Second Grade MathematicsFocus Standards: Major, Supporting, and Additional Work Major Work of the Grade Supporting Work

o Additional Work

Represent and solve problems involving addition and subtraction.

Add and subtract within 20. Understand place value. Use place value understanding and properties of operations to

add and subtract. Measure and estimate lengths in standard units. Relate addition and subtraction to length. Work with equal groups of objects to gain foundations for

multiplication. Work with time and money. Represent and interpret data.

o Reason with shapes and their attributes.

Fluency Expectations (automaticity)*Every student should have these skills fully mastered in May.

Single-digit sums and differences (sums from memory by end of Grade 2)

Add/subtract within 100

Problem Solving (with concrete representations)

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Internet LinksEureka Math Grade Level Modules

Learn Zillion

Illustrative Mathematics

K-5 Math Teaching Resources

Oakdale Joint Unified School District Eureka Math Module Resources

Second Grade Math Task (from North Carolina Dept. of Ed.)

Mrs. Samuelson’s Swamp Frogs-for 1 st and 2 nd grade teachers

Kindergarten Common Core Math: Resources Organized by Domain

PleasantMoodle Math Journal Prompts

Second Grade Common Core Math Formative Assessments

Questioning Stems and Resources for the Mathematical Practice Standards

Posters of Mathematical Practice Standards

Printable Mathematical Practice Standards for Display

Materials List (broken down for each Eureka lesson)

The material below should be covered within this time frame; specific pacing should be determined in school-based PLCs.

Second Grade Mathematics-4th Nine WeeksTopics and Concepts to be covered during the second quarter of the year.

TN State Standards and Math Practices:These standards are the final outcomes to reach mastery before the next grade level. Major Work Supporting Work

Additional Work

Eureka Content:Content listed in the section is recommended in order to appropriately teach the identified standards, not only in preparation for the test, but most importantly for success in later courses.

Assessment:Both formative and summative assessments should be given to track student learning. The purpose of assessment is to help students identify both areas of strength and areas in which they need more support in order to achieve mastery.

Focus Grade Level Standards:

2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers,yardsticks, meter sticks, and measuring tapes.

Module 7 Problem Solving with Length, Money, and Data)

Topic A: Problem Solving with Categorical Data (5 days)

Lesson 1: Sort and record data into a table using up to four categories;use category counts to solve word problems.Lesson 2: Draw and label a picture graph to represent data with up tofour categories.

Formative (Not Graded):SprintsCore Fluency ChecksExit TicketsAmplify Quick Checks (Possible after first quarter

Summative (Graded):Mid-Module assessment Topics A-BEnd-of-Module Assessment Topics A-FCommon Assessments

Supplementary Resources for Differentiation

Department of Curriculum & InstructionCurriculum Guide

2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

2.MD.3 Estimate lengths using inches, feet, centimeters, and meters.

2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and

differences within 100 on a number line diagram.

2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Mathematical Practice:

MP.1 Make sense of problems and persevere in solving them.MP.2 Reason abstractly and quantitatively.MP.4 Model with mathematics.MP.5 Use appropriate tools strategically.MP.6 Attend to precision.

Vocabulary: use Familiar Terms and Symbols from the vignettes

Benchmark number (e.g., numbers like the multiples of 10)

Centimeter (cm, a unit of length measure) Cents (e.g., 5¢) Coins (e.g., penny, nickel, dime, and quarter) Compare Compose Decompose Difference Dollars (e.g., $2) Endpoint Equation Estimation (an approximation of the value of a

quantity or number) Hash mark (the marks on a ruler or other

measurement tool) Height

Lesson 3: Draw and label a bar graph to represent data; relate the countscale to the number line.Lesson 4: Draw a bar graph to represent a given data set.Lesson 5: Solve word problems using data presented in a bar graph.

Topic B: Problem Solving with Coins and Bills (8 days)

Lesson 6: Recognize the value of coins and count up to find their totalvalue.Lesson 7: Solve word problems involving the total value of a group ofcoins.Lesson 8: Solve word problems involving the total value of a group ofbills.Lesson 9: Solve word problems involving different combinations of coinswith the same total value.Lesson 10: Use the fewest number of coins to make a given value.Lesson 11: Use different strategies to make $1 or make change from $1.Lesson 12: Solve word problems involving different ways to make changefrom $1.Lesson 13: Solve two-step word problems involving dollars or cents withtotals within $100 or $1.

