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# Math Challenges - Algebraic Thinking "Bubbles" Problem Solving Task Cards

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The Teacher Studio
17k Followers
3rd - 5th, Homeschool
Subjects
Resource Type
Standards
Formats Included
• PDF
Pages
20 pages
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The Teacher Studio
17k Followers

### Description

Understanding the concept of “equal” is a critical part of developing number sense and algebraic thinking. This problem solving resource helps students get more flexible “playing” with numbers as they try to use algebra thinking to figure out what numbers can fit to make the problems true. It can really help solidify addition, subtraction, and estimation skills but in a super fun way!

Each task card has a set of bubbles that are connected to either 2 or 3 other bubbles. Students are given the total for each adjoining bubbles, and students need to use their reasoning and even “guess and check” to determine which numbers will work in the bubbles to make all the totals accurate.

Look at the preview for more explanation. Considering modeling with a few to help students see some of the strategies they can use as they tackle these great challenges!

Use as a math station…as a class review…with an intervention group—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! Check the preview for even more ideas and suggestions. ENJOY!

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Total Pages
20 pages
Included
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### Standards

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.