Second+grade+curriculum

|| § Develop math vocabulary and symbols § Reflect on or clarify thinking about mathematical ideas and situations § Restate math concepts § Explain and justify answers § Explain methods of solving a problem § Describe what extra information is needed to solve a problem
 * Lansing School District Math Curriculum **
 * **Second Grade:** Second graders continue with more sophisticated work in addition and subtraction of whole numbers, and begin conceptual development of multiplication and division, grounded in contexts and modeled using concrete objects. Teachers can emphasize the inverse relationships between addition and subtraction, and multiplication and division. Children will be using strategies and algorithms, to compute using whole numbers. Students should be fluent with addition and subtraction facts up to 10 + 10 by the end of second grade. Simple ideas about fractions are introduced. In geometry, children continue to learn about geometric shapes and their elements.
 * ==== ** Year long instructional strategies, processes, skill development, or content expectations ** ==== ||
 * ** Communication ** || ** Reasoning ** || ** Connections ** || ** Problem Solving ** || ** Data Analysis ** ||
 * § Discuss, write, or draw to show depth of mathematical ideas and relationships

|| § Verify and justify answers § Use logical spatial and proportional reasoning § Generalize from a set of observations § Evaluate accuracy of a solution to a problem § Solve a variety of non-routine, real world problems § Make and test conjectures § Develop rules and procedures

|| § Recognize mathematical connections that occur in everyday experience § Recognize relationships using number lines, calendars, graphing, and money § Recognize mathematical relationships that occur between various mathematical topics § Identify mathematical concepts that occur in other disciplines § Recognize the need for math in order to pursue various careers § Use mathematics to describe the physical world § Utilize technology to enhance mathematical understanding || § Use students’ prior knowledge of mathematical content and process § Solve a simpler problem to suggest a solution for a more complex problem § Solve multi-step problems § Formulate problems for real world situations § Use manipulatives § Draw a figure § Guess and check § Look for a pattern § Retell a story problem § Explain a problem solution § Make a list § Simplify § Draw a diagram or table § Work backwards

|| § Collect, organize, interpret and describe data from tables § Analyze data § Analyze patterns § Formulate and solve problems using given data § Construct and interpret graphs § Utilize a variety of graphic displays using appropriate scales with given sets of numerical data: ||  Integration Teacher Notes |||| = Curriculum = // What do we want students to learn? // |||||| Instructional Strategies // How will we deliver the curriculum? // |||| Resources // What materials/resources will we need to ensure mastery //. |||| Assessment // How will we know if students learn? // || || Count to 1,000 by ones, tens, and hundreds starting from any number in the sequence N.ME.02.02 Read and write numbers to 1,000 in numerals and words, and relate them to the quantities they represent. N.M.E.02.05 Express numbers up to 1,000 using place value, e.g. 137 is 1 hundred, 3 tens, and 7 ones; use concrete materials. N.M.E.02.03 Compare and order numbers to 1,000; use the symbols <, =, and >. [|Ordering numbers to 1,000] N.M.E.02.04 Count orally by 3s and 4s starting with 0, and by 2s, 5s, and 10s starting from any whole number.
 * 
 * ** 1st ** Quarterly focused instructional strategies, processes, skill development, or content expectations
 * ** Units: Place Value (6 weeks), starting Addition and Subtraction (3 weeks) ** ||
 * |||| N.ME.O2.01

N.F.L.02.10 Add fluently two numbers through 99, using strategies including formal algorithms; subtract fluently two numbers through 99 N.M.R.02.09 Given a contextual situation that involves addition and subtraction using numbers through 99; model using objects or pictures; explain in words; record using numbers and symbols; solve. || Use concrete objects to explore and discuss groups of tens and ones, the value of a digit in 2-digit and 3-digit numbers, and read and write numbers

Use concrete objects to explore and discuss ordinal positions to twentieth, and compare and order 2-digit numbers

Use the problem-solving strategy. Make a model to show money amounts.

Use hundreds charts to explore numbers up to 1,000, including place value, counting by multiples of 2, 3, 4, 5, 10, and 100, etc.

Also see year-long content.

Use concrete objects and drawing pictures to explore and discuss addition and subtraction strategies.

Use the strategies counting on, doubles, and doubles plus one, and make a ten to solve addition sentences.

Explore and discuss finding the sum of 3 addends.

Count back to solve subtraction sentences.

Use inverse operations and fact families to relate addition and subtraction.

Explore and discuss identifying missing numbers, number expressions, and writing number sentences.

