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n grade two students further build a mathematical, foundation that is critical to learning higher math. 6 ematics In previous grades students developed, a foundation for understanding place value including. grouping in tens and ones They built understanding of. 5 whole numbers to 120 and developed strategies to add. subtract and compare numbers They solved addition, and subtraction word problems within 20 and developed. fluency with these operations within 10 Students also. 4 worked with non standard measurement and reasoned. about attributes of geometric shapes adapted from,Charles A Dana Center 2012. Critical Areas of Instruction, In grade two instructional time should focus on four crit.

2 ical areas 1 extending understanding of base ten nota. tion 2 building fluency with addition and subtraction. 3 using standard units of measure and 4 describing. and analyzing shapes National Governors Association. 1 Center for Best Practices Council of Chief State School. Officers NGA CCSSO 2010i Students also work, toward fluency with addition and subtraction within 20. K using mental strategies and within 100 using strategies. based on place value properties of operations and the. relationship between addition and subtraction They. know from memory all sums of two one digit numbers. California Mathematics Framework Grade Two 119,Standards for Mathematical Content. The Standards for Mathematical Content emphasize key content skills and practices at each. grade level and support three major principles, l Focus Instruction is focused on grade level standards. l Coherence Instruction should be attentive to learning across grades and to linking major. topics within grades, l Rigor Instruction should develop conceptual understanding procedural skill and fluency. and application, Grade level examples of focus coherence and rigor are indicated throughout the chapter.

The standards do not give equal emphasis to all content for a particular grade level Cluster. headings can be viewed as the most effective way to communicate the focus and coherence. of the standards Some clusters of standards require a greater instructional emphasis than. others based on the depth of the ideas the time needed to master those clusters and their. importance to future mathematics or the later demands of preparing for college and careers. Table 2 1 highlights the content emphases at the cluster level for the grade two standards. The bulk of instructional time should be given to Major clusters and the standards within. them which are indicated throughout the text by a triangle symbol However stan. dards in the Additional Supporting clusters should not be neglected to do so would result. in gaps in students learning including skills and understandings they may need in later. grades Instruction should reinforce topics in major clusters by using topics in the addition. al supporting clusters and including problems and activities that support natural connec. tions between clusters, Teachers and administrators alike should note that the standards are not topics to be. checked off after being covered in isolated units of instruction rather they provide content. to be developed throughout the school year through rich instructional experiences present. ed in a coherent manner adapted from Partnership for Assessment of Readiness for College. and Careers PARCC 2012,120 Grade Two California Mathematics Framework. Table 2 1 Grade Two Cluster Level Emphases,Operations and Algebraic Thinking 2 OA. Major Clusters, Represent and solve problems involving addition and subtraction 2 OA 1. Add and subtract within 20 2 OA 2,Additional Supporting Clusters.

Work with equal groups of objects to gain foundations for multiplication 2 OA 3 4. Number and Operations in Base Ten 2 NBT,Major Clusters. Understand place value 2 NBT 1 4, Use place value understanding and properties of operations to add and subtract. Measurement and Data 2 MD,Major Clusters, Measure and estimate lengths in standard units 2 MD 1 4. Relate addition and subtraction to length 2 MD 5 6. Additional Supporting Clusters,Work with time and money 2 MD 7 8. Represent and interpret data 2 MD 9 10,Geometry 2 G.

Additional Supporting Clusters,Reason with shapes and their attributes 2 G 1 3. Explanations of Major and Additional Supporting Cluster Level Emphases. Major Clusters Areas of intensive focus where students need fluent understanding and application of the core. concepts These clusters require greater emphasis than others based on the depth of the ideas the time needed to. master them and their importance to future mathematics or the demands of college and career readiness. Additional Clusters Expose students to other subjects may not connect tightly or explicitly to the major work of the. Supporting Clusters Designed to support and strengthen areas of major emphasis. Note of caution Neglecting material whether it is found in the major or additional supporting clusters will leave gaps. in students skills and understanding and will leave students unprepared for the challenges they face in later grades. Adapted from Achieve the Core 2012,California Mathematics Framework Grade Two 121. Connecting Mathematical Practices and Content, The Standards for Mathematical Practice MP are developed throughout each grade and together with. the content standards prescribe that students experience mathematics as a rigorous coherent useful. and logical subject The MP standards represent a picture of what it looks like for students to under. stand and do mathematics in the classroom and should be integrated into every mathematics lesson. for all students, Although the description of the MP standards remains the same at all grade levels the way these. standards look as students engage with and master new and more advanced mathematical ideas does. change Table 2 2 presents examples of how the MP standards may be integrated into tasks appropriate. for students in grade two Refer to the Overview of the Standards Chapters for a description of the MP. Table 2 2 Standards for Mathematical Practice Explanation and Examples for Grade Two. Standards for,Mathematical Explanation and Examples.

