Math - Second Grade

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Intro

Resources by Strand

Resources by Strand

Mathematical Practices
(2.MP) Operations and Algebraic Thinking
(2.OA) Number and Operations in Base Ten
(2.NBT) Measurement and Data
(2.MD) Geometry
(2.G)

Strand: MATHEMATICAL PRACTICES (2.MP)

The Standards for Mathematical Practice in Second Grade describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes (Standards 2.MP.1-6).

Standard 2.MP.1
Make sense of problems and persevere in solving them. Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. When a solution pathway does not make sense, look for another pathway that does. Explain connections between various solution strategies and representations. Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.
Standard 2.MP.2
Reason abstractly and quantitatively. Make sense of quantities and their relationships in problem situations. Contextualize quantities and operations by using images or stories. Decontextualize a given situation and represent it symbolically. Interpret symbols as having meaning, not just as directions to carry out a procedure. Know and flexibly use different properties of operations, numbers, and geometric objects.
Standard 2.MP.3
Construct viable arguments and critique the reasoning of others. Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.
Standard 2.MP.4
Model with mathematics. Identify the mathematical elements of a situation and create a mathematical model that shows the relationships among them. Identify important quantities in a contextual situation, use mathematical models to show the relationships of those quantities, analyze the relationships, and draw conclusions. Models may be verbal, contextual, visual, symbolic, or physical.
Standard 2.MP.5
Use appropriate tools strategically. Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.
Standard 2.MP.6
Attend to precision. Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.
Standard 2.MP.7
Look for and make use of structure. Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.
Standard 2.MP.8
Look for and express regularity in repeated reasoning. Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.

Strand: OPERATIONS AND ALGEBRAIC THINKING (2.OA)

Represent and solve problems involving addition and subtraction (Standards 2.OA.1)

Core Guide

OER Curriculum

Instructional Tasks

Standard 2.OA.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, for example, by using drawings and equations with a symbol for the unknown number to represent the problem.

Fluently add and subtract within 20 (Standards 2.OA.2).

Standard 2.OA.2
Fluently add and subtract within 20.
Add and subtract within 20 using mental strategies such as counting on; making ten (for example, 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (for example, 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (for example, knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (for example, adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
By the 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 (Standards 2.OA.3–4).

Standard 2.OA.3
Determine whether a group of objects (up to 20) has an odd or even number of members, (for example, by pairing objects or counting them by twos). Write an equation to express an even number as a sum of two equal addends.
Standard 2.OA.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.

Strand: NUMBER AND OPERATIONS IN BASE TEN (2.NBT)

Understand place value (Standards 2.NBT.1–4).

Core Guide

OER Curriculum

Instructional Tasks

Boxes and Cartons of Pencils
In this task students are given information about quantities of pencils packed in boxes and cartons and asked to solve problems such as "Jem has 1 carton and 4 boxes. How many pencils does Jem have all together?"
Comparisons 1
This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers.
Comparisons 2
The comparisons here involve sums and differences - not primarily to provide an opportunity to calculate, but rather in order to stimulate studentsâ thinking about the magnitudes of the base-ten units of which numbers are composed.
Counting Stamps
This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps.
Digits 2-5-7
This task asks students to use all the digits 5, 7, and 2 to create different 3-digit numbers.
Largest Number Game
In this task students are told "Dona had cards with the numbers 0 to 9 written on them. She flipped over three of them. Her teacher said: 'If those three numbers are the digits in another number, what is the largest three-digit number you can make?'" Students should be asked to think through possibilities and then draw on their ability to compare three digit numbers to complete the task.
Making 124
Not all students have seen base-ten blocks. This task should only be used with students who know what they are or have some on-hand to use themselves. Students are asked explain how they found all the possible ways to make 124 using base-ten blocks.
Number Line Comparisons
The purpose of this task is for students to use the number line to make comparisons between 3-digit numbers. The task is designed, in part, to help students understand how the number line works and that numbers on the right of the number line are greater than numbers on the left.
Ordering 3-digit numbers
In this task each number has at most 3 digits so that students have the opportunity to think about how digit placement affects the size of the number. Each group also contains a two-digit number so that students have to do more than just compare the first digit, the second digit, etc.
Saving Money 2
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This problem shows the work advanced second graders might use for adding 2-digit numbers.
Using Pictures to Explain Number Comparisons
The purpose of this task is for students to compare three-digit numbers and explain the comparisons based on the meaning of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Review Activitiy

Bundling and Unbundling
In this task students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. The student must, in some cases, decompose hundreds to tens and tens to ones.
Looking at Numbers Every Which Way
This task gives students the opportunity to work with multiple representations of base-ten numbers. The standard asks students to read and write numbers to 1000 using base-ten numerals, number names, and expanded form. This task addresses all of these and extends it by asking students to represent the numbers with pictures and on the number line.
One, Ten, and One Hundred More and Less
This task acts as a bridge between understanding place value and using strategies based on place value for addition and subtraction. Within the classroom context, this activity can be differentiated using numbers that are either simpler or more difficult to manipulate across tens and hundreds.
Party Favors
The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred.
Regrouping
This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition. Place-value notation leaves a lot of information implicit. The way that the numbers are represented in this task makes this information explicit, which can help students transition to adding standard base-ten numerals.
Teaching Different Methods To Count Collections
This Teaching Channel video shows students recording and sharing strategies when skip counting. (8 minutes)
Ten $10s make $100
This task uses one, ten, and one-hundred dollar bills to help students think about bundling by ten.
Three Composing/Decomposing Problems
The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.

