6.EE.Matching game to increase students abilities to evaluate and solve numerical expressions

Common Core Standards:

 6.EE.A.1 – Write and evaluate numerical expressions involving whole-number exponents.

6.EE.A.2 – Write, read, and evaluate expressions in which letters stand for numbers

2.A – Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5-y.

2.B – Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms.

2.C – Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V=s^3 and A=6s^2 to find the volume and surface area of a cube with sides of lengths s=1/2.

6.EE.A.3 – Apply properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2+x) to produce the equivalent expression 6+3x; apply the distributive property to the expression 24x+18y to produce the equivalent expression 6(4x+3y); apply properties of operations to y+y+y to produce the equivalent expression 3y.

6.EE.A.4 – Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y+y+y and 3y are equivalent because they name the same number regardless of which number y stands for.

 

Description of the Activity:

The game is a modified version of the classic card matching game, “Concentration.” Just like “Concentration,” our matching game requires players to match cards; however, instead of looking for cards with the same image, the players in our game will be asked to turn over one card – an “Equation Card” – and solve the equation. Then, the players match the Equation Card to a number that is hidden behind an “Answer Card.” For example:

A player flips over an Equation Card and sees the following equation: 3x + 4 = 10

On a sheet of paper, the player solves the equation, and he or she must show his or her work. The student solves for “x” and finds that the answer is 2.

After the player has solved the equation, he or she tries to find the card with the number 2 on it. If the player finds the match, he or she is allowed to keep the pair (the Equation Card and Answer Card) of cards and that player can continue to flip over cards until he or she answers incorrectly or a match is not found. If the player solves the equation card but cannot find the matching Answer Card, the cards are turned back over and the player does not keep the pair of cards.

The player who is the oldest takes the first turn, and the game ends when all cards have been collected. The player with the most correctly matched pairs wins.

All cards in the game will have a number on them, and while showing their work on their paper, the players will be asked to identify the number on the Equation Card. When they find the matching answer on the Answer Card, the players will need to identify the number on the matching Answer Card. For example, a player’s sheet of paper should look like the following:

 

Equation Card Number

Equation

Answer

Answer Card Number

 

4

3x + 4 = 10

     – 4    -4

3x = 6

3     3

x = 2

X = 2

10

Identify CCSS Mathematical Practices:

Our game requires our students to use multiple mathematical practices. The first practice is “Deductive and Quantitative Reasoning.” Students will use deductive and quantitative reasoning in order to determine the accuracy of the answers that they give. The answers that the students generate through working through the problem on the Equation Card should make sense; therefore, it should be easy for a student to prove his or her answer is correct. Students should be able to state and defend their answers by using mathematical terminology and logic in applying their answer to the original problem. By being able to use logic and mathematical terminology in defending their answer, students will be able to demonstrate their ability to use the mathematical practice, “Logical Argument.”

Students will also use the mathematical practice, “Modeling,” by filling out tables in their worksheets, making assumptions by claiming an answer to be true, looking for revision and analyzing the answers’ relationship to the equation by challenging each other’s answers, and reflect on their answers. By using modeling in these ways, students will be able to see how they solved the equation, and they will be able to identify how they solved the problem and if their thinking makes sense. Reflecting on their work allows students to identify problem areas, and it also makes it easier for the teacher to give useful and timely feedback.

Students will also be able to use and develop their “Structure” and “Related Patterns” practices. Students will be afforded the opportunity to sharpen their skills in these practices during the game because they need to look for mathematical patterns and evaluate the structure of the problems on the Equation Cards. In order to correctly solve and understand the equations, noticing the structure and patterns in a problem helps the students increase the speed in solving the problem and their overall understanding of how the parts of the equations work together to provide an answer.

 

How Modeling Enhances teaching effectiveness

This model enhances the teaching effectiveness by giving the students something other than a worksheet to review the Expressions and Equations unit of the common core state standards. Because students can work in small groups or pairs, the assessment activity becomes less stressful for the students, and they become more engaged. The activity presents a challenge to the students, but is designed to immediately show the student if their answer is correct. This also allows time for the teachers walk around the class and get a good view of how the students are doing with the current material; this can help them decide if re-teaching is necessary. Because the students can get credit for turning in their work, it gives students who are hard to get engaged incentive to participate.

Other ways to use this activity

This activity can target nearly any common core standard, though this particular game was designed as a review of the 6th grade Expression and Equations standards. You could easily design your own version of the game for any grade level, for any concept in any content area.

This game is easily manipulated to fit your classroom needs.

As the matching game is fun and engaging, teachers can assign this activity as a pre-assessment to determine prior knowledge, post assessment to decide if re-teaching is necessary, practice a difficult concept, and/or as a review of a unit, concept, or end of year. This would be an excellent way to practice for larger state exams as well.

This game can be turned around to where the students are making the matching game themselves—getting the practice or review while making the game—then the game is played by another team or pair—getting further practice or review. This would allow students to learn from and teach each other, and be more excited about the activity.

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