the Counting On Strategy can be found in the book What to Look For on page 162.

Math Activity to Teach Subitizing: Fifty Chips

Math Activity: Fifty Chips

Strand: Number Sense and Numeration - Addition and Subtraction Continuum

Math Strategy: Subitizing

Fifty Chips:

Fifty Chips- The object of the game is to be the first player to fill all 50 squares on the game board(MK4).  Players take turns rolling the die, then puts that number of chips on their game board, one per square. The game ends when one player successfully fills all squares on his or her game board; or, when played cooperatively, when all game boards are filled. This game can be played as early as Kindergarten, but you may consider using game boards with only 20 or 30 squares, then giving each child 20 or 30 chips.

How this Supports Learning:

These games promote components of counting and the strategy of subitizing.   There are three components of counting that children must learn in order to count accurately: one-to-one pointing (pointing at or touching each object that is being counted only once), the correct counting sequence (the sequence of number words you use to count 1,2,3,4,5,…), and coordinating (assigning a count to each object as you point at or touch it).  As children learn to count accurately, they may have difficulty with any one, or all of these components.  Counting accurately requires a great deal of time and many opportunities to count and to count for a purpose.

Overview of Games to support these strategies:  What to Look For, pages 158-161

Where to next?

Once students have developed confidence with counting and subitizing they should move towards using the counting on strategy,  which is when the student hold one of the numbers from an equation in their heads and continues to count on until they have counted as many as the second number.  Games and activities to promote the Counting On Strategy can be found in the book What to Look For on page 162.

Math Activity to Teach Subitizing: Tug of War

Math Activity: Tug of War

Strand: Number Sense and Numeration - Addition and Subtraction Continuum

Math Strategy: Subitizing

 Tug of War:

Tug of War- Using the Tug of War game board, roll the dice and "tug" the game piece to your side by moving it the number of places you rolled.  Take turns "tugging" the game piece.  The winner is declared when one player successfully moves the game piece to their side…winning the tug of war

How this Supports Learning:

These games promote components of counting and the strategy of subitizing.   There are three components of counting that children must learn in order to count accurately: one-to-one pointing (pointing at or touching each object that is being counted only once), the correct counting sequence (the sequence of number words you use to count 1,2,3,4,5,…), and coordinating (assigning a count to each object as you point at or touch it).  As children learn to count accurately, they may have difficulty with any one, or all of these components.  Counting accurately requires a great deal of time and many opportunities to count and to count for a purpose.

Overview of Games to support these strategies:  What to Look For, pages 158-161

Where to next?

Once students have developed confidence with counting and subitizing they should move towards using the counting on strategy,  which is when the student hold one of the numbers from an equation in their heads and continues to count on until they have counted as many as the second number.  Games and activities to promote the Counting On Strategy can be found in the book What to Look For on page 162.

Math Activity to Teach Subitizing: Dot Bingo

Math Activity: Dot Bingo

Strand: Number Sense and Numeration - Addition and Subtraction Continuum

Math Strategy: Subitizing

 Dot Bingo:

Dot Bingo - In this whole class or small group game, students play bingo using cards that represent numbers 1-6 in a variety of ways (Numerals, dots, fingers, etc.). Games cards need to be constructed using the "What to Look For" Masters MK1 MK2.  Game can easily be adapted for larger numbers, decimals.  Let's play BINGO!

How this Supports Learning:

These games promote components of counting and the strategy of subitizing.   There are three components of counting that children must learn in order to count accurately: one-to-one pointing (pointing at or touching each object that is being counted only once), the correct counting sequence (the sequence of number words you use to count 1,2,3,4,5,…), and coordinating (assigning a count to each object as you point at or touch it).  As children learn to count accurately, they may have difficulty with any one, or all of these components.  Counting accurately requires a great deal of time and many opportunities to count and to count for a purpose.

Overview of Games to support these strategies:  What to Look For, pages 158-161

Where to next?

Once students have developed confidence with counting and subitizing they should move towards using the counting on strategy,  which is when the student hold one of the numbers from an equation in their heads and continues to count on until they have counted as many as the second number.  Games and activities to promote the Counting On Strategy can be found in the book What to Look For on page 162.

Pedagogical Documentation in Early Years

Pedagogical documentation:
- creates a shared understanding
- celebrates the rights of individual learners
- recognizes students' ownership of their learning
- actualizes shared accountability
- provides voice in the learning for everyone

For more information, a first step is the pedagogical documentation monograph.

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).

Math Activity to Teach Skip Counting: Target 75

Math Activity:  Target 75 

Math Strand:  Number Sense and Numeration
Math Strategy:  Skip Counting 
Key Idea: Unitizing

Materials:  
one die, paper and pencil

Overview:
This activity is found the Alex Lawson’s “What To Look For” on page 188.
After 6 turns, students are trying to have a total close to 75 without going over.

Students will roll a die and select a factor to multiply by:  1, 2, 3, 4, 5 or 10.
The game will encourage students to think about which number to select to multiply by so they are get as close to 75 as possible.