Standard 2.NBT.1
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; for example, 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
100 can be thought of as a bundle of ten tens called a "hundred."
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).
Standard 2.NBT.2
Count within 1,000; skip-count by fives, tens, and hundreds.
Standard 2.NBT.3
Read and write numbers to 1,000 using base-ten numerals, number names, and expanded form.
Standard 2.NBT.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.

They use place value understanding and properties of operations to add and subtract (Standards 2.NBT.5–9).

Core Guide

OER Curriculum

Engage NY

Grade 2 Math Module 1: Sums and Differences to 100 (EngageNY)
Module 1 sets the foundation for students to master sums and differences to 20. Students subsequently apply these skills to fluently add one-digit to two-digit numbers at least through 100 using place value understanding, properties of operations, and the relationship between addition and subtraction.
Grade 2 Math Module 4: Addition and Subtraction Within 200 with Word Problems to 100 (EngageNY)
In Module 4, students develop place value strategies to fluently add and subtract within 100; they represent and solve one- and two-step word problems of varying types within 100; and they develop conceptual understanding of addition and subtraction of multi-digit numbers within 200. Using a concrete to pictorial to abstract approach, students use manipulatives and math drawings to develop an understanding of the composition and decomposition of units, and they relate these representations to the standard algorithm for addition and subtraction.
Grade 2 Math Module 5: Addition and Subtraction Within 1,000 with Word Problems to 100 (Engage NY)
In Module 5, students build upon their mastery of renaming place value units and extend their work with conceptual understanding of the addition and subtraction algorithms to numbers within 1,000, always with the option of modeling with materials or drawings. Throughout the module, students continue to focus on strengthening and deepening conceptual understanding and fluency.

Georgia Standards of Excellence Curriculum Frameworks

Grade 2 Unit 2: Becoming Fluent with Addition and Subtraction (Georgia Standards)
In this unit students will cultivate an understanding of how addition and subtraction affect quantities and are related to each other, will reinforce the multiple meanings for addition (combine, join, and count on) and subtraction (take away, remove, count back, and compare), further develop their understanding of the relationships between addition and subtraction, recognize how the digits 0-9 are used in our place value system to create numbers and manipulate amounts and continue to develop their understanding solving problems with money.
Grade 2 Unit 4: Applying Base Ten Understanding (Georgia Standards)
In this unit students will continue to develop their understanding of and facility with addition and subtraction, add up to 4 two-digit numbers, use a variety of models (base ten blocks- ones, tens, and hundreds only; diagrams; number lines; place value strategies; etc.) to add and subtract within one thousand and continue to develop their understanding of, and facility with, money.

Instructional Tasks

Ford and Logan Add 45+36
This task was designed to give students opportunities to solve a problem and analyze other students solutions while working on adding two-digit numbers.
How Many Days Until Summer Vacation?
The purpose of the task is to allow children an opportunity to subtract a three-digit number including a zero that requires regrouping.
Jamir's Penny Jar
The purpose of this task is to help students articulate their addition strategies as in and would be most appropriately used once students have a solid understanding of coin values. It also provides a context where it makes sense to "skip count by 5s and 10s" for the combinations that involve more than one nickel or dime.
Many Ways to do Addition 2
The purpose of this task is not to teach or model the addition strategies. Rather the purpose of this task is make explicit different ways students can solve problems so that they will be able to find the most efficient strategy in any given situation and increase their addition fluency.
Peyton and Presley Discuss Addition
This purpose of this task is to support students in developing an understanding of a place value strategy for adding numbers.
Saving Money 1
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money.
Saving Money 2
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This problem shows the work advanced second graders might use for adding 2-digit numbers.
Toll Bridge Puzzle
This task is intended to assess adding of four numbers as given in the standard while still being placed in a problem-solving context. As written this task is instructional; due to the random aspect regarding when the correct route is found, it is not appropriate for assessment.

Review Activitiy

Standard 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.
Standard 2.NBT.6
Add up to four two-digit numbers using strategies based on place value and properties of operations.
Standard 2.NBT.7
Add and subtract within 1,000 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, and ones and ones, and that it is sometimes necessary to compose or decompose tens or hundreds.
Standard 2.NBT.8
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.
Standard 2.NBT.9
Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects

Strand: MEASUREMENT AND DATA (2.MD)

Measure and estimate lengths in standard units (Standards 2.MD.1–4).

Core Guide

OER Curriculum

Instructional Tasks

Standard 2.MD.1
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
Standard 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.
Standard 2.MD.3
Estimate lengths using units of inches, feet, centimeters, and meters.
Standard 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. For example, after measuring a pencil and a crayon, a student uses the measurements to determine that the pencil is two inches longer than the crayon.

Relate addition and subtraction to length (Standards 2.MD.5–6).

Core Guide

OER Curriculum

Instructional Tasks

Standard 2.MD.5
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units. For example, use drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
Standard 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... Represent whole number sums and differences within 100 on a number line diagram.

They work with time and money (Standards 2.MD.7–8).

Standard 2.MD.7
Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
Standard 2.MD.8
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. For example, if you have 2 dimes and 3 pennies, how many cents do you have?

They represent and interpret data (Standards 2.MD.9–10).

Standard 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.
Standard 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 comparison problems using information presented in a bar graph.

Strand: GEOMETRY (2.G)

Reason with shapes and their attributes. (Standards 2.G.1–3).

Standard 2.G.1
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Sizes are compared directly or visually, not compared by measuring. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Standard 2.G.2
Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares.
Standard 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, or four fourths. Recognize that equal shares of identical wholes need not have the same shape.

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Math - Second Grade