Model and discuss adding and subtracting 1-digit numbers

Utilize math websites for practice and exploration

|||| Harcourt Math Chapters 1, 27

Chapters 1, 27

Chapters 1, 2

Chapters 3, 28

Chapter 28

Chapters 5 (one-digit addition and subtraction)

Resources for Place Value

Resources for 2-digit Addition and Subtraction |||| Effective Questioning (see appendix)

Classroom observation and discussion

Student reasoning and justification

Student math journals (writing and reflection)

Harcourt Math Investigations unit:
 * Chapter tests
 * End-of-chapter review pages
 * Assessment guide
 * MEAP resource book unit tests
 * Teacher Checkpoints
 * Assessment Activities

|| ||  Notes || = Curriculum = // What do we want students to learn? // |||||| Instructional Strategies // How will we deliver the curriculum? // |||| Assessment // How will we know if students learn? // || Resources // What materials/resources will we need to ensure mastery //. || || || Add fluently two numbers through 99, using strategies including formal algorithms; subtract fluently two numbers through 99 N.MR.02.09 Given a contextual situation that involves addition and subtraction using numbers through 99; model using objects or pictures; explain in words; record using numbers and symbols; solve. N.MR.2.07 Find the distance between numbers on the number line, e.g. how far is 79 from 26? N.MR.02.08 Find missing values in open sentences, e.g. 42 + ⁯ = 57; use relationship between addition and subtraction N.FL.02.11 Estimate the sum of two numbers with three digits. N.FL.02.12 Calculate mentally sums and differences involving three-digit numbers and ones; three-digit numbers and tens; three-digit numbers and hundreds. N.FL.2.06 Decompose 100 into addition pairs, e.g. 99 + 1, 98 + 2…  || Use concrete objects and drawing pictures to explore and discuss addition and subtraction strategies.
 * Integration Teacher
 * ** 2nd ** Quarterly focused instructional strategies, processes, skill development, or content expectations
 * ** Units: Addition and subtraction of 1- and 2-digit numbers (cont.; 6 weeks); beginning 3-digit addition (3 weeks) **
 * |||| N.FL.02.10

Use the strategies counting on, doubles, and doubles plus one, and make a ten to solve addition sentences.

Explore and discuss finding the sum of 3 addends.

Count back to solve subtraction sentences.

Use inverse operations and fact families to relate addition and subtraction.

Explore and discuss identifying missing numbers, number expressions, and writing number sentences.

Model and discuss adding and subtracting 2-digit numbers

Use count back and regroup to subtract 2-digit numbers

Utilize math websites for practice and exploration |||| Effective Questioning (see appendix)

Classroom observation and discussion

Student reasoning and justification

Student math journals (writing and reflection)

Harcourt Math Investigations unit: 
 * Chapter tests
 * End-of-chapter review pages
 * Assessment guide
 * MEAP resource book unit tests
 * Teacher Checkpoints
 * Assessment Activities

|||| Harcourt Brace Chapter 6 (one-digit addition and subtraction) Chapters 7-9 (two-digit addition and subtraction)

Specific Resources ||  Notes || = Curriculum = // What do we want students to learn? // |||| Instructional Strategies // How will we deliver the curriculum? // |||| Resources // What materials/resources will we need to ensure mastery //. || Assessment // How will we know if students learn? // || ||
 * Integration Teacher
 * ** 3rd ** Quarterly focused instructional strategies, processes, skill development, or content expectations
 * ** Units: 2-digit addition and subtraction (cont.; 6 weeks); fractions (3 weeks) ** ||

|| N.FL.02.10 Add fluently two numbers through 99, using strategies including formal algorithms; subtract fluently two numbers through 99 N.MR.02.09 Given a contextual situation that involves addition and subtraction using numbers through 99; model using objects or pictures; explain in words; record using numbers and symbols; solve. N.MR.2.07 Find the distance between numbers on the number line, e.g. how far is 79 from 26? N.MR.02.08 Find missing values in open sentences, e.g. 42 + ⁯ = 57; use relationship between addition and subtraction N.FL.02.11 Estimate the sum of two numbers with three digits. N.FL.02.12 Calculate mentally sums and differences involving three-digit numbers and ones; three-digit numbers and tens; three-digit numbers and hundreds. N.FL.2.06 Decompose 100 into addition pairs, e.g. 99 + 1, 98 + 2…

N.ME.02.22 Recognize that fractions such as 2/2, 3/3, and 4/4 are equal to the whole (one). N.ME.02.18 Recognize, name, and represent commonly used unit fractions with denominators 12 or less; model ½, 1/3, and ¼ by folding strips. N.ME.02.19 Recognize, name, and write commonly used fractions: 1/2., 1/3, 2/3, ¼, 2/4, ¾. N.ME.02.20 Place 0 and halves, e.g. ½, 1 ½,2 1/2, on the number line; relate to a ruler. N.ME.02.21 For unit fractions from 1/12 to ½, understand the inverse relationship between the size of the unit fraction and the size of the denominator; compare unit fractions from 1/12 to ½. || Use concrete objects and drawing pictures to explore and discuss addition and subtraction strategies.

