# Grade 2 Math Curriculum

## Family-facing version of the grade 2 math curriculum

## Quarterly Overview of Grade 2 Mathematics

The objectives and outcomes for each unit are common across FCPS and based on the Virginia Standards of Learning. The pacing by quarter and by week provides an example of how the curriculum can be organized throughout the year. Teacher teams may adjust the pacing or order of units to best meet the needs of students.

## Units and Details

**Students will:**

- Ask questions based on a given situation that require collecting small amounts of data (up to 25 points in no more than six categories).
- Figure out what information is needed to answer a question and gather this information using various methods (like voting, creating lists, tables, or charts, and tallying).
- Organize and represent a data set using a pictograph where each symbol represents up to 2 data points. Use a key to help analyze the data.
- Show forward counting patterns by counting in groups of 2 up to at least 50, starting at different multiples of 2 and using different tools (like objects, number lines, or hundreds charts).
- Identify that there are 60 minutes in an hour and 24 hours in a day.
- Decide which unit of time (minutes, hours, days, or weeks) is best for measuring a given activity or situation and explain why.

**Students will:**

- Show, solve, and explain solutions to single-step and multistep real-life problems (like joining, separating, part-part-whole, comparison) involving addition or subtraction of whole numbers where the numbers do not exceed 100.
- Add and subtract fluently within 20 by using strategies like doubles, near doubles, making a ten, compensations, and inverse relationships.
- Quickly recall addition and subtraction facts within 20.
- Use patterns, models, and strategies to understand the properties of addition and subtraction (for example, 4 + 3 is the same as 3 + 4; 0 + 8 = 8).
- Find the missing number in an addition or subtraction equation within 20 by modeling and explaining (for example, 3 + __ = 5 or __ + 2 = 5; 5 – __ = 3 or 5 – 2 = __).
- Use inverse relationships to write all related facts for a given addition or subtraction problem within 20 (for example, given 3 + 4 = 7, write 4 + 3 = 7, 7 – 4 = 3, and 7 – 3 = 4).
- Understand the "not equal" symbol (≠) as showing that the values on either side are different and explain why.
- Show and explain the relationship between values and expressions as equal or not equal using models and/or symbols (for example, 9 + 24 = 10 + 23; 45 - 9 = 46 - 10; 15 + 16 ≠ 31 + 15).

**Students will:**

- Show forward counting patterns by counting in groups of 2 up to at least 50, starting at different multiples of 2 and using different tools (like objects, number lines, or hundreds charts).
- Show forward counting patterns by counting in groups of 5, 10, and 25 starting at different multiples up to at least 200 using different tools (like objects, number lines, or hundreds charts).
- Describe and use patterns in skip counting by multiples of 2 (to at least 50) and multiples of 5, 10, and 25 (to at least 200) to figure out the next number in the sequence.
- Show backward counting patterns by counting in groups of 10 from 200 or less using different tools (like objects, number lines, calculators, or hundreds charts).
- Describe and use patterns in skip counting backward by 10s (from at least 200) to figure out the next number in the sequence.
- Choose a reasonable estimate up to 1,000 when given a real-life problem (for example, "What would be the best estimate for the number of students in our school – 5, 50, or 500?").
- Show even numbers (up to 50) with objects by making two equal groups or two equal addends.
- Show odd numbers (up to 50) with objects by making two equal groups with one leftover or two equal addends plus 1.
- Decide if a number (up to 50) is even or odd using objects and explain why (for example, by dividing collections of objects into two equal groups or pairing objects).
- Write the three-digit number represented by a given model (like concrete objects or pictures of base 10 blocks).
- Read, write, and represent three-digit numbers in standard form, expanded form, and word form using concrete or pictorial representations.
- Use patterns within the base 10 system to determine and explain the place (ones, tens, hundreds) and value of each digit in a three-digit number (for example, in 352, the 5 represents 5 tens and its value is 50).
- Explore and explain the ten-to-one relationships among ones, tens, and hundreds using models.
- Break down and build up whole numbers up to 200 by connecting different models (like base 10 blocks, place value cards) and counting strategies (for example, 156 can be 1 hundred, 5 tens, 6 ones; 1 hundred, 4 tens, 16 ones; or 15 tens, 6 ones).
- Plot and explain the position of a given number up to 100 on a number line with pre-marked benchmarks of 1s, 2s, 5s, 10s, or 25s.
- Compare two whole numbers, each 999 or less, using concrete objects, pictures, or symbols with words (greater than, less than, or equal to) and symbols (>, <, or =). Explain your reasoning orally, in writing, or with a model.
- Order up to three whole numbers, each 999 or less, using concrete objects, pictures, or symbols from least to greatest and greatest to least.
- Identify and describe repeating and increasing patterns.
- Look at a repeating or increasing pattern, figure out the change, and continue the pattern using objects, pictures, and numbers.
- Create a repeating or increasing pattern using various representations (like objects, pictures, or numbers).
- Change a given repeating or increasing pattern from one form to another (like objects, pictures, or numbers) and explain the connection between the two patterns.
- Count by ones, fives, tens, and twenty-fives to find the value of a collection of mixed coins and one-dollar bills with a total value of $2.00 or less.