Mid-Module Assessment: Topics A–B (assessment ó day, return ó day,remediation or further applications 1 day)

Topic C: Creating an Inch Ruler (2 days)

Lesson 14: Connect measurement with physical units by using iterationwith an inch tile to measure.Lesson 15: Apply concepts to create inch rulers; measure lengths usinginch rulers.

Topic D: Measuring and Estimating Length Using Customary and Metric Units (4 days)

Lesson 16: Measure various objects using inch rulers and yardsticks.Lesson 17: Develop estimation strategies by applying prior knowledge oflength and using mental benchmarks.Lesson 18: Measure an object twice using different length units andcompare; relate measurement to unit size.Lesson 19: Measure to compare the differences in lengths using inches,feet, and yards.

Topic E: Problem Solving with Customary and Metric Units (3 days)

Lesson 20: Solve two-digit addition and subtraction word problemsinvolving length by using tape diagrams and writing equationsto represent the problem.Lesson 21: Identify unknown numbers on a number line diagram by usingthe distance between numbers and reference points.Lesson 22: Represent two-digit sums and differences involving length byusing the ruler as a number line.

Extra Practice

2.NBT.5 Math Task: Jamir’s Penny Jar2.NBT.5 Math Task: Saving Money2.NBT. 5 Math Task: Saving Money 2

2.MD.1 Math Task: Determining Length

2.MD.5 Math Task: High Jump Competition

2. MD.6 Math Task: Frog and Toad on the Number Line

2.MD.8 Math Task: Choices, Choices, Choices2.MD.8 Math Task: Pet Shop2.MD.8 Math Task: Susan’s Choice2.MD.8 Math Task: Saving Money 12.MD.8 Math Task: Visiting the Arcade2.MD.8 Math Task: Alexander, Who used to be rich

last Sunday

2.MD.9 Math Task: Hand Span Measure2.MD.9 Math Task: The Longest Walk2.MD.9 Math Task: Growing Bean Plants

2.MD.10 Math Task: Favorite Ice Cream Flavor

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Length Length unit Meter (m, a unit of length measure) Meter strip, meter stick Number bond Number line (a line marked at evenly spaced

intervals) Overlap (to extend over or cover partly) Ruler Tally mark Tape diagram Unit Value

Math Tools:

Bar graph (representation of data) Centimeter cube Centimeter ruler Dice Grid paper Inch and centimeter ruler Inch tiles Line plot Measuring tape Meter stick Money (i.e., dollars, coins) Number bond Number line Personal white board Picture graph Table Tape diagram Yardstick

Focus Grade Level Standards:

2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.)

2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three

thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Mathematical Practice:

MP.1 Make sense of problems and persevere in solving them.MP.3 Construct viable arguments and critique the reasoning of others.MP.6 Attend to precision.MP.7 Look for and make use of structure.

Vocabulary: use Familiar Terms and Symbols from the vignettes

Attributes (the characteristics of an object such as number of sides, angles, or faces)

Cube (a three-dimensional shape composed of six squares)

Digital clock Face (a two-dimensional side of a three-

dimensional shape) Fourth of (shapes), fourths (four equal shares) Half hour (an interval of time lasting 30

Topic F: Displaying Measurement Data (4 days)

Lesson 23: Collect and record measurement data in a table; answerquestions and summarize the data set.Lesson 24: Draw a line plot to represent the measurement data; relate themeasurement scale to the number line.Lessons 25–26: Draw a line plot to represent a given data set; answer questionsand draw conclusions based on measurement data.

End-of-Module Assessment: Topics A–F (assessment ó day, return ó day,remediation or further applications 1 day)

Module 8 Time, Shapes, and Fractions as Equal Parts of Shapes

Topic A: Attributes of Geometric Shapes (5 days)

Lesson 1: Describe two-dimensional shapes based on attributes.Lesson 2: Build, identify, and analyze two-dimensional shapes withspecified attributes.Lesson 3: Use attributes to draw different polygons including triangles,quadrilaterals, pentagons, and hexagons.Lesson 4: Use attributes to identify and draw different quadrilateralsincluding rectangles, rhombuses, parallelograms, andtrapezoids.Lesson 5: Relate the square to the cube, and describe the cube based onattributes.

