Mathematical Learning Object: Capture the Flag Board Game
Jamie Andrews & Ruth Esteves
The Inspiration
The idea for this game comes from the popular “Capture the Flag” activity, often played
in the field with players using strategies to obtain the opposing team’s flag. While wandering
through the toy section of a store, a package of soldiers with flags triggered the idea of creating a
grid that students would traverse to capture their opponent’s flag. The students would need to use
strategies to cross the grid and answer math questions to move even closer to their opponent’s
flag. Later, for an added level of challenge, we came up with the idea to organize the grid as a
maze through which players would need to navigate. The math concept prepared for this
particular assignment is the order of operations.
The Target Grade Level
Our target grade levels are grade 6 and grade 7. In grade six and then continuing in grade
7, students work with the order of operations (BEDMAS). The curriculum has them working
with brackets, division, multiplication, addition and subtraction, but not exponents (this is
introduced in grade 8).
The curricular objectives that it addresses/supports
BC Curricular Content
● Multiplication and Division Facts to 100
● Order of Operation with Whole Numbers
BC Competencies:
● Developing mental math strategies and abilities to make sense of quantities
● Developing, demonstrating and applying mathematical understanding through play,
inquiry and problem solving
● Developing and using multiple strategies to engage in problem solving
● Use mathematical vocabulary and language to contribute to mathematical discussions
● Communicate math thinking in many ways
● Represent mathematical ideas in concrete, pictorial and symbolic forms
● Reflect on mathematical thinking
● Use mathematical argument to support personal choices
Any special features that were included to increase the educational utility
The educational utility within this game is limited only by the scope of your imagination.
It can be adjusted for any grade level, subject area, or unit of study. For example, in math, you
can use flashcards for addition, subtraction, multiplication, division, pattern recognition,
geometry, etc. One could also use this template and modify the questions to focus on topics in
science, or social studies. The possibilities are endless!
Some guidance on how to use
In the game, the players’ objective is to have their pawn reach the opponent’s flag. For a
longer game, the student can retrieve an opponent’s flag back to their home base. As the player
traverses the grid, they are encouraged to land on a star and solve a math question (or flashcard)
in order to have another role of the die during their turn to advance further in the game.
The game can be played by 2-8 players (4 teams of 2 max).
1. Each player chooses a pawn
2. Each team chooses a flag and places it in their corresponding corner, their
opponent occupies the opposite corner.
3. Each team can have one math support chart to help solve math problems
4. Play rock/paper/scissors to determine who goes first and rolls a die. The play
continues clockwise.
5. If playing by teams (i.e. 2 players to a team), the pair alternates turns to play.
That is, player 1 from each team will go first, then player 2 from each team will
go, and then repeat.
6. You must land exactly on a GOLD star to teleport. Then you will need to
correctly answer a BLUE or PINK question (your choice) for the teleportation to
work. If answered correctly, you can then teleport to the gold star in your
immediate surrounding on the board and complete the amount of moves
remaining from your original roll (e.g. 4 spaces). If, however, you answer the
question incorrectly, you can either stay where you are or complete the remaining
moves from your original roll away from your current position. If you teleport
successfully, your turn is over and the turn passes to the next team (i.e. you do not
roll again).
7. Players must land on BLUE (Word Problems), PINK (Equation Solving
Problems) or GREEN (You choose word or equation problem) STAR to obtain a
math problem card.
● If the student answers correctly, they get a second role and move
accordingly.
● If a student is not able to solve, they ask if another student in an opposing
team has a strategy for the answer. They are allowed to share it with the
player to help them solve the problem. When the player achieves the
correct answer, both the player and the peer who assisted them get to
move their pawn 2 spaces. The teacher can provide a strategy if none of
the students can.
● You can only move backward when and if you hit a dead end to move
toward another route
How to assess
Student math fluency within order of operations (Multiplication, Division, Addition,
Subtraction) can be assessed by
● Observing student reflection and problem solving and documenting with anecdotal notes.
