# Which One Doesn't Belong (Number Talks) FREEBIE

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(1 MB|4 pages)
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Which One Doesn't Belong? are open-ended questions / number talks. They are a fantastic way to get even your most reluctant students to analyze problems and persevere in solving them, reason abstractly and quantitatively, engage in deep mathematical thinking while justifying conclusions, communicate to and with others, and respond to the ideas of others.

These are a staple in my First Grade classroom.

Designed for Grades 1-2, there are plenty of opportunities to use these Number Sense slides in your unit or throughout the year. Use as an opener, a Do-Now in the morning, for homework, or in your math workstations. There is always more than one answer and I am always impressed when a child comes up with a way that I didn't even think of. That happens all the time!

What's Included in this freebie?

*2 colorful pages to project that can be used for whole group instruction.

*Matching B&W copies for individual use.

To see videos of these in action and find out exactly why I use these in my classroom, visit my blog post Which One Doesn't Belong?

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Which One Doesn't Belong Number Talks

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Open-Ended Math Questions

Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (π¦ β 2)/(π₯ β 1) = 3. Noticing the regularity in the way terms cancel when expanding (π₯ β 1)(π₯ + 1), (π₯ β 1)(π₯Β² + π₯ + 1), and (π₯ β 1)(π₯Β³ + π₯Β² + π₯ + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
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 Γ 8 equals the well remembered 7 Γ 5 + 7 Γ 3, in preparation for learning about the distributive property. In the expression π₯Β² + 9π₯ + 14, older students can see the 14 as 2 Γ 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 β 3(π₯ β π¦)Β² 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 π₯ and π¦.
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.
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