Use dice or playing cards (1-9; Ace =1) and grid paper.
Take turns rolling two dice or picking two playing cards. The two numbers that are picked are used for the width and length dimensions of a rectangle. The rectangle can be placed anywhere in the grid paper as long as it does not overlap with another rectangle. Play continues until one player does not have a place for their rectangle. The picture below shows the start of a game.
Each player should have a 3 x 3 grid. In each box a number from 2 to 12 is placed. The same number can be used more than once. The goal of the game is to be the first person to have all of your boxes crossed off. Once all players have their boxes filled in, two dice are rolled. The two numbers are summed and all players check their boxes to see if the number appears in a box. Players may only cross one number off for each roll. For example, if a player had the number 6 in three boxes and a total of 6 is rolled, the player can only cross off one six. The picture below shows the start of a game with a sample board. The two dice continue to be rolled until one player has all numbers crossed off.
After playing the game multiple times, ask students what totals are more likely to be rolled. The image below has the number of ways each total can be rolled and the probability of each sum being rolled.
Small, Large, or Target
This game can be played by having players try to get the smallest number, the largest number, or be closest to a target number. This should be decided at the start of the game along with what operation will be used (addition, subtraction, multiplication, or division). The number of boxes used in this game can be varied with 2, 4, 6, or 8 boxes. 10 playing cards are needed for these games (2-9 and Ace =1 and Jack = 0). Let one player pick one of the 10 cards while the cards are face down. After the card is selected each player needs to decide what box to place the number in. Once a number is placed in a box it cannot be changed. The selected card is then removed from the pile and another card is selected. Play continues until all boxes are filled with a number. Players then solve the problem and the winner is determined. The winner is based on what was selected at the start of the game. Either trying for the smallest number, the largest number, or being closest to a target number.
A focus on vocabulary in math is vital for students to be able to discuss mathematics with precision. In the meme above it is conveyed that the student thinks the word "cross" refers to a crossover dribble in basketball. There are often words that have an everyday meaning and then also an academic meaning. In math, there is important vocabulary that has a mathematical meaning that students need to develop understanding with. The table below has some examples.
Consistency in teaching math within a grade level and across grade levels is important. Consistent usage of vocabulary can help reduce cognitive load on students and help them make connections better. It also assists students in understanding mathematical questions that are posed and to discuss math clearly with other students.
Word walls are a great way to help students learn vocabulary. There are a variety of games that can be used with word walls. One example is below.
Bluff word wall game
Split the class into 2 teams. Ask a question of one team about the words on the wall. Students who would like to be considered to answer stand up. They can either KNOW the question or BLUFF. The teacher or someone from the other team chooses one student to answer. If they get it correct, the team gets points for everyone standing up (even if they were bluffing!). If the student does not get it correct then the team gets no points. The question moves to the next team OR you can tell the answer and give the next team a new question.
For most students, games are an everyday part of their lives. For example, between June 2018 and March 2019, 125 million new players registered to play the online video game Fortnite, putting the total number of players at nearly 250 million. A large portion of these players are school-aged kids. In addition, universities now offer full-ride scholarships for students good at video games with esports scholarships. Kids can play games for hours with little to no breaks and the time can go by quickly because they are so engaged. The question becomes why can’t learning in school foster this kind of engagement?
When students play games they persevere in problem solving, try new approaches, use all of their resources, and continue to develop their strategies when encountering setbacks of failures. These are all characteristics that will help students be successful in life and in the math classroom.
In the math classroom game-based learning should move beyond just incorporating drill and practice though. An example of a typical game includes students solving traditional, non-contextual practice problems in order to get more speed for a race car and attempts to take advantage of students’ interest in video games. However, in this type of game, students only receive feedback if the answers are correct or incorrect and do not receive support for improving their conceptual understanding. These types of games also emphasize that mathematics is about speed and focus on the memorization of ideas
The following are three productive examples of game-based learning.
