Balancing Equations Problem Solving Task Cards - Math Challenge Activity

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248 Ratings
The Teacher Studio
Grade Levels
3rd - 5th, Homeschool
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20 pages
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What educators are saying

Love these! Great to use as a center to get kids thinking of equations in a different way. Thank you!
My students really enjoyed this resource because it made them think differently about balancing equations. Some were quite challenging but we had great math conversations. Thank you!


Understanding the concept of “equal” is a critical part of developing number sense and algebraic thinking. This resource helps students get more flexible “playing” with numbers as they try to use algebra thinking to “balance” the gems on the two sides of the balance.

These cards help students develop their math reasoning AND computation skills while having a fun and engaging task! My students LOVE these--and feel like real mathematicians when they figure them out!


The first group of cards works to build understanding—and then they get increasingly more open-ended for students to “build” their own problems and show their understanding. I've even created a video to help you see how to teach using these cards. Just CLICK HERE to check it out!

Using algebraic thinking, logic, and number sense helps students begin to see how algebra concepts can make sense--even for elementary students! This set of 30 cards can be a fun and meaningful way to get students thinking.

Use as a math station…as a class review…with an intervention send digitally—or throw individual cards under a document camera for a class warm up! I have included the cards in color and gray tones for complete flexibility. Recording sheets and answer key are included as well. Also included is a list of “rules” that can be shared with the class and/or printed to include with the cards.

Check out the preview and preview videos for more!

Not quite sure? Grab this free sample to try one! Balancing Equation Task Cards FREEBIE

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Total Pages
20 pages
Answer Key
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to see state-specific standards (only available in the US).
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression 𝑥² + 9𝑥 + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(𝑥 – 𝑦)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers 𝑥 and 𝑦.


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