**Students will:**

- Explain the purpose of different measurement tools and how to use them correctly by:
- Identifying a ruler as a tool to measure length.
- Identifying different types of scales as tools to measure weight.
- Identifying different types of measuring cups as tools to measure liquid volume.

- Use U.S. Customary units to estimate, measure, and compare for reasonableness:
- The length of an object to the nearest inch using a ruler.
- The weight of an object to the nearest pound using a scale.
- The liquid volume of a container to the nearest cup using a measuring cup.

- Identify that there are 60 minutes in an hour and 24 hours in a day.
- Decide which unit of time (minutes, hours, days, or weeks) is best for measuring a given activity or situation and explain why (for example, "Would you measure the time it takes to brush your teeth in minutes or hours?").
- Show, tell, and write time to the nearest five minutes using analog and digital clocks.
- Match a written time (for example, 1:35, 6:20, 9:05) to the time shown on an analog clock to the nearest five minutes.

**Students will:**

- Use strategies (like rounding to the nearest 10, using compatible numbers, and other number relationships) to estimate the answer for single-step addition or subtraction problems, including real-life situations, where the numbers do not exceed 100.
- Use strategies (like concrete and pictorial models, place value, properties of addition, and the relationship between addition and subtraction) to find the sum or difference of two whole numbers where the numbers do not exceed 100.
- Show, solve, and explain solutions to single-step and multistep real-life problems (like joining, separating, part-part-whole, and comparison) involving addition or subtraction of whole numbers where the numbers do not exceed 100.
- Add and subtract fluently within 20 by using strategies like doubles, near doubles, making a ten, compensations, and inverse relationships.
- Quickly recall addition and subtraction facts within 20.
- Use patterns, models, and strategies to understand the properties of addition and subtraction (for example, 4 + 3 is the same as 3 + 4; 0 + 8 = 8).
- Find the missing number in an addition or subtraction equation within 20 by modeling and explaining (for example, 3 + __ = 5 or __ + 2 = 5; 5 – __ = 3 or 5 – 2 = __).
- Use inverse relationships to write all related facts for a given addition or subtraction problem within 20 (for example, given 3 + 4 = 7, write 4 + 3 = 7, 7 – 4 = 3, and 7 – 3 = 4).
- Understand the "not equal" symbol (≠) as showing that the values on either side are different and explain why.
- Show and explain the relationship between values and expressions as equal or not equal using models and/or symbols (for example, 9 + 24 = 10 + 23; 45 - 9 = 46 - 10; 15 + 16 ≠ 31 + 15).
- Identify a quarter and its value, and find multiple ways to represent the value of a quarter using pennies, nickels, and/or dimes.
- Count by ones, fives, tens, and twenty-fives to find the value of a collection of mixed coins and one-dollar bills with a total value of $2.00 or less.
- Create a set of coins and/or bills to total a given amount of money with a value of $2.00 or less.