Use the strategies counting on, doubles, and doubles plus one, and make a ten to solve addition sentences.

Explore and discuss finding the sum of 3 addends.

Count back to solve subtraction sentences.

Use inverse operations and fact families to relate addition and subtraction.

Explore and discuss identifying missing numbers, number expressions, and writing number sentences.

Model and discuss adding and subtracting 2-digit numbers

Use count back and regroup to subtract 2-digit numbers

Utilize math websites for practice and exploration

Use concrete objects to explore and discuss commonly used unit fractions (equal parts).

Use concrete objects to explore and discuss fractions other than unit fractions and fractions equal to 1.

Use fractions to identify parts of a group.

Utilize math websites for practice and exploration |||| Effective Questioning (see appendix)

Classroom observation and discussion

Student reasoning and justification

Student math journals (writing and reflection)

Harcourt Math Investigations unit: |||| Harcourt Math Chapters 10, 11 (two-digit addition and subtraction)
 * Chapter tests
 * End-of-chapter review pages
 * Assessment guide
 * MEAP resource book unit tests
 * Teacher Checkpoints
 * Assessment Activities

Harcourt Math Chapter 26

||  Integration Teacher Notes |||| = Curriculum = // What do we want students to learn? // |||||| Instructional Strategies // How will we deliver the curriculum? // |||| Resources // What materials/resources will we need to ensure mastery //. |||| Assessment // How will we know if students learn? // || || Measure lengths in meters, centimeters, inches, feet, and yards approximating to the nearest whole unit and using abbreviations; cm, m, in, ft, yd.
 * 
 * ** 4th ** Quarterly focused instructional strategies, processes, skill development, or content expectations
 * ** Unit: Measurement and Geometry (7weeks), Multiplication and Division (2 weeks) ** ||
 * |||| M.UN.02.01

M.PS.02.02 Compare lengths; add and subtract lengths (no conversion of units). M.UN.02.03 Measure area using non-standard units to the nearest whole unit. M.TE.02.04 Find the area of a rectangle with whole number side lengths by covering with unit squares and counting, or by using a grid of unit squares; write the area as a product. M.TE.02.11 Determine perimeters of rectangles and triangles by adding lengths of sides, recognizing the meaning of perimeter. G.GS.02.01 Identify, describe, and compare familiar two-dimensional and three-dimensional shapes, such as triangles, rectangles, squares, circles, semi-circles, spheres, and rectangular prisms. G.GS. 02.02 Explore and predict the results of putting together and taking apart two-dimensional and three-dimensional shapes. G.GS.02.04 Distinguish between curves and straight lines and between curved surfaces and flat surfaces. G.SR.02.05 Classify familiar plane and solid objects, e.g., square, rectangle, rhombus, cube, pyramid, prism, cone, cylinder, and sphere, by common attributes such as shape, size, color, roundness, or number of corners and explain which attributes are being used for classification. G.TR.02.06 Recognize that shapes that have been slid, turned, or flipped are the same shape, e.g., a square rotated 45 degrees.

|| Use inches, feet, yards, centimeters and meters to explore and discuss measuring length

Specific Resources for Measurement

Use concrete objects and real-life situations to explore and discuss perimeter and area

Use nonstandard units to explore and discuss measuring length

Use concrete objects to explore and discuss measuring length |||| Chapters 22.1-22.4,24.1

Not in Text

Chapter 25.2

Not in Text

Chapter 25.1

Chapters 18, 19

Chapters 18, 19

Chapters 18, 19

Chapters 18, 19

Chapter 20.3 |||| Classroom Observation and Discussion

Student Reasoning and Justification

Student Math journals (Writing & Reflection)

Harcourt Math: · Chapter tests · End-of-the chapter review pages · Assessment guide · MEAP Resource Book unit tests