How this activity supports student learning?
Target 75 helps students make sense of quantity and the numbers they are using.

Students will begin to realize that if they select a higher factor in the beginning, they will need to use smaller ones and adjust their choices accordingly as the game goes on. For example, during their final rolls, they will need to decide between multiplying by 1 or 2 to get as close to 75 as possible. 

Students may play the game with a partner.  This encourages them to communicate with each other their mathematical thinking and reasoning. (e.g. It's our first roll, we should multiply the 5 by 10!  That equals 50.  We will be close to 75.) 

This game supports students understand of unitizing, which is the idea that objects can simultaneously be viewed as individual objects and as a composite unit that can be counted.    Through game play, students may use direct modelling to solve the problems, such as making 3 groups of 4 objects, then counting each object.  Moving beyond counting by ones, children may begin to rhythmically count the groups or they may repeatedly count groups on their fingers. This will then move to skip counting, then doubling, repeated addition or even a ratio table.



Students can use rekenreks, hundreds charts, number lines, counters or colour tiles  to help support their calculations. 



Where to next?
Challenge students to work with numbers larger than 75 or change the factors (e.g. 1, 5,6,7,8,9,10 ). 

Another game to try is Multiplication Challenge.

If students are not yet ready for all these factors  1,2,3,4,5,6, reduce the number of choices (Alter the Die by using masking tape or switch to number cards)

Math Activity to Teach Doubling: Spinning for Doubles

Math Activity: Spinning for Doubles

Strand: Number Sense and Numeration, Addition & Multiplication
Math Strategy: Doubling

English:

French:

Materials:
• a copy of the board game and spinner
• counters, a pencil,
• a paper clip
• 2 players

Overview:
During this game students develop their understanding of the making doubles strategy as they work to find all the doubles needed to fill their game board. They take turns spinning the spinner; once the spinner stops, the student needs to identify what the double of that number is and place a counter on their side of the game board.  The players continue taking turns until one of them fills their entire game board.

How this Supports Student Learning: 
This game provides students an opportunity to practice learning their doubles.  Learning their doubles is an important milestone towards adding and multiplication.  Once students know their doubles, they can are quickly able to recognize near doubles and doubles plus one. This allows students to work with numbers flexibly, as they adjust numbers to make them easier to work with.

Where to next?
Concentrating on Doubles, Magic-Doubles, Over-Easy Doubles and Last One to School are all games that support the making doubles strategy. Practice with a variety of games will help the student to develop mastery of this strategy. Once the student is confident with making doubles you can introduce games that support the near doubles strategy, like Snappy Doubles, Find a Friendly Neighbour and Spinning for Near-Doubles.

These activities can be found, beginning on page 72, in the English Guide to Effective Instruction in Math Volume 5 https://bit.ly/2FNcQju and in the French Guide d'enseignement efficace des mathématiques, de la maternelle à la 6e année:Fascicule 5 on page 74-77 here.

Resource Review: Go Show the World

Go Show the Word: A Celebration of Indigenous Heroes written by Wab Kinew is an amazing book full of hope and pride and is an appropriate way for teachers to share Indigenous history and perspectives with their students. Wab Kinew has done a great job highlighting the achievements of Indigenous People of Turtle Island.  This book has a really positive message for all students: go show the world what people who matter can do.

This book challenges stereotypes and calls people to action to go out and show the world how Indigenous people matter.

Where to next?

This is a fantastic book to use in your classroom as a read-aloud or shared reading experience.  Feel free to take several days to experience this book. Allow time for student questions and wonderings.

Each page includes a beautiful illustration of a historical or present-day Indigenous hero including Tecumseh, Jim Thorpe, Waneek Horn-Miller and Dr. Evan Adams.  These short glimpses into what makes these Indigenous people heroes can lead to some excellent inquiries.

Joe Morse, the illustrator of the book, has done a fantastic job capturing the strength and resilience of the people highlighted in the book.  When you do your picture walk through this book have students come up with questions that arise when they look at the pictures.

There are lots of ways to connect this book to social studies expectations.

The above picture can be connected to expectations that focus on perspective, land and resource use.  For example:

Grade 4 Overall Expectation B.2 Inquiry:  Use the Social Studies inquiry process to investigate some issues and challenges associated with balancing human needs/wants and activities with environmental stewardship in one or more of the political and/or physical regions of Canada.

Grade 5 overall expectation B1: Application: Governments and Citizens Working Together

Grade 6 Overall Expectation A2. Inquiry: Use the social studies inquiry process to investigate different perspectives on the historical and/or contemporary experiences of a few distinct communities, including First Nations, Metis, and/or Inuit communities in Canada.

By including books written by Indigenous authors in your classroom and school libraries you are providing your students with perspectives that might not be present in your classroom otherwise.  Including these perspectives in your classroom not only allows your students to experience diverse perspectives, but they also challenge stereotypes and help students to gain empathy and understanding.

The publisher of this book has provided a class discussion guide for teachers to use when reading this book in their class as well.  It can be found here:

https://tundrabooks.files.wordpress.com/2018/09/go-show-the-world_discussion-guide.pdf