**Students will:**

- Explore a shape using different tools (like paper folding, geoboards, or drawings) to find and explain a line of symmetry, if it has one.
- Create shapes with at least one line of symmetry using different objects and drawings.
- Describe the two shapes formed by a line of symmetry as being congruent (having the same shape and size).
- Trace the faces of solid shapes (like cubes and rectangular prisms) to create the related flat shapes.
- Compare and contrast models and cutouts (nets) of cubes and rectangular prisms by looking at the number and shapes of their faces, edges, and vertices.
- Given a concrete or pictorial model, name and describe the solid shape (sphere, cube, and rectangular prism) by its characteristics (like the number of edges, number of vertices, and shapes of faces).
- Compare and contrast flat shapes and solid shapes (like circles/spheres, squares/cubes, and rectangles/rectangular prisms) according to their characteristics (like the number and shapes of their faces, edges, and vertices).
- Show and describe fractions as representing equal-size parts of a whole.
- Explain the relationship between the number of fractional parts needed to make a whole and the size of the parts (for example, as the whole is divided into more parts, each part becomes smaller).

**Students will:**

- Show forward counting patterns by counting in groups of 2 up to at least 50, starting at different multiples of 2 and using different tools (like objects, number lines, or hundreds charts).
- Show forward counting patterns by counting in groups of 5, 10, and 25 starting at different multiples up to at least 200 using different tools (like objects, number lines, or hundreds charts).
- Describe and use patterns in skip counting by multiples of 2 (to at least 50) and multiples of 5, 10, and 25 (to at least 200) to figure out the next number in the sequence.
- Show forward counting patterns by counting in groups of 100 up to at least 1,000 starting at 0 using different tools (like objects, number lines, calculators, or one thousand charts).
- Show backward counting patterns by counting in groups of 10 from 200 or less using different tools (like objects, number lines, calculators, or hundreds charts).
- Describe and use patterns in skip counting backward by 10s (from at least 200) to figure out the next number in the sequence.
- Choose a reasonable estimate up to 1,000 when given a real-life problem (for example, "What would be the best estimate for the number of students in our school – 5, 50, or 500?").
- Show even numbers (up to 50) with objects by making two equal groups or two equal addends.
- Show odd numbers (up to 50) with objects by making two equal groups with one leftover or two equal addends plus 1.
- Decide if a number (up to 50) is even or odd using objects and explain why (for example, by dividing collections of objects into two equal groups or pairing objects).
- Write the three-digit number represented by a given model (like concrete objects or pictures of base 10 blocks).
- Read, write, and represent three-digit numbers in standard form, expanded form, and word form using concrete or pictorial representations.
- Use patterns within the base 10 system to determine and explain, both orally and in writing, the place (ones, tens, hundreds) and value of each digit in a three-digit number (for example, in 352, the 5 represents 5 tens and its value is 50).
- Explore and explain the ten-to-one relationships among ones, tens, and hundreds using models.
- Break down and build up whole numbers up to 200 by connecting different models (like base 10 blocks, place value cards) and counting strategies (for example, 156 can be 1 hundred, 5 tens, 6 ones; 1 hundred, 4 tens, 16 ones; or 15 tens, 6 ones).
- Plot and explain the position of a given number up to 100 on a number line with pre-marked benchmarks of 1s, 2s, 5s, 10s, or 25s.
- Compare two whole numbers, each 999 or less, using concrete objects, pictures, or symbols with words (greater than, less than, or equal to) and symbols (>, <, or =). Explain your reasoning orally, in writing, or with a model.
- Order up to three whole numbers, each 999 or less, using concrete objects, pictures, or symbols from least to greatest and greatest to least.
- Identify a quarter and its value, and find multiple ways to represent the value of a quarter using pennies, nickels, and/or dimes.
- Count by ones, fives, tens, and twenty-fives to find the value of a collection of mixed coins and one-dollar bills with a total value of $2.00 or less.
- Create a set of coins and/or bills to total a given amount of money with a value of $2.00 or less.
- Show the value of a collection of coins and one-dollar bills (limited to $2.00 or less) using the cent (¢) and dollar ($) symbols and decimal point (.).
- Ask questions based on a given situation that require collecting small amounts of data (up to 25 points in no more than six categories).
- Figure out what information is needed to answer a question and gather this information using various methods (like voting, creating lists, tables, or charts, and tallying).
- Organize and represent a data set using a pictograph where each symbol represents up to 2 data points. Use a key to help analyze the data.
- Organize and represent a data set using a bar graph with a title and labeled axes (limited to 25 or fewer data points for up to six categories, and limit increments of scale to multiples of 1 or 2).
- Analyze data represented in pictographs and bar graphs and communicate results:
- Ask and answer questions about the data represented in pictographs and bar graphs (like the total number of data points, how many are in each category, and how many more or less are in one category than another). Pictograph keys will be limited to symbols representing 1, 2, 5, or 10 pieces of data and bar graphs will be limited to scales with increments in multiples of 1, 2, 5, or 10.
- Draw conclusions about the data and make predictions based on what you see.