Investigations Unit: · Teacher Checkpoints · Assessment Activities || ||  Integration Teacher Notes |||| = Curriculum = // What do we want students to learn? // |||||| Instructional Strategies // How will we deliver the curriculum? // |||| Resources // What materials/resources will we need to ensure mastery //. |||| Assessment // How will we know if students learn? // || || Understand multiplication as the result of counting the total number of objects in a set of equal groups, e.g., 3 x 5 gives the number of objects in 3 groups of 5 objects, or 3 x 5 = 5 + 5 + 5 = 15. N. MR.02.14 Represent multiplication using area and array models. N.MR.02.15 Understand division (÷) as another way of expressing multiplication, using fact families within the 5 x 5 multiplication table; emphasize that division “undoes” multiplication, e.g., 2 x 3 = 6 can be rewritten as 6 ÷ 2 = 3 or 6 ÷ 3 = 2. N. MR.02.16 Given a situation involving groups of equal size or of sharing equally, represent with objects, words, and symbols; solve.* N. MR.02.17 Develop strategies for fluently multiplying numbers up to 5 x 5.*
 * 
 * ** Unit: Multiplication and Division (2 weeks) **
 * |||| N.MR.02.13

|| Model and discuss equal groups and use repeated addition and multiplication sentences to find how many in all

Model and discuss arrays to show multiplication

Explore and discuss multiplying numbers in order

Explore and discuss the division concept of equal groups, and making equal groups |||| Chapter 30

Chapter 30

Chapter 30

Chapter 30

Chapter 30  |||| Classroom Observation and Discussion

Student Reasoning and Justification

Student Math Journals (Writing & Reflection)

Harcourt Math: · Chapter tests · End-of-the chapter review pages · Assessment guide · MEAP Resource Book Unit tests

Investigations Unit: · Teacher Checkpoints · Assessment Activities

|| || Notes || = Curriculum = // What do we want students to learn? // |||||| Instructional Strategies // How will we deliver the curriculum? // |||| Assessment // How will we know if students learn? // || Resources // What materials/resources will we need to ensure mastery //. || ||
 * Integration Teacher
 * ** Year-long instructional strategies, processes, skill development, and content expectations **

|||| N.ME.02.05 Express numbers through 999 using place value, e.g., 137 is 1 hundred, 3 tens, and 7 ones; use concrete materials.* M.UN.02.05 Using both A.M. and P.M., tell and write time from the clock face in 5 minute intervals and from digital clocks to the minute; include reading time: 9:15 as nine-fifteen and 9:50 as nine-fifty. Interpret time both as minutes after the hour and minutes before the next hour, e.g., 8:50 as eight-fifty and ten to nine. Show times by drawing hands on clock face. M.UN.02.06 Use the concept of duration of time, e.g., determine what time it will be half an hour from 10:15. M.UN.02.07 Read and write amounts of money using decimal notations, e.g., $1.15. M.PS.02.08 Add and subtract money in mixed units, e.g., $2.50 + 60 cents and $5.75 - $3, but not $2.50 + $3.10. M.UN.02.09 Read temperature using the scale on a thermometer in degrees Fahrenheit. M.PS.02.10 Solve simple word problems involving length and money. G.LO.02.07 Find and name locations using simple coordinate systems such as maps and first quadrant grids. D.RE.02.01 Make pictographs using a scale representation, using scales where symbols equal more than one. D. RE. 02.02 Read and interpret pictographs with scales, using scale factors of 2 and 3. D. RE. 02.03 Solve problems using information in pictographs; include scales such as each ■ represents 2 apples; avoid using partial pictographs.

|| Model and discuss strategies using base ten blocks. Use concrete objects to explore and discuss groups of tens and ones, the value of a digit in 2-digit and 3-digit numbers, and read and write numbers in expanded and written form. Use an analog and digital clock to explore, discuss, read and write time. Use concrete objects to explore, discuss and write money amounts (same amount, dollar and cent signs, mixed collection of coins, total amount, compare amounts)

Explore and discuss adding and subtracting money

Explore and discuss measuring temperature using a Fahrenheit thermometer and a Celsius thermometer

Use the problem solving strategy, make a model to show money amounts

Use concrete data to explore, discuss and create tally tables and pictographs

Explore and discuss mean, median and mode

Explore and discuss predictions and determining outcomes of events

|||| Chapters 1, 27

Chapters 14, 15

Chapters 14, 15

Not in Text

Not in Text

Chapter 24.4, 25.5

Chapter 22.1 – 22.4

Not in Text

Chapter 4

Chapter 4

Chapter 4 |||| Classroom observation and discussion

Student Reasoning and Justification

Student Math Journals (Writing & Reflection)

Harcourt Math: · Chapter tests · End-of-the chapter review pages · Assessment guide · MEAP Resource Book Unit tests

Investigations Unit: · Teacher Checkpoints · Assessment Activities

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