Topic B: Composite Shapes and Fraction Concepts (3 days)

Lesson 6: Combine shapes to create a composite shape; create a newshape from composite shapes.Lessons 7–8: Interpret equal shares in composite shapes as halves, thirds,and fourths.

Topic C: Halves, Thirds, and Fourths of Circles and Rectangles

Lessons 9–10: Partition circles and rectangles into equal parts, and describethose parts as halves, thirds, or fourths.

Formative (Not Graded):SprintsCore Fluency ChecksExit TicketsAmplify Quick Checks (Possible after first quarter

Summative (Graded):Mid-Module assessment Topics A-BEnd-of-Module Assessment Topics A-FCommon Assessments

Supplementary Resources for DifferentiationExtra Practice

2.MD.7 Math Task: Ordering Time

2.G.1 Math Task: Polygons

2.G.3 Math Task: Which picture represents one half?

2.G.3 Math Task: Representing Half of a Rectangle

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minutes) Half of (shapes), halves (two equal shares) Half past (an expression for 30 minutes past a

given hour) Hour (a unit for measuring time, equivalent to

60 minutes or 1/24 of a day) Minute (a unit for measuring time, equivalent to

60 seconds or 1/60 of an hour) O’clock (used to indicate time to a precise hour

with no additional minutes) Quarter of (shapes), quarters (four equal

shares) Tangram (a special set of puzzle pieces with five

triangles and two quadrilaterals that compose asquare)

Two-dimensional shapes (familiar prior to Grade 2):

Circle Half-circle Hexagon (a two-dimensional figure

enclosed by six straight sides and six angles)

Quarter-circle Rectangle (a two-dimensional figure

enclosed by four straight sides and four right angles)

Rhombus (a two-dimensional figure enclosed by four straight sides of the same length)

Square (a rectangle with four sides of the same length)

Trapezoid (a two-dimensional figure enclosed by four straight sides with at least one pair of parallel sides)

Triangle (a two-dimensional figure enclosed by three straight sides and three angles)

Lesson 11: Describe a whole by the number of equal parts including 2halves, 3 thirds, and 4 fourths.Lesson 12: Recognize that equal parts of an identical rectangle can havedifferent shapes.

Topic D: Application of Fractions to Tell Time

Lesson 13: Construct a paper clock by partitioning a circle into halves andquarters, and tell time to the half hour or quarter hour.Lesson 14: Tell time to the nearest five minutes.Lesson 15: Tell time to the nearest five minutes; relate a.m. and p.m. totime of day.Lesson 16: Solve elapsed time problems involving whole hours and a halfhour.

End-of-Module Assessment: Topics A–D (assessment ½ day, return ½ day,remediation or further applications 1 day) (2 days)

The material below should be covered End of Nine Weeks

Second Grade Enduring Understandings and Essential QuestionsTopic Enduring Understandings Essential

Questions 1 1. Addition should be used in problems about joining and

subtraction should be used in problems about separating and comparing.2. Addition and subtraction are related.

1. How do you know when to use addition and subtraction given a word problem?2. How can we write related addition and subtraction facts?

2 1. Strategies can be applied to solve addition problems. 1. What strategy to do you use when you add? Why?

3 1. Strategies can be applied to solve addition problems. 1. What strategy to do you use? Why?

4 1. The placement of any number written in standard form has a meaning.2. Numbers can be compared using greater than, less than, and equal to.

1. How do you know the value of a number?2. How can you find the number that is one before or one after another number, or the number between two other numbers?

5 1. Specific coins each have a unique value.2. Money amounts can be counted in different ways.3. Different combinations of coins can make the same amounts.

1. How is each coin counted?2. What is the easiest way to count a group of coins?3. Is there more than one way to make the same amount of money?

6 1. Adding tens is like adding ones.2. Two digit numbers can be broken apart using tens and ones and added in different ways.3. Patterns on a hundred chart can be used to add numbers and to develop mental math strategies and number sense.

1. When tens are added to a two-digit number, how does the tens digit in the sum change?2. What are two different ways of adding tens and ones mentally?3. How can patterns on a hundred chart be used to think about adding two-digit numbers?

