Algebraic Thinking Task Card SET 2: Concept of "Equals" Grades 4 -5

Grade Levels
4th - 6th, Homeschool
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By popular request--a second set of algebra thinking task cards! This second set of 52 The concepts of “equals” is such an essential mathematical concept—and one that is often not taught explicitly in many math programs. This set adds additional work with multiplication and division in the earlier cards. Not sure what these cards do? Consider the following problem:

5 + 8 = ____ + 3

Students have a good sense of the concept of equals know that “10” goes in the box. Every year, I am shocked by the number of students who think it is “13”—or that the problem can’t be done at all! Many students are programmed to think that the “=“ sign means “find the answer” when, in actuality, it is a sign indicating that the two sides balance. Deep understanding of this helps down the road with algebra and other more advanced math—and also makes a smooth transition to INequalities as well. Moving our “box” (or “variable”, or a letter, or a line, or a question mark) to different places in equations helps students think about numbers and equality and not just filling in the blank. This task card set is geared toward helping students develop this understanding. I tell them that they are doing algebra—and they absolutely love it! Consider doing a few of the early cards as a class to teach the concept and then let your students take off! They get more and more challenging as they progress--but you will be AMAZED at the math thinking your students will do!

One of my students’ favorite activities is to make their OWN task cards, so once they have learned this concept, send them off to make their own cards at a variety of levels and then print and laminate those for your class to use as well. ENJOY!


Interested in the first set?


Set 1 of this resource is also available as part of a "Teaching Tandem" product where you can get this resource AND a set of algebra thinking concept sorts combined at a reduced price.


Set 1 is also available as a digital task card resource in my GOOGLE EDITION resources!



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Total Pages
32 pages
Answer Key
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to see state-specific standards (only available in the US).
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.
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.
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.
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
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.


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