Category: Grade 2 Math

Measurement and Data

Unit description: In this unit students will learn to recognize the need for standard units of measure (centimeter and inch) and apply this understanding to addition and subtraction problems involving length. The students will learn to recognize that the smaller the unit, the more iterations needed to cover a given length and they will learn to select appropriate tools to measure understanding that linear measure involves an iteration of units. The students will also learn to interpret and represent data in multiple ways, such as: line plot, bar graph, picture graph, and a tally chart.

Essential Outcomes of the Unit

Measurement and Data- Measure and estimate lengths in standard units.

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

Measurement and Data- Represent and interpret data.

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 picture graph or a bar graph.

Other Standards Addressed in the Unit

Measurement and Data- Measure and estimate lengths in standard units.

• 2.MD.2 Measure the length of an object twice, using different “length units” for the two measurements; describe how the two measurements relate to the size of the unit chosen.
• 2.MD.3 Estimate lengths using units of 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.”

Measurement and Data- Relate addition and subtraction to length.

• 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units.
• 2.MD.6 Represent whole numbers as lengths from 0 on a number line with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line.

Measurement and Data- Represent and interpret data.

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. Present the measurement data in a line plot, where the horizontal scale is marked off in whole-number units.

Essential Questions and Big Ideas

• Why do standards units matter?
  • A standard unit of measure are the accepted, consistent increments we use to measure.
  • A standard unit of measure for length are centimeters and meters and inches and feet.
  • A nonstandard unit of measure is something that we use to measure, such as a paperclip or pencil,  if we want to compare the measure of two things without using a standard unit.
• How do we choose appropriate tools and use them to measure the length of an object?
  • Identify the appropriate tool to measure the length of various objects.
  • Measure various objects to the closest whole number length with correct units.
• How do we use picture graphs and bar graphs to display and analyze data?
  • Data collection is used to develop picture graphs and bar graphs with a single unit scale.
  • Picture and bar graphs can be used to analyze and interpret data and to answer questions about a data set.

Download the complete Grade 2 Math Unit 5 framework to customize for your own planning.

Geometry and Fractions/Money and Time

Unit description: In this unit students will learn about two-dimensional shapes, time and money. They will learn to describe and classify shapes as polygons or non-polygons. They will decompose and combine shapes to make other shapes and they analyze two-dimensional shapes to develop a foundation for understanding area, congruence, similarity, and fractions in later grades. Students will work to solve problems involving money up to $1 including counting mixed coins and making change. They will identify all coins and be able to arrange them in order from greatest to least value. Students will also be able to tell time using both analog and digital clocks to the nearest 5 minute and identify a.m. and p.m.

Download the complete Geometry and Fractions/Money and Time framework to customize for your own planning.

Essential Outcomes of the Unit

Geometry- Reason with shapes and their attributes.

• 2.G.1 Classify two-dimensional figures as polygons or non-polygons.
• 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. Describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Measurement and Data- Work with time and money.

• 2.MD.7 Tell and write time from analog and digital clocks in five minute increments, using a.m. and p.m. Develop an understanding of common terms, such as, but not limited to, quarter past, half past, and quarter to.
• 2.MD.8a Count a mixed collection of coins whose sum is less than or equal to one dollar.

Other Standards Addressed in the Unit

Geometry- Reason with shapes and their attributes.

• 2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them

Measurement and Data- Work with time and money.

• 2.MD.8b Solve real world and mathematical problems within one dollar involving quarters, dimes, nickels, and pennies, using the ¢ (cent) symbol appropriately.

Essential Questions and Big Ideas

How do I tell time? 

• Time is told in hours and minutes.  
• An hour is made of 60 minutes. 
• In a day there are 24 hours.  
• Hours are broken into AM (morning) and PM (afternoon).  

How do I count coins?  

• A penny is worth 1 cent. 
• A nickel is worth 5 cents
• A dime is worth 10 cents. 
• A quarter is worth 25 cents. 
• When counting coins, it is efficient to start with the largest value.  

How do we reason with shapes and their attributes?

• Polygons are closed two-dimensional figures made of line segments.
• Shapes can be combined to make new shapes called composite shapes.

What does dividing shapes into equal shares tell us?

• Understanding equal shares helps us understand area.
• Understanding equal shares helps us understand fractions.

Download the complete Geometry and Fractions/Money and Time framework to customize for your own planning.

Three-Digit Addition and Subtraction

Unit description: In this unit the students will learn to represent and solve three digit addition and subtraction problems within 1,000. Students will recognize when it is necessary to compose or decompose tens or hundreds. They will apply their understanding of the relationship between addition and subtraction to solve two-step word problems.

Download the complete Three Digit Addition and Subtraction framework to customize for your own planning.

Essential Outcomes of the Unit

Number and Operations in Base Ten- Use place value understanding and properties of operations to add and subtract.

• NY-2.NBT.7a . 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 representation. Note: A written representation is any way of showing a strategy using words, pictures, or numbers.

Other Standards Addressed in the Unit

Number and Operations in Base Ten- Use place value understanding and properties of operations to add and subtract.

• NY-2.NBT.7b Understand that in adding or subtracting up to 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.

