CCSS-M Teacher Professional Learning Session #1, October 2014 Grade 2 Packet Contents (Selected pages relevant to session work) Content Standards Standards for Mathematical Practice California Mathematical Framework Kansas CTM Flipbook Learning Outcomes Sample Assessment Items 2 Grade 2 Operations and Algebraic Thinking 2.OA Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Add and subtract within 20. 2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers. Work with equal groups of objects to gain foundations for multiplication. 3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Number and Operations in Base Ten 2.NBT Understand place value. 1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2. Count within 1000; skip-count by 2s, 5s, 10s, and 100s. CA 3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Use place value understanding and properties of operations to add and subtract. 5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 6. Add up to four two-digit numbers using strategies based on place value and properties of operations. 7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 7.1 Use estimation strategies to make reasonable estimates in problem solving. CA 8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. 1 See Glossary, Table 1. 2 See standard 1.OA.6 for a list of mental strategies. Prepublication Version, April 2013 California Department of Education 17 | Common Core State Standards - Mathematics Standards for Mathematical Practices – 2nd Grade Standard for Mathematical Practice 2nd Grade 1: Make sense of problems and persevere in solving them. In second grade, students realize Mathematically proficient students start by explaining to themselves the meaning of a problem that doing mathematics involves and looking for entry points to its solution. They analyze givens, constraints, relationships, and solving problems and discussing goals. They make conjectures about the form and meaning of the solution and plan a solution how they solved them. Students pathway rather than simply jumping into a solution attempt. They consider analogous problems, explain to themselves the and try special cases and simpler forms of the original problem in order to gain insight into its meaning of a problem and look solution. They monitor and evaluate their progress and change course if necessary. Older for ways to solve it. They may use students might, depending on the context of the problem, transform algebraic expressions or concrete objects or pictures to change the viewing window on their graphing calculator to get the information they need. help them conceptualize and Mathematically proficient students can explain correspondences between equations, verbal solve problems. They may check descriptions, tables, and graphs or draw diagrams of important features and relationships, graph their thinking by asking data, and search for regularity or trends. Younger students might rely on using concrete objects themselves, -Does this make or pictures to help conceptualize and solve a problem. Mathematically proficient students check sense? They make conjectures their answers to problems using a different method, and they continually ask themselves, “Does about the solution and plan out a this make sense?” They can understand the approaches of others to solving complex problems problem-solving approach. and identify correspondences between different approaches. 2: Reason abstractly and quantitatively. Younger students recognize that Mathematically proficient students make sense of quantities and their relationships in problem a number represents a specific situations. They bring two complementary abilities to bear on problems involving quantitative quantity. They connect the relationships: the ability to decontextualize-to abstract a given situation and represent it quantity to written symbols. symbolically and manipulate the representing symbols as if they have a life of their own, without Quantitative reasoning entails necessarily attending to their referents-and the ability to contextualize, to pause as needed creating a representation of a during the manipulation process in order to probe into the referents for the symbols involved. problem while attending to the Quantitative reasoning entails habits of creating a coherent representation of the problem at meanings of the quantities. hand; considering the units involved; attending to the meaning of quantities, not just how to Second graders begin to know compute them; and knowing and flexibly using different properties of operations and objects. and use different properties of operations and relate addition and subtraction to length. 3: Construct viable arguments and critique the reasoning of others. Second graders may construct Mathematically proficient students understand and use stated assumptions, definitions, and arguments using concrete previously established results in constructing arguments. They make conjectures and build a referents, such as objects, logical progression of statements to explore the truth of their conjectures. They are able to pictures, drawings, and actions. analyze situations by breaking them into cases, and can recognize and use counterexamples. They practice their mathematical They justify their conclusions, communicate them to others, and respond to the arguments of communication skills as they others. They reason inductively about data, making plausible arguments that take into account participate in mathematical the context from which the data arose. Mathematically proficient students are also able to discussions involving questions compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning like -How did you get that? - from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary Explain your thinking, and -Why is students can construct arguments using concrete referents such as objects, drawings, diagrams, that true?‖They not only explain and actions. Such arguments can make sense and be correct, even though they are not their own thinking, but listen to generalized or made formal until later grades. Later, students learn to determine domains to others’ explanations. They decide which an argument applies. Students at all grades can listen or read the arguments of others, if the explanations make sense decide whether they make sense, and ask useful questions to clarify or improve the arguments. and ask appropriate questions. 4: Model with mathematics. In early grades, students Mathematically proficient students can apply the mathematics they know to solve problems experiment with representing arising in everyday life, society, and the workplace. In early grades, this might be as simple as problem situations in multiple writing an addition equation to describe a situation. In middle grades, a student might apply ways including numbers, words proportional reasoning to plan a school event or analyze a problem in the community. By high (mathematical language), school, a student might use geometry to solve a design problem or use a function to describe drawing pictures, using objects, how one quantity of interest depends on another. Mathematically proficient students who can acting out, making a chart or list, apply what they know are comfortable making assumptions and approximations to simplify a creating equations, etc. Students complicated situation, realizing that these may need revision later. They are able to identify need opportunities to connect important quantities in a practical situation and map their relationships using such tools as the different representations and diagrams, two-way tables, graphs, flowcharts and formulas.