Algebraic Thinking Task Cards: Number Sense for Grades 3-5

Grade Levels
3rd - 5th
Standards
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Description

This set of 52 differentiated algebraic thinking task cards is perfect to help students use problem solving to learn about balancing simple equations and truly understanding what that equal sign means. The concepts of “equals” is such an essential mathematical concept—and one that is often not taught explicitly in many math programs. 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!

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!

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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.

CLICK HERE TO VIEW

Want even MORE of them? Now there is a "Set 2". Just CLICK HERE TO VIEW Set 2

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

CLICK HERE TO VIEW

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All rights reserved by ©The Teacher Studio. Purchase of this resource entitles the purchaser the right to reproduce the pages in limited quantities for single classroom use only. Duplication for an entire school, an entire school system, or commercial purposes is strictly forbidden without written permission from the author at fourthgradestudio@gmail.com. Additional licenses are available at a reduced price.

Total Pages
32 pages
Answer Key
Included
Teaching Duration
N/A
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Standards

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.
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
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.
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

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