● Providing Self Assessment Form (see appendix)
● Collecting written evidence of problem solving processes
Math game- Jamie and Ruth part 2 of 2
Appendix
EQUATION SOLVING PROBLEMS: Simplify the following numerical expressions
1. 7 – 24 ÷ 8 x 4 + 6
= 7 – 3 x 4 + 6
= 7 – 12 + 6
= -5 + 6
= 1
2. 18 ÷ 3 – 7 + 2 x 5
= 6 – 7 + 2 x 5
= 6 – 7 + 10
= -1 + 10
= 9
3. 6 x 4 ÷ 12 + 72 ÷ 8 – 9
= 24 ÷ 12 + 72 ÷ 8 – 9
= 2 + 72 ÷ 8 – 9
= 2 + 9 – 9
= 11 – 9
= 2
4. (9 – 3) × 5 ÷ 2
=6 × 5 ÷ 2
=30 ÷ 2
=15
5. (6 + 3) × 7 ÷ 3
=9 x 7 ÷ 3
=63÷3
=21
6. (10 – 5) × 2 ÷ 2
=5 × 2 ÷ 2
=10 ÷ 2
=5
7. (7 – 3) × 4 ÷ 4
=4 × 4 ÷ 4
=16 ÷ 4
=4
8. (9 – 4) × 4 ÷ 5
=5 × 4 ÷ 5
=20 ÷ 5
=4
9. (7+2) × 4 ÷ 9
=9 × 7 ÷ 9
=36 ÷ 9
=4
10. (9 – 3) × 4 ÷ 4
=6 × 4 ÷ 4
=24 ÷ 4
=6
11. (7 – 2) × 3 ÷ 3
=5 × 3 ÷ 3
=15 ÷ 3
=5
12. (12 – 8) × 3 ÷ 6
=4 × 3 ÷ 6
=12 ÷ 6
=2
13. (10 – 4) × 4 ÷ 3
5
=6 × 4 ÷ 3
=24 ÷ 3
=8
14. (17 – 6 ÷ 2) + 4 x 3
= (17 – 3) + 4 x 3
= 14 + 4 x 3
= 14 + 12
= 26
15. -2 (1 x 4 – 2 ÷ 2) + (6 + 2 – 3)
= -2 (4 – 1) + (6 + 2 – 3)
= -2 (3) + (6 + 2 – 3)
= -2 (3) + (8 – 3)
= -2 (3) + (5)
= -6 + 5
= -1
16. -1 x [(3 – 4 x 7) ÷ 5] – 2 x 24 ÷ 6
= -1 x [(3 – 28) ÷ 5] – 2 x 24 ÷ 6
= -1 x [(-25) ÷ 5] – 2 x 24 ÷ 6
= -1 x [-5] – 2 x 24 ÷ 6
= 5 – 2 x 24 ÷ 6
= 5 – 48 ÷ 6
= 5 – 8
= -3
WORD PROBLEMS: Translate the following word problems into numerical expressions and
then solve them.
1. Alicia bought 4 bananas for 50 cents each, and 1 apple for 80 cents. Write a numerical
expression to represent this situation and then find the total cost in dollars.
4 x 50 + 80
= 200 + 80
= 280 cents
= $2.80
2. Anna travelled to the Caribbean. She found that pie in Jamaica was $2/slice and pie in
The Bahamas was $3/slice (these are the pie rates of the Caribbean). She bought 8 slices
in Jamaica and 4 slices in The Bahamas. How many dollars did she spend on pie while on
this trip to the Caribbean? Write a numerical expression to represent this situation and
then find the total cost in dollars.
8 x 2 + 4 x 3
= 16 + 12
= 28
= $28
3. Anne pays 20 dollars for materials to make earrings. She makes 10 earrings and sells 7
for 5 dollars each and 3 for 2 dollars each. Write a numerical expression to represent this
situation and then find Anne’s profit (remembering to include the money that she spent
on materials).
6
7 x 5 + 3 x 2 – 20
= 35 + 3 x 2 – 20
= 35 + 6 – 20
= 41 – 20
= 21
= $21
4. Brie bought 3 pants for 25 dollars each and paid with a one-hundred dollar bill. Write a
numerical expression to represent this situation and then find out how much money Brie
will receive back from the cashier.
100 – 3 x 25
= 100 – 75
= 25
= $25
5. The price of a shirt is 100 dollars. The store manager Colin gives a discount of 50 dollars.
Connor and Dane are loving this discount and so together they buy 4 shirts and decide to
split the cost evenly. Write a numerical expression to represent this situation and find the
price paid by both Connor and Dane.
(100 – 50) x 4 ÷ 2
= (50) x 4 ÷ 2
= 200 ÷ 2
= 100
= $100
6. Denée withdrew 1,000 dollars from her bank account today. She uses $500 to fix her car.
Then, she uses the remaining money and divides it into 5 equal parts. She gives 4 of those
parts to four different charities and keeps 1 part for herself. Feeling ever so generous, she
then takes a friend out for a meal and she spends 60 dollars on food and drinks. Write a
numerical expression to represent this situation and find out how much money Denée has
left.