An escape room is a game in which teams solve multiple puzzles using clues, hints, and strategy in order to figure out how to escape from a locked room. Setting up a mathematical escape room can be a great way for students to apply and practice mathematics they have learned. When students are engaged in a task with high intrinsic motivation it creates an ideal environment for learning. Students also learn valuable teamwork and communication skills as they learn from each other. See if you can figure out the following from one of the escape rooms I have developed.
Programming and robotics
There is a movement for more schools to require computer science courses for students. Current technologies for programming are becoming more user-friendly, which can make it more likely for mathematics teachers to feel comfortable integrating programming. Exposing students to this work is essential as applications software developers is the largest STEM occupation. The following images are some example games: golf and racing.
Desmos has a collection of activities with some of the activities being game-based.
One example game is mini golf. Students plot points in the coordinate plane in order to make a slide that will get marbles to land in a hole.
Stohlmann, M. (In press). Escape room math: Luna’s lines. Mathematics Teacher: Learning and Teaching PK-12.
Stohlmann, M. (2019). Integrated steM education through open-ended game based learning. Journal of Mathematics Education, 12(1), 16-30.
Stohlmann, M., & Kim, Y.R. (In review). Game-based learning: Robotics and escape rooms. The Australian Mathematics Education Journal.
Watch the following video and see how the math anxiety was overcome.
Nate, the fifth grader, dreaded these days at school. It was another math class where a chapter test was being handed back. Nate did not even want to look at his score as Mrs. Miller handed him his test. There at the top of his paper was a big fat grade of "F". Read the book to find out what Nate learns during an engineering design project that helps him to do well in mathematics.
In my book, The Natural?, Nate holds the assumption that some students are just naturally good at math and others cannot do it. This is a message that is too prevalent in schools and is something that students latch on to. This message is too often reinforced by parents who may say, "I never got math." It is vital to emphasize that all students are capable of doing well in mathematics. The table below has phrases to avoid and what to state instead. We want students to hold a growth mindset, that they can learn new things and improve, as they approach mathematics.
Positive math messages
Math like life takes effort
Math is not a spectator sport!
Have a growth mindset—you can always learn new things and improve.
Persevere- Find your grit.
Math is important for understanding life and graduating from college.
Stay positive and optimistic. Everyone can do well in mathematics!
Deliberate practice is purposeful and systematic. In mathematics it is important that students learn from their mistakes. They need to realize what they know and what they need to work on or understand better. The quality of the time spent practicing is more important than the quantity of time.
4 Components of deliberate practice
Stohlmann, M. (2019). The natural? Seattle, WA: KDP.
Duckworth, A. (2016). Grit. New York: Scribner.
Engineering is increasingly being included in curriculum in schools because engineers design technologies by using applications of mathematics and science. Engineering innovations, inventions, and discoveries create new products, jobs, and a better world. Engineers work in teams, are women or men, come from all different ethnicities, and work in diverse fields from biomedical to mechanical. If the following statements seem interesting to you, you should consider a career in engineering.
Support for Veterans
Over 3,000,000 troops have served in Iraq and Afghanistan. There have been over 46,000 American troops that have been wounded in action in Iraq or Afghanistan. These men and women have served our country to protect those that cannot protect themselves and to secure our freedom. Freedom is not free and they have sacrificed much for us. There are a variety of ways to thank and support these veterans. No one person can do everything, but everyone can do something.
Stohlmann, M. (2012). The little engineer that could. Seattle, WA: CreateSpace.
Phases of Basic Fact Mastery
Students can go through the three phases below for fact mastery.
Phase 1: Counting (Count with objects or mentally).
Phase 2: Deriving (Use reasoning strategies based on known facts).
Phase 3: Mastery (Efficient production of answers).
Too often students are not given experiences in phase 2 and the emphasis is on memorization to go from phase 1 to phase 3. Phase 2 is crucial for developing mathematical thinking and mastery based on understanding.
Addition Fact Strategies
The problems presented in the book align with the strategies below. The strategies are listed in the order they can be used in the book. Problems can be solved in more than one way. The use of base 10 blocks and 10 frames can aid students’ thinking. There are a number of websites that have base 10 blocks and 10 frames.