7 1. Subtracting tens is like subtracting ones.2. Patterns on a hundred chart can be used to subtract numbers and to develop mental math strategies and number sense.3. The difference between two numbers can be found by adding up from the smaller number to the larger number.

1. Why does only the tens digit change when subtracting tens from a two-digit number?2. How can a hundred chart be used to subtract two-digit numbers?3. How can you add on to find the difference between 2 two-digit numbers mentally?

8 1. Adding tens is like adding ones.2. At times regrouping is necessary.3. Some problems can be solved by identifying elements that repeat.4. Information in a problem can be showed using a diagram.

1. How is adding tens like adding ones?2. When do you need to regroup?3. Why is it easier to draw a picture when answering a word problem?4. How can finding a pattern help you solve a problem?

9 1. Subtracting tens is like subtracting ones.2. Addition can be used to check subtraction.3. Some word problems have missing data and some have extra information.4. Information in a problem can be showed using a diagram.

1. How is subtracting tens like subtracting ones?2. How can you use addition to check your subtraction?3. How can you determine whether there is extra information in a word problem? Or missing information?4. Why is it easier to draw a picture when answering a two-step word problem?

10 1. Estimating can be used when an exact number is not needed.2. Different strategies can be used to add/subtract two more numbers.3. The guess and check strategy can be used to problem solve.

1. Why do we need to estimate?2. How can you estimate a two-digit sum?3. How does guessing and checking help you solve a problem?

11 1. Two and three-dimensional objects can be described, classified and analyzed by their attributes.2. Objects in space can be transformed in an infinite number of ways, and those transformations can be described and analyzed mathematically.

1. How are attributes used to describe and classify three-dimensional figures?2. How can translations, reflections and rotations be used to change an object’s orientation in space?

12 1. There are a variety of situations when you need to divide something into equal parts.2. A fraction describes the division of a whole into equal parts.8. To subtract fractions with like denominators, subtract the numerators and write the difference over the same denominator.

1. Why would you want to divide something into equal parts?2. How would you divide something into equal parts?

13 1. Attributes are measurable.2. The length of objects is measurable in different units.3. Measurements need the same unit of measure in order to be compared.

1. How can you tell which attributes of an object can be measured?2. Which classroom objects can be used to approximate standard units of inches, feet, yards, centimeters and meters?3. How can you compare measurements?

14 1. Capacity is a measure of the amount of liquid a container can hold.2. The weight of an object is a measure of how heavy an object is.3. Mass is a measure of the quantity of matter in an object.2. Different units can be used to estimate and measure capacity, weight, and mass.

1. How can you tell if an object holds more than, less than, or about 1 liter?2. How can you find if one object is heavier than another?3. How can you use ounces and pounds to estimate how much object weights?4. How can you use grams and kilograms to measure objects?

15 1. Time can be given in more than one way.2. A calendar shows days, weeks and months.

1. Which clock do you prefer to tell time on, analog or digital?2. How can a calendar help you plan events in the future?

16 1. Data can be organized in different ways.2. Each type of graph is most appropriate for certain types of data.

1. What are some ways data can be organized?2. How can you decide what type of graph to use once you have collected data?

17 1. Our number system is based on groups of ten. 1. How does understanding place value help you compare three digit numbers?

18 1. There is more than one way to estimate a sum/difference.2. There is more than one way to do a mental calculation.3. Solving three-digit add/subtraction problems can be broken down using place value starting with the ones, tens, then hundreds.4. Some problems can be solved by making, reading and analyzing a graph.

1. How can you estimate sums/differences of three-digit numbers?2. How can you use mental math to add multiples of 100?3. How can you count on or count back to find a missing part?4. How can you use data from a table to create a bar graph?

19 1. Repeated addition involves joining equal groups and is one way to think about multiplication.2. An array involves joining equal groups and is one way to think about multiplication.3. Some real world situations involve repeated addition and/or arrays and can be solved using multiplication.4. Multiplication expressions can be written in a variety of ways.

1. How can repeated addition help you to understand multiplication?2. How can an array be used to help write a multiplication sentence?3. How can you use a picture to write a multiplication story?4. Does order of factors affect the product?

20 1. Multiplication and division have an inverse relationship.2. Division is used when a real world problem has sharing or repeated subtraction.

1. How are multiplication and division related?2. When do we use division to solve problems?