Operations and Algebraic Thinking- Represent and solve problems involving addition and subtraction

• NY-2.OA.1b Use addition and subtraction within 100 to develop an understanding of solving two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

Essential Questions and Big Ideas

How do we solve three digit addition problems?

• Strategies such as modeling, using 10s blocks, extended form, mental math and standard algorithms can be used to solve addition within 1,000.
• Some multi-digit addition problems involve regrouping 10s to the next place value.

How do we solve three digit subtraction problems? 

Strategies such as modeling, using 10s blocks, extended form, mental math and standard algorithms can be used to solve subtraction within 1,000.
Some multi-digit subtraction problems involve regrouping 10s to the prior place value.

How do we check our answers when adding and subtracting within 1,000?

• The reverse relationship between addition and subtraction can be used to check answers.

How do we solve two step word problems involving addition and subtraction within 100?

• Identifying key words and understandings within word problems can help determine whether to add or subtract to solve problems in our daily life.
• Understanding of properties of operations and the relationship between addition and subtraction can help to solve word problems.
• Marking up the question and drawing pictures can help to visualize word problems.

Download the complete Three Digit Addition and Subtraction framework to customize for your own planning.

Two Digit Addition and Subtraction

Unit description: The students will use strategies and models to solve two digit addition and subtraction problems with and without regrouping within 100. They will also apply these strategies and models when solving one-step word problems with unknowns in all positions.

Download the complete Two Digit Addition and Subtraction framework to customize for your own planning.

Essential Outcomes of the Unit

Represent and solve problems involving addition and subtraction.

OA.1a. Use addition and subtraction within 100 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

Use place value understanding and properties of operations to add and subtract.

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. Notes: Students should be taught to use strategies based on place value, properties of operations, and the relationship between addition and subtraction; however, when solving any problem, students can choose any strategy.

Other Standards Addressed in this Unit

Represent and solve problems involving addition and subtraction.

OA.1b. Use addition and subtraction within 100 to develop an understanding of solving two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

Use place value understanding and properties of operations to add and subtract.

2.NBT.6. Add up to four two-digit numbers using strategies based on place value and properties of operations.

Essential Questions and Big Ideas

How can you use number sense to help when adding and subtracting 2-digit numbers?

• Number sense helps to solve addition and subtraction problems.
• Using multiple models to represent addition and subtraction helps to solve.
• Using mental strategies can allow for more fluent addition & subtraction
• Various methods and models can be used to represent and solve problems involving addition & subtraction

How can we apply our knowledge of addition and subtraction to solve word problems?

• Identifying key words and understandings within word problems can help determine whether to add or subtract to solve problems in our daily life.
• Understanding of properties of operations and the relationship between addition and subtraction can help to solve word problems.

Prerequisite Standards

NY-1.OA.1. Use addition and subtraction within 20 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and/or comparing, with unknowns in all positions.

NY-1.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20: e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Assessment of these skills: Word problems allowing students to write and/or draw to find solutions, interactive math notebook entries, using a number line/ bar model/manipulatives to solve problems.

Download the complete Two Digit Addition and Subtraction framework to customize for your own planning.

Number Sense and Place Value 

Students will develop an understanding of place value through 100s. Students will learn to compare values of up to three digit numbers. Students will develop fluency with adding and subtracting within 20.

Download the complete Grade 2 Math Unit 1 framework to customize for your own planning

Essential Outcomes

Operations and Algebraic Thinking

• NY-2.OA.2a: Fluently add and subtract within 20 using mental strategies. Strategies could include:
  • counting on;
  • making ten;
  • decomposing a number leading to a ten;
  • using the relationship between addition and subtraction; and
  • creating equivalent but easier or known sums.
• NY-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.

Number and Operations in Base Ten

• NY-2.NBT.1: Understand that the digits of a three-digit number represent amounts of hundreds, tens, and ones.
• NY-2.NBT. 3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Other Standards Addressed in this Unit

Operations and Algebraic Thinking

• NY-2.OA.2b: Know from memory all sums within 20 of two one-digit numbers.
• NY-2.OA.3a: 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 2’s.
• NY-2.OA.3b: Write an equation to express an even number as a sum of two equal addends.

Number and Operations in Base Ten

• NY-2.NBT.1a: Understand 100 can be thought of as a bundle of ten tens, called a “hundred.”
• NY-2.NBT.1b: Understand 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).
• NY-2.NBT. 2: Count within 1000; skip-count by 5s, 10s, and 100s.
• NY-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.
• NY-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.

Essential Questions and Big Ideas

• How much is a digit worth? How does the position of a number affect its value?
  • The value of a digit depends on its place, or position in the number.
  • Each place has a value of 10 times the place to its right.
  • A digit in the one’s place is worth that number. In the number 524, The one’s place is worth 4 ones, the ten’s place is worth 2 tens or 20 and the hundred’s place is worth 5 hundreds or 500.
• How do mathematical relationships relate to each other?
  • Using mental strategies can allow for more fluent addition & subtraction
  • Using various methods to represent and solve problems involving addition & subtraction
  • Expressing rows and columns of an array using repeated addition equations
• How do we solve word problems?
  • Keywords help us determine if we need to add or subtract to solve a word problem.

Download the complete Grade 2 Math Unit 1 framework to customize for your own planning