1 more/2 more
In this strategy, students solve problems that require adding 1 or 2 to a number. Students can do this by counting on from the given number or adding two.
4 + 2 = 6
The counting on strategy for this problem would be to start at 4 and count two more to get the answer 5, 6.
Combinations that make 10
These facts involve numbers that add up to 10. These are important facts for students to know.
7 + 3 = 10
In this strategy, students would decompose one number in order to make a 10 and then add the remaining part of the number.
8 + 6
8 + 2 + 4
10 + 4
Students can work with problems that involve adding the same number.
4 + 4 = 8
If students know their doubles, they can then use those facts to be able to solve near doubles problems.
6 + 7
6 + 6 + 1
12 + 1
In this strategy, students decompose numbers to work with fives and then add the remaining numbers.
7 + 8
5 + 2 + 3 + 5
5 + 5 + 2 + 3
10 + 5
The commutative property of addition states that you can add numbers in any order. Students can double the number of facts that they know when they use this property. This property is not true for subtraction.
3 + 4 = 7
4 + 3 = 7
Questions to ask children while reading the book or while they play the games in the back of the book
-How did you figure it out?
-Can you say out loud how you thought about it in your head?
-Is there another way you could figure it out?
-Can you think of another fact that strategy would work well with?
-If someone didn’t know the answer to ____, how would you tell them to figure it out?
Stohlmann, M. (2019). Go knights go! Seattle, WA: KDP.
Integrated steM is an effort to combine mathematics with at least one of the three disciplines of science, technology, and engineering based on natural connections between the subjects. One way to do this is through the integration of technology within mathematics through game-based learning, which has the potential to engage students and develop their mathematical understanding. In the past, game-based learning in mathematics education was generally limited to traditional practice problems. Moving forward, game-based learning within mathematics education should be done at the transformation level of the SAMR hierarchy (Puentendura, 2006).
There are several important implications for the development and selection of games intended for use in the mathematics classroom. Games that are implemented should be worthwhile tasks. There are two main features of worthwhile tasks. First, the tasks have no prescribed rules or methods. Second, there is no perception that there is a specific “correct” solution method (Hiebert et al., 1997). With this design, students are more willing to share and discuss their mathematical thinking. It also enables students to activate their prior knowledge to assist in gameplay because there are multiple entry points.
The games selected for incorporation in mathematics education should be those that align with mathematics standards and mathematical learning objectives. In past research, this has been noted as an issue when games have been used (Chen & Hwang, 2014; Schenke, Rutherford, & Farkas, 2014). In order to ensure that the mathematics that is used in the games is made explicit, there should be time for discussion and reflection after gameplay. Teachers can also make connections to the gameplay in their other class activities. The absence of this process in which the teacher makes connections between the games and other class content and in which students are given time to discuss and think about the gaming experience has been suggested as a reason for why game-based learning might not lead to positive results (Rutherford et al., 2014).
As further games are developed, it is important that the games be designed to help students make connections between multiple representations, provide students feedback, and enable students to do non-routine problem solving with a focus on conceptual understanding. It has been noted that most game-based learning in mathematics has been limited to number and operations and algebra (Byun & Joung, 2018). Expanding the mathematical topics that are available should be done as long as the games are well-designed and enable mathematics teachers to implement effective mathematical teaching practices (NCTM, 2014).
Technology integration is an essential element of quality mathematics teaching. Technology-based games are a relevant context for students that can motivate them to engage in mathematical thinking and discussion. Further research is needed on the impact of game-based learning in the mathematics classroom when the games are well-designed and allow for open-ended mathematics.
As further work is done with game-based learning in mathematics, it is important that the games are designed at the transformation level of the SAMR hierarchy, are worthwhile tasks, are aligned with standards, incorporate multiple representations, provide students feedback, and are open-ended.
Stohlmann, M. (2019). Integrated steM education through open-ended game based learning. Journal of Mathematics Education, 12(1), 16-30.