I always tell my students to remember that math is a language. Sometimes writing expressions and finding equivalent expressions can be difficult for students. When they just see variable expressions on a page, it can be tough to figure out what the letters and numbers mean. But if we talk about concrete objects to introduce variables, then expressions start to make a bit more sense.
Unpacking Equivalent Expressions
Packs of items are very helpful to show basic equivalent expressions. When I first introduced equivalent expressions, I try to bring in a fresh pack of tennis balls and pop it open right in front of the class! Tennis balls are great to use because the container is clear; they can see the 3 balls in the pack. Sometimes it even says “3-pack” on the side. Anyway, I ask the students to tell me how to describe the pack of balls. They say things like “It’s 3 tennis balls” or “It’s a 3-pack”.
Then I pull some tennis balls out of a bag. I place the balls one by one on the table and say something like “Here I have one tennis ball plus one tennis ball, plus one tennis ball or t + t + t” And I write the expression on the board. “Can anyone come up with an equivalent expression?” and I hold up the fresh 3-pack.
Almost every time the whole class says “3t”! Or “One 3-pack!” If they only say “A pack” I ask if they can describe the pack. Fairly quickly, we get a visual of 2 equivalent expressions.
And that is when I introduce the activity. Have you ever played the card game where you stick a playing card on your forehead? Every player has a card, but they can’t see it. The goal of the game is to figure out what card is on your head. This is like that, but in addition to finding out what card they have, students also need to find the other student in the class who is holding an equivalent expression. Once the students find their partners, they play a game of Equivalent Expression Memory and try to find as many matches as possible.
Set up for the Equivalent Expressions Memory Card Activity
- Have two 3-pack of tennis balls to demonstrate equivalent expressions for the class.
- Print multiple sets of the Equivalent Expressions Memory Cards for your class. You will need one set for the first part of the activity (one card per student) and then you will need one complete set per every 2 students. Another option for the second part where the students play the memory game, if you have enough devices, is to use this online game with the cards. You will still need to print one set though for part 1.
- If playing with paper cards, print the cards provided onto cardstock, or glue or write them on index cards. Cardstock or another thicker paper is important because you don’t want the print showing through the back. You may want to color code the packs or write a symbol on each pack so they are easier to sort if they get mixed up.
- Print one copy of the Find Your Match Equivalent Expressions Worksheet for each student.
Here are the things you will need to download for the lesson:
Launch the Lesson: Teaching Equivalent Expressions 6th Grade Math
Students should already be familiar with variable expressions. Review the vocabulary associated with equivalent expressions with students by providing examples on the board, while the students identify them on the first page of their worksheets.
A variable expression is a combination of mathematical terms and operations that contains at least one variable.
Review that a variable expression has several parts. Have students write some examples of variable expressions, then let give the parts.
Here is an example:
When you share expressions or have students contribute ideas, be sure to have students say them aloud as well as write them.
Then present the tennis ball example, or something similar, to show how variable expressions can be equivalent.
- Hold up a single tennis ball and ask the students “If one tennis ball is represented by the variable “t”, then what do I have in my hand?”
t, or 1t (At this point you can review that 1t is equivalent to t)
- Show a new pack of 3 tennis balls. Ask the students something like: “If each tennis ball is represented by the variable “t”, what is the pack of tennis balls?”
3t This is a variable term, but it is also an expression!
- Then show 1 tennis ball, and add 1 and then 1 more. Share and write that now you have t + t + t. This is also an expression! And it is Equivalent to 3t
- Students will write down the equivalent expressions
- Then put the 3 single balls into a pack and close the top. Put the 2 packs next to each other and start again. “How many tennis balls are there now?” and “How many packs”
- Work together to come up with equivalent expressions.
- The goal is to have students put it into words and variable expressions. You want them to SEE that six tennis balls is equivalent to 2 packs of 3 tennis balls.
- The equivalent expressions are 6t and 2(3t) – THEY MATCH!
Once the students have an idea of how to find equivalent expressions, start part 1 of the activity. This is where students will find their partner for the memory game.
The Activity: Equivalent Expressions Game
Part 1: Find your match
- Give students about 5 minutes to complete this activity.
- Provide each student one variable expression from the set of Equivalent Expressions Memory Cards.
- Tell them to hold it out in front of them and try not to peek! Or you could tape it to their backs. It’s not a big deal if the students see their expression, but it’s more fun if they need to ask another student what their card says. This helps build the language part of math!
