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GRID GAMES: Gamification of the Math Classroom

Presented by Christine King, CKingEducation

March 8, 2018

VCTM 2019

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Overview

Session Goal and Essential Questions
What is Gamification
Grid Games: Game Structures and Discourse
Taking it Back to the Classroom

Session Resources: www.ckingeducation.com under “Resources/Workshops”

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Session Goal

Use game structures to promote engagement, collaboration and discourse, while deepening conceptual understanding.

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Essential Questions

Why bother to play games in the classroom?
How can we adapt lessons to include game structures?

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Concept of Gamification

Gamification is the concept of applying game mechanics and game design techniques to engage and motivate people to achieve their goals. Games are a part of the process of gamification.

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Principles of Gamification

Game structures are adaptable and can increase in difficulty over time.
Improvement and progress on skills are noted over time and are connected to time, effort and perseverance.
Discourse and conversation are essential to de-stigmatize failure and promote deeper understanding through acknowledgement of misconceptions or errors.
Reward behaviors (discourse, explaining thinking, evaluating work of others, showing thinking), not results.
Winning can be a byproduct of the work, but learning is the goal.

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What are Grid Games?

Grid games are games that are played on a rectangular matrix using rows and columns. Play is based on use of the game structure, the content of the grid game and the mathematical concept(s) being addressed.

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Top 3 Features of Grid Games

Adaptable to many conceptual areas and grade levels
Relatively easy to learn the structures
Quick setup and easily accessible materials

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Featured Games

Game	Aim
Connect It	Get 4 or 5 in a row, either horizontally, vertically or diagonally. Similar to Connect 4.
Claim It	Claim a cell by following specific criteria. Similar to Blokus.
Clue It	Partners give clues to get a cell. Similar to Pictionary or Charades.
Capture It	Capture an area by counting or performing an operation.

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Materials Needed

Neon Colored Cardstock

Dry Erase

Markers

Sheet

Protectors

Dice

Cards

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Reminders for Students

Reminders for Students:

The goal is to practice and apply the math you are learning.
You are cheating if you don’t explain your thinking.
Use precise math language.
Look for patterns to build understanding.

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Connect IT!

Grade	Goal of the Game	Talk Prompt	Materials
K	Students have to tell ways to make that amount.	“I picked ____. I can make ____ by…”	Single-Digit
1	Tell 10 More/10 Less of the number given.	“My number is ___. Ten less is ____.”	Double-Digit
2	Tell 101 more/101 less of the number given. Teacher needs to model first example.	“My picked ____ and 101 less is ____. I figured that out by…”	Triple-Digit

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Connect IT!

Grade	Goal of the Game	Talk Prompt	Materials
3	Mentally add triple-digit numbers to a constant.	“I selected ____. I have to add 234 to 18. I would…”	Triple-Digit, Card (as constant)
4	Multiply the amount by 11. Teacher should model how to multiply by 10 first, then by 1 to get the partial products, then combine the sums. For example, 23 x 11 can be seen as 23 x 10 and 23 x 1 or 230 + 23, equalling 253.	“I selected ____. To figure out 11 times ____, I would…”	Double-Digit
5	Convert measurements with a given measurement system and show thinking in a ratio table.	“I have to change ____ m to cm. First, I would…”	Single-Digit

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Connect IT! - Single Digit Mat

Grade	Goal of the Game	Grade	Goal of the Game	Grade	Goal of the Game
K	Students have to tell ways to make that amount.	3	Equally partition a strip of paper into amount chosen and name the fractional parts	6	Show ___ less on a number line. Write an equation. Explain your thinking. (Use dice)
1	Use three addends to get the number and explain how you combined the addends.	4	Let the amount chosen represent a unit of measurement, e.g., hours, meters, etc. Convert to a smaller unit of measurement.	7	Treat the amounts like money and find 11% of the amount shown. For example, 11% of $10 is 1 + 1/10 or $1.10. Show your thinking using a tape diagram/bar model.
2	Tell how many more, in coins, are needed to make 20.	5	Let the amount represent the sum of a mixed numbers and the constant. Must use unlike denominators.	8	The amount selected represents the height and radius. Determine the volume of a cylinder. Draw and label the amount. Estimate the volume, then use a calculator. Estimate must be within one to get the spot on the grid.

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Connect It - Choose Your Own Adventure

Color	Side	Side
Yellow	Populations: Tell the amount rounded to the nearest ____ and show on a number line.	Mixed Numbers: Use two addends to get that amount. Cannot use whole numbers. Regrouping must be involved.
Green	Triple-Digit: Add 18 to the amount. Use a compensation strategy. Do mentally. Think out loud.	Single-Digit: Let the amount chosen represent a unit of measurement, e.g., hours, meters, etc. Convert to a smaller unit of measurement.
Orange	Decimals: Say the amount and tell that amount in as tenths and as hundredths. Explain how you know.	Multi-Digit: Divide that number by 2 using mental math strategies and decomposing by place value.
Blue	Multiple of Ten: Multiply by the amount rolled and tell closest product to that multiple of ten.	Unit Fractions: Multiply by the amount rolled and show product on a number line.