(1000 – 500) ÷ 5 – 60
= (500) ÷ 5 – 60
= 100 – 60
= 40
= $40
7
7. Mitra bought 2 flower pots for her front porch. Her friend Emily and Jess both bought her
a flower pot for her birthday, which she also displayed on her front porch. One of the
flower pots was destroyed when a cat knocked it over. She decided to divide the
remaining flower pots between herself and her two sisters. How many flower pots did
Mitra keep?
[(2 + 2) – 1] ÷ 3
= (4 – 1) ÷ 3
= 3 ÷ 3
= 1
8. John has 20 pieces of candy corn. He gives half to his brother. After this he eats 3 pieces.
How many pieces of candy corn does John have now?
(20 ÷ 2) – 3
= 10 – 3
= 7
9. Janel has a collection of 37 toy cars. For his birthday he receives 5 more cars as gifts. He
then sells 2 cars. He makes so much from that sale that he decides to sell half of the
remaining cars. How many cars are left in Janel’s collection?
(37 + 5 -2) ÷ 2
= 40 ÷ 2
= 20
10. There are 100 bats in a cave. Twenty-five bats fly away and twice as many return. How
many bats are in the cave now?
100 – 25 (25 x 2)
= 75 + 50
=125
11. Jamie has $450. He spends $210 on food. Later he divides all the money into four
parts out of which three parts were distributed and one part he keeps for himself. Then he
found $50 on the road. Write the final expression and find the money he has left?
(450 – 210) ÷ 4 + 50
= (240) ÷ 4 + 50
= 60 + 50
= 110
= $110
8
12. Sam has $1,000 to be distributed among two groups equally. Later, the first part is
divided among five children and the second part is divided among two brothers. Give the
expression that represents how the money distribution between the two groups was
dispersed?
Group 1:
(1,000 ÷ 2) ÷ 5
= (500) ÷ 5
= 100
Each of the five children represented in
the first part will receive $100.
Group 2:
(1,000 ÷ 2) ÷ 2
= (500) ÷ 2
= 250
Each of the two brothers represented in
the second part will receive $250.
13. Andy has $1,500 that he invested in stock. In one day, his money was doubled. The next
day he got a profit of $165 and later loss of $238. Write an expression for this and
determine his present amount.
(1,500 x 2) + 165 – 238
= (3,000) + 165 – 238
= 3,165 – 238
= 2,927
14. Linda bought 3 notebooks for $1.20 each, a box of pencils for $1.50, and a box of pens
for $1.70. She had a giftcard with $5 on it, and she paid the rest in cash. How much did
Linda need to pay in cash?
(3 x 1.2) + 1.5 + 1.7 – 5
= (3.6) + 1.5 + 1.7 – 5
= 5.1 + 1.7 – 5
= 6.8 – 5
= 1.8
= $1.80
15. Mel had $35 in cash and withdrew $200 from his bank account. He bought a pair of
trousers for $34.00, 2 shirts for $16.00 each, and 2 pairs of shoes for $24.00 each. Give
the final expression, and determine how much money Mel had at the end of the shopping
day.
35 + 200 – 34 – (2 x 16) – (2 x 24)
= 35 + 200 – 34 – (32) – (2 x 24)
= 35 + 200 – 34 -32 – (48)
= 235 – 34 – 32 – 48
= 201 – 32 – 48
= 169 – 48
= 121
= $121
9
16. George Michael Bluth works at the Banana Stand selling delicious banana treats. He
starts the day with $350 in the cash register. On this day, he sells 18 banana smoothies at
a price of $2 each, 4 banana montanas at a price of $5 each, and 6 bonanza busters at a
price of $7 each. Unfortunately, while on lunch break the Banana Bandit swooped in and
stole 400 hard earned banana dollars. How much money did George end up with by the
end of the day?
350 + (18 x 2) + (4 x 5) + (6 x 7) – 400
= 350 + (36) + (4 x 5) + (6 x 7) – 400
= 350 + 36 + (20) + (6 x 7) – 400
= 350 + 36 + 20 + (42) – 400
= 350 + 56 + 42 – 400
= 350 + 98 – 400
= 448 – 400
= 48
= $48
Problems Retrieved from:
https://www.basic-mathematics.com/order-of-operations-word-problems.html
https://www.mathworksheetsland.com/extras/5/1ops3step/pract1.pdf
https://www.woojr.com/order-of-operations-worksheets-for-halloween/halloween-word-problem
s-key/
https://www.chilimath.com/lessons/introductory-algebra/order-of-operations-practice-problems/