MP 1 In grade two students realize that doing mathematics involves reasoning about and solving. problems Students explain to themselves the meaning of a problem and look for ways to. Make sense of solve it They may use concrete objects or pictures to help them conceptualize and solve. problems and problems They may check their thinking by asking themselves Does this make sense. persevere in They make conjectures about the solution and plan out a problem solving approach. solving them, MP 2 Younger students recognize that a number represents a specific quantity They connect the. quantity to written symbols Quantitative reasoning entails creating a representation of a. Reason problem while attending to the meanings of the quantities. abstractly and, quantitatively Students represent situations by decontextualizing tasks into numbers and symbols For. example a task may be presented as follows There are 25 children in the cafeteria and. they are joined by 17 more children How many students are in the cafeteria Students. translate the situation into an equation such as 25 17 and then solve the problem. Students also contextualize situations during the problem solving process To reinforce stu. dents reasoning and understanding teachers might ask How do you know or What is. the relationship of the quantities, MP 3 Grade two students may construct arguments using concrete referents such as objects. pictures math drawings and actions They practice their mathematical communication. Construct via skills as they participate in mathematical discussions involving questions such as How did. ble arguments you get that Explain your thinking and Why is that true They not only explain their. and critique own thinking but also listen to others explanations They decide if the explanations make. the reasoning sense and ask appropriate questions, Students critique the strategies and reasoning of their classmates For example to solve. 74 18 students might use a variety of strategies and discuss and critique each other s. reasoning and strategies, MP 4 In early grades students experiment with representing problem situations in multiple ways.

including writing numbers using words mathematical language drawing pictures using. Model with objects acting out making a chart or list or creating equations Students need opportuni. mathematics ties to connect the different representations and explain the connections. 122 Grade Two California Mathematics Framework,Table 2 2 continued. Standards for,Mathematical Explanation and Examples. Students model real life mathematical situations with an equation and check to make sure. that their equation accurately matches the problem context They use concrete manipula. tives or math drawings or both to explain the equation They create an appropriate. problem situation from an equation For example students create a story problem for the. equation 43 82 such as There were 43 mini balls in the machine Tom poured in. some more mini balls There are 82 mini balls in the machine now How many balls did. Tom pour in Students should be encouraged to answer questions such as What math. drawing or diagram could you make and label to represent the problem or What are. some ways to represent the quantities, MP 5 In second grade students consider the available tools including estimation when solving. a mathematical problem and decide when certain tools might be better suited than others. Use appro For instance grade two students may decide to solve a problem by making a math drawing. priate tools rather than writing an equation,strategically. Students may use tools such as snap cubes place value base ten blocks hundreds number. boards number lines rulers virtual manipulatives diagrams and concrete geometric shapes. e g pattern blocks three dimensional solids Students understand which tools are the. most appropriate to use For example while measuring the length of the hallway students. are able to explain why a yardstick is more appropriate to use than a ruler Students should. be encouraged to answer questions such as Why was it helpful to use. MP 6 As children begin to develop their mathematical communication skills they try to use clear. and precise language in their discussions with others and when they explain their own. Attend to reasoning, Students communicate clearly using grade level appropriate vocabulary accurately and.

precise explanations and reasoning to explain their process and solutions For example. when measuring an object students carefully line up the tool correctly to get an accurate. measurement During tasks involving number sense students consider if their answers are. reasonable and check their work to ensure the accuracy of solutions. MP 7 Grade two students look for patterns and structures in the number system For example. students notice number patterns within the tens place as they connect counting by tens to. Look for and corresponding numbers on a hundreds chart Students see structure in the base ten number. make use of system as they understand that 10 ones equal a ten and 10 tens equal a hundred Teachers. structure might ask What do you notice when or How do you know if something is a. Students adopt mental math strategies based on patterns making ten fact families. doubles They use structure to understand subtraction as an unknown addend problem. e g 50 33 can be written as 33 50 and can be thought of as How much. more do I need to add to 33 to get to 50, MP 8 Second grade students notice repetitive actions in counting and computation e g number. patterns to count by tens or hundreds Students continually check for the reasonableness of. Look for their solutions during and after completion of a task by asking themselves Does this make. and express sense Students should be encouraged to answer questions such as What is happening in. regularity in this situation or What predictions or generalizations can this pattern support. Adapted from Arizona Department of Education ADE 2010 and North Carolina Department of Public Instruction NCDPI 2013b. California Mathematics Framework Grade Two 123,Standards Based Learning at Grade Two. The following narrative is organized by the domains in the Standards for Mathematical Content and. highlights some necessary foundational skills from previous grade levels It also provides exemplars to. explain the content standards highlight connections to Standards for Mathematical Practice MP and. demonstrate the importance of developing conceptual understanding procedural skill and fluency and. application A triangle symbol indicates standards in the major clusters see table 2 1. Domain Operations and Algebraic Thinking, In grade one students solved addition and subtraction word problems within 20 and developed fluency. with these operations within 10 A critical area of instruction in grade two is building fluency with ad. dition and subtraction Second grade students fluently add and subtract within 20 and solve addition. and subtraction word problems involving unknown quantities in all positions within 100 Grade two. students also work with equal groups of objects to gain the foundations for multiplication. Operations and Algebraic Thinking 2 OA, Represent and solve problems involving addition and subtraction. foundation that is critical to learning higher math ematics In previous grades students developed a foundation for understanding place value including grouping in tens and ones They built understanding of whole numbers to 120 and developed strategies to add subtract and compare numbers They solved addition and subtraction word problems within 20 and developed fluency with these

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