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Connect IT! - Single Digit Mat

Grade	Goal of the Game	Grade	Goal of the Game	Grade	Goal of the Game
K	Students have to tell ways to make that amount.	3	Equally partition a strip of paper into amount chosen and name the fractional parts	6	Show ___ less on a number line. Write an equation. Explain your thinking. (Use dice)
1	Use three addends to get the number and explain how you combined the addends.	4	Let the amount chosen represent a unit of measurement, e.g., hours, meters, etc. Convert to a smaller unit of measurement.	7	Treat the amounts like money and find 11% of the amount shown. For example, 11% of $10 is 1 + 1/10 or $1.10. Show your thinking using a tape diagram/bar model.
2	Tell how many more, in coins, are needed to make 20.	5	Let the amount represent the sum of a mixed numbers and the constant. Must use unlike denominators.	8	The amount selected represents the height and radius. Determine the volume of a cylinder. Draw and label the amount. Estimate the volume, then use a calculator. Estimate must be within one to get the spot on the grid.

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Claim IT!

Grade	Goal of the Game
K	Decompose numbers. For example, if selecting a 6, the student can say that 6 has a 5 and a 1 in it. Use game mat with single-digit numbers.
1	Decompose numbers 11 - 19. For example, if selecting a 16, the student can say that 16 is a 10 and 6. Use game mat with teen numbers.
2	Decompose triple-digit numbers. For example, if selecting a 124, the student can say that the number is made up of 1 hundred, 2 tens, 4 ones. Use game mat with triple-digit numbers.

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Claim IT!

Grade	Goal of the Game
3	Decompose triple-digit numbers. For example, if selecting a 124, the student can say that the number is made up of 1 hundred, 2 tens, 4 ones. Use game mat with triple-digit numbers.
4	Round to the nearest 100. For example, if selecting a 824, the student can say that the number rounds to 800 when rounding to the hundred place and prove on number line. Use game mat with triple-digit numbers.
5	Divide by 2 mentally. For example, if selecting a 84, the student can say that 84 divided by 2 is 42 and prove using mental math or with base-ten blocks. Use game mat with even numbers.

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Claim It - Use the other side

Color	Side	Side
	Populations: Tell the amount rounded to the nearest ____ and show on a number line.	Mixed Numbers: Use two addends to get that amount. Cannot use whole numbers. Regrouping must be involved.
	Triple-Digit: Add 18 to the amount. Use a compensation strategy. Do mentally. Think out loud.	Single-Digit: Let the amount chosen represent a unit of measurement, e.g., hours, meters, etc. Convert to a smaller unit of measurement.
	Decimals: Say the amount and tell that amount in as tenths and as hundredths. Explain how you know.	Multi-Digit: Divide that number by 2 using mental math strategies and decomposing by place value.
	Multiple of Ten: Multiply by the amount rolled and tell closest product to that multiple of ten.	Unit Fractions: Multiply by the amount rolled and show product on a number line.

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Claim IT! - Fractions Mat

Show the amount on a number line and also indicate where 0, ½ and 1 are located.

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Clue IT! - Multi-digit Numbers Mat

Work with a partner.
Give clues about the population of a country.

The number that represents the population of this country…

The digit in the hundreds place is 1/10 or 10 times less that the digit in the thousands place.
The number is an odd number and goes into the millions period.
The digit in the hundred thousands place is 10,000 times greater than the digit in the tens place.

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Capture IT! - Triple-Digit

Divide the amount by 10 and round the quotient. Capture the quotient rounded to the nearest whole number.

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Bonus: Heads Up

Group Structure: triads or group of 4

Grade	Goal of the Game	Talk Prompt	Materials
3	Tell the products.	“The product of your two factors is _____.”	cards
4	Tell how many more are needed to make 1 whole.	“You need ____ more to get to 1 whole.”	fraction cards
5	Tell amounts as money, decimals and as fractions. Tell results of verbal expressions.	Your amount as a fraction is ____. One plus the sum of the addends is _____. 1 + ( ____ + ____ ) =	coin cards cards

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Ponder This

Tips for Successful Classroom Games (Aldridge & Badham, 1993):

Make sure the game matches the mathematical objective;
Use games for specific purposes, not just time-fillers;
Keep the number of players from two to four, so that turns come around quickly;
The game should have enough of an element of chance so that it allows weaker students to feel that they have a chance of winning;
Keep the game completion time short;
Use five or six ‘basic’ game structures so the children become familiar with the rules – vary the mathematics rather than the rules;
Send an established game home with a child for homework; and
Invite children to create their own board games or variations of known games.

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Ponder This

Group Structure: partners

“Playing games encourages strategic mathematical thinking as students find different strategies for solving problems and deepen their understanding of numbers.” - Kathy Rutherford, NCTM, 2015

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The Digits Game

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Essential Questions

Why bother to play games in the classroom?
How can we adapt lessons to include game structures?

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3, 2, 1

3 things you really enjoyed

2 things you are learned

1 thing you are committed to doing

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Thank You!

Email: christine@ckinged.com