No Series: Related Problems: Reasoning About Addition
Math.Practice.MP3
 Common core State Standards
 Math: Math
 Practice: Mathematical Practice Standards

MP3: 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, andif there is a flaw in an argumentexplain 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.
Math.Practice.MP8
 Common core State Standards
 Math: Math
 Practice: Mathematical Practice Standards

MP8: 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 (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 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.
Math.1.OA.B.3
Common core State Standards
 Math: Math
 1: Grade 1
 OA: Operations & Algebraic Thinking
 B: Understand and apply properties of operations and the relationship between addition and subtraction

3:
**Apply properties of operations as strategies to add and subtract. Students need not use formal terms for these properties. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 =
 : (Associative property of addition.)**
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Discussion and Supporting Materials
Thought starters
 What kinds of problems work best for this activity?
 How are students encouraged to learn from each other throughout the lesson?
 What do student learn from analyzing related problems?
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