# Ages: Math, Problem Solving and Critical Thinking

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(4 MB|28 pages)
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1. This bundle includes 3 context-driven problem-solving activity sets. Each of the problems in this bundle ask students to apply number sense, arithmetic, and logical thinking skills in order to find the solution. Students will build flexibility with numbers, as well as critical thinking skills as the
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• StandardsNEW

What are the ages of Tom’s kids?

How did Lisa figure out the ages, based on the clues given, even when it doesn’t seem like enough information?

Challenge your students to problem solve their way through Tom’s clues to figure out the ages of his children, as Lisa did!

This download includes a complete problem-solving journey to get your students thinking, including 2 unique, engaging, problem-solving tasks; the Problem, and its Exstemsion.

Created by teachers, with teachers and parents in mind, each task is built to challenge students to use their prior knowledge, and think creatively as they strive to solve the context-driven problems.

•Thinking skills (what kind of thinking are kids building here?)

•Problem/Solution

•Exstemsion/Solution

•Supporting Questions (ideas for the questions you might as a student when they are stuck, place where they are most likely to get stuck!)

•Big Ideas (what are the math ideas built through this problem?)

No PREP required! Each challenge is ready to PRINT, and comes with an easy to use, 100% complete, and detailed solution!

Math Category: Number theory/sense and logical thinking

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.
Total Pages
28 pages
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