- Once the students figure out which expression they have, it is their job to find the student in the class who is holding the equivalent expression. Students walk around and communicate which expression they see and which they have until they find their match. Encourage students to explain aloud to their partner why they think their expressions are (or are not) equivalent. Once the find their match, they should stay together as a pair.
- When students are sorted into pairs by their equivalent expressions, they should sit together, and get a set of cards to play memory.
Part 2: Equivalent Expressions Memory Game
- Each pair of students gets a full set of Equivalent Expressions Memory Cards (or devices to play the online game with the cards).
- If using paper cards, lay the cards face down on the table. The goal of the game is to find as many equivalent expressions as they can.
- Player 1 turns over 2 cards. The student should say the expressions aloud and say whether they are equivalent or not.
- If they are equivalent, they keep the match and play again
- If they are not equivalent, the cards are turned back over and it’s the other player’s turn.
- Play continues until the cards are all gone.
- Players should record the equivalent expressions they collect on the Find Your Match Equivalent Expressions Worksheet.
- Count up the pairs and see who won!
- Walk around and help students as they play memory. Give prompts to suggest helpful words and phrases and reinforce when students use the language of math.
- Two sheets will be given to each student.
- The students will cut the expressions on the first sheet and then glue them on the next page to match the equivalent expressions.
Reflecting on the Equivalent Expressions Game
Students should discuss with their partners and the class which equivalent expressions were the most difficult to match and why.
Each student will pick a pair of equivalent expressions that they used today. Have the students come up with a word problem or scenario that would represent those expressions – just like the tennis balls were used to show 6t = 2(3t).
Have students share word problems or scenarios with the class. Draw a picture to go with the expressions.
Look at the challenges on the worksheet and have the partners work together to figure out which expressions are equivalent. Expressions that use the distributive property can be challenging, so these may need to be done together or in small groups.
Examples of this include:
2(x+3) = 2x+6
Find a two pan balance scale, and see if you can find equivalent expressions using base ten blocks. You can use this online pan balance.
Try to make the pans balance, then try to write related equivalent expressions using variables.
FREE Equivalent Expressions Worksheets and Resources
These are all PDF Files. They will open and print easily. The Student Edition Files are labeled SE and the Teacher Editions Files are labeled TE. Click the links below to download the different resources.
- 4-6 Assignment SE – Equivalent Expressions (PDF)
- 4-6 Assignment TE – Equivalent Expressions (Members Only)
- 4-6 Bell Work SE – Equivalent Expressions (PDF)
- 4-6 Bell Work TE – Equivalent Expressions (Members Only)
- 4-6 Exit Quiz SE – Equivalent Expressions (PDF)
- 4-6 Exit Quiz TE – Equivalent Expressions (Members Only)
- 4-6 Guide Notes SE – Equivalent Expressions (PDF)
- 4-6 Guide Notes TE – Equivalent Expressions (Members Only)
- 4-6 Interactive Notebook – Equivalent Expressions (PDF)
- 4-6 Lesson Plan – Equivalent Expressions (PDF)
- 4-6 Online Activities – Equivalent Expressions (Members Only)
- 4-6 Slide Show – Equivalent Expressions (PDF)
Equivalent Expressions Worksheets and Resources
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- 4-6 Slide Show – Equivalent Expressions (PPT – Members Only)
- 4-6 Online Activities – Equivalent Expressions (Doc – Members Only)
- 4-6 Lesson Plan – Equivalent Expressions (Doc – Members Only)
- 4-6 Interactive Notebook – Equivalent Expressions (Doc – Members Only)
- 4-6 Guided Notes TE – Equivalent Expressions (Doc – Members Only)
- 4-6 Guided Notes SE – Equivalent Expressions (Doc – Members Only)
- 4-6 Exit Quiz TE – Equivalent Expressions (Doc – Members Only)
- 4-6 Exit Quiz SE – Equivalent Expressions (Doc – Members Only)
- 4-6 Bell Work TE – Equivalent Expressions (Doc – Members Only)
- 4-6 Bell Work SE – Equivalent Expressions (Doc – Members Only)
- 4-6 Assignment TE – Equivalent Expressions (Doc – Members Only)
- 4-6 Assignment SE – Equivalent Expressions (Doc – Members Only)
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