Resources: Here are the links to the different folders for the games shared during the video that support students with Getting to a Decade Number and making jumps of 10 forward and backwards.
Resources: Here are the links to the different folders for the games shared during the video that support students with Getting to a Decade Number and making jumps of 10 forward and backwards.
Math Game for Addition & Subtraction: Handful of Dice
Math Strategy: Up/Down over 10 Math Strand: Number Sense and Numeration
Overview: This game has many extensions and adaptations to suit your students' needs. With making pairs of 10, there are limited choices which let them focus on that amount. Then, by changing the number it allows students to practice decomposing other numbers of varying amounts. You can also change the amount of dice being used for each number. For example, you could choose the number 15 and have students use 2,3 or 4 dice to decompose it into. This is an excellent activity to support part-whole understanding. It also requires very little materials and could be played with 2-4 players.
* It could also be adapted for multiplication by giving a larger number, such as 24 and asking students to find pairs of numbers that when multiplied = 24.
How this activity supports learning: This game helps students understand that a number can be decomposed into smaller numbers. For example, to add 7 + 5, a child may use the up over 10 strategy and take 3 from the 5 and add it to the 7 to make 10, plus the remaining 2 = 12.
Composing and decomposing small sets of objects can allow young students to see the whole group as well as the subsets that created the whole
Students need a strong understanding of part-whole relationships in order to use mental mathematics strategies to add, subtract, multiply and divide.
Students who are able to fluently decompose quantities and then compose quantities are able to adapt their calculations to different sets of numbers.
Where to next? If a student is having difficulty decomposing, reduce the quantity of objects the student is using. Students may also benefit from having physical tools they can refer to, such as snap cubes or counters. For example, if the student is decomposing 5, have the, demonstrate the two parts with a 2 and 3 then take another 5 blocks and do it again with different numbers. You can ask if they are able to decompose it into other parts, such as 3 or 4.
If a student is fluent and confident with decomposing, move towards using larger numbers and having students explain their proof, “How do you know you have found all the ways to decompose this number?”
You can also focus on the next strategies, which would be splitting, where numbers are split into their place value to make them easier to add or subtract.
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 Strand: Number Sense and Numeration Math Strategy: Skip Counting
English video:
Video french:
Materials: One die, whiteboard and whiteboard marker
(Extension: colour tiles)
Overview:
This game is very engaging for students and helps to prepare students to move from using repeated addition to using grouping of numbers when modeling arrays when solving multiplication problems. After completing this lesson you would then begin a lesson using arrays for equal groups.
On each turn, students roll a 1–6 number cube to find out how many circles to draw and then roll the cube again to find out how many stars to draw in each circle. For example, for a first roll of 4 and a second roll of 3, the student would draw this:
How this activity supports student learning?
Playing Circles and Stars helps students understand that multiplication
can be thought of as combining equal groups and is, therefore, related to addition when the same number is added multiple times. From playing, students become familiar with multiplying numbers from 1X1 to 6X6.
As an extension, you could use try using an 8 sided die.
After students know how to play the game, they learn to represent each
of their turns with addition and multiplication equations. This helps them connect the standard symbols to their experience and also strengthens the connection between addition and multiplication.
Where to next?
In the Alex Lawson text, What To Look For there are several other games that can be played to support unitizing, such as: - How Long? How Many?, which uses Cuisenaire rods - Skip Counting Race - Target 75 - Multiplication Challenge
These can all be found on page 185-189.
Share your classroom experiences with us on Instagram and Twitter at @LKelempro #EngageLK!
Strand: Number Sense Numeration multiplication
Math Strategy: Using Familiar Facts
Materials: variety of Arrays cards, corresponding multiplication fact cards
Overview:
During this activity, each student has a different card. Each card shows a different array on one side and the corresponding multiplication fact on the back. Student will ‘mill about the room’ finding another student to Quiz, by showing them their array picture and having the opponent say the multiplication fact on the back. Then the other student will Quiz (show) his/her array and have their opponent say the multiplication fact. Before finding another opponent, the two students trade their cards and move on. The activity ends when students have had a chance to subitizing a few different arrays and time is up.
How this supports students learning:
This activity supports students developing a conceptual understanding of math facts by giving them the opportunity to represent multiplication facts pictorially. Using models, students can use various objects and materials that will help them make sense of operations such as array formations.
“Arrays are powerful models for representing multiplication, division, and area. Many objects in real life can be arranged in arrays, and such arrays provide visual, concrete contexts for multiplication and division. The construction and understanding of an array as a model is an important concept for students to develop over time and with experience.” (GEIM., vol.5 pg. 35)
Where to next: once students have mastered arrays, they will be able to break multi-digit factors into smaller parts for easier solutions such as; 14 x 9 = 4 x 9 + 10 x 9. The student can further their understanding of breaking arrays into smaller factors by using base ten blocks to represent larger numbers and breaking them into smaller factors.
Strand: Number Sense & Numeration Strategy: Up Over 10
Adapted from the updated e-text by Alex Lawson, ‘What to Look For’
Materials:
A deck of cards (Only use the 5, 6, 7, 8, & 9s)
Counters
Overview: The goal is to be the player with the most ‘change’ at the end of the game. With 2 or more players, split a deck of cards made up of the numbers 5-9. On each players turn, the player flips over 2 cards. They keep one number whole and decompose the other to make a ten with the number that was kept whole. The remaining amount is ‘change’. The change is the player’s points for that round. Students then take counters for that amount. This helps the students keep track of their score.
How This Supports Student Learning: This game will help solidify the Anchors of 10 and the Up Over 10 strategies. By decomposing one number to create a ten students’ will increase their flexibility with numbers and strengthen their understanding of the part-whole relationship between numbers. As well, the Up Over 10 strategy is a precursor to grasping ‘carrying’ that happens in the standard algorithm for addition.
Where to Next: When students are ready to extend this strategy, make the values of the cards drawn worth ten times the amount, as seen in the video. This will help them use the strategy with bigger numbers.
If your students are grasping the Up Over 10 strategy, encourage them to transfer the skill to Up Over other decade numbers. For example,
27 + 8
=27 + 3 + 5
= 30 + 5
= 35
Want a home extension? Send this link home with students and ask them to play Break Apart!
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).
“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).
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.
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.