- Identify and describe repeating and increasing patterns.
- Look at a repeating or increasing pattern, figure out the change, and continue the pattern using objects, pictures, and numbers.
- Create a repeating or increasing pattern using different representations (like objects, pictures, or numbers).
- Change a given repeating or increasing pattern from one form to another (like objects, pictures, or numbers) and explain how the two patterns are connected.

**Students will:**

- Use strategies (like rounding to the nearest 10, using compatible numbers, and other number relationships) to estimate the answer for single-step addition or subtraction problems, including real-life situations, where the numbers do not exceed 100.
- Use strategies (like concrete and pictorial models, place value, properties of addition, and the relationship between addition and subtraction) to find the sum or difference of two whole numbers where the numbers do not exceed 100.
- Show, solve, and explain solutions to single-step and multistep real-life problems (like joining, separating, part-part-whole, and comparison) involving addition or subtraction of whole numbers where the numbers do not exceed 100.
- Add and subtract fluently within 20 by using strategies like doubles, near doubles, making a ten, compensations, and inverse relationships.
- Quickly recall addition and subtraction facts within 20.
- Use patterns, models, and strategies to understand the properties of addition and subtraction (for example, 4 + 3 is the same as 3 + 4; 0 + 8 = 8).
- Find the missing number in an addition or subtraction equation within 20 by modeling and explaining (for example, 3 + __ = 5 or __ + 2 = 5; 5 – __ = 3 or 5 – 2 = __).
- Use inverse relationships to write all related facts for a given addition or subtraction problem within 20 (for example, given 3 + 4 = 7, write 4 + 3 = 7, 7 – 4 = 3, and 7 – 3 = 4).
- Understand the "not equal" symbol (≠) as showing that the values on either side are different and explain why.
- Show and explain the relationship between values and expressions as equal or not equal using models and/or symbols (for example, 9 + 24 = 10 + 23; 45 - 9 = 46 - 10; 15 + 16 ≠ 31 + 15).
- Ask questions based on a given situation that require collecting small amounts of data (up to 25 points in no more than six categories).
- Figure out what information is needed to answer a question and gather this information using various methods (like voting, creating lists, tables, or charts, and tallying).
- Organize and represent a data set using a pictograph where each symbol represents up to 2 data points. Use a key to help analyze the data.
- Organize and represent a data set using a bar graph with a title and labeled axes (limited to 25 or fewer data points for up to six categories, and limit increments of scale to multiples of 1 or 2).
- Analyze data represented in pictographs and bar graphs and communicate results:
- Ask and answer questions about the data represented in pictographs and bar graphs (like the total number of data points, how many are in each category, and how many more or less are in one category than another). Pictograph keys will be limited to symbols representing 1, 2, 5, or 10 pieces of data and bar graphs will be limited to scales with increments in multiples of 1, 2, 5, or 10.
- Draw conclusions about the data and make predictions based on what you see.

- Identify and describe repeating and increasing patterns.
- Look at a repeating or increasing pattern, figure out the change, and continue the pattern using objects, pictures, and numbers.
- Create a repeating or increasing pattern using different representations (like objects, pictures, or numbers).
- Change a given repeating or increasing pattern from one form to another (like objects, pictures, or numbers) and explain how the two patterns are connected.

**Students will:**

- Show and describe fractions as representing equal-size parts of a whole.
- Explain the relationship between the number of fractional parts needed to make a whole and the size of the parts (for example, as the whole is divided into more parts, each part becomes smaller).
- Create the whole for a given fractional part and its value (in context) for halves, fourths, eighths, thirds, and sixths (for example, when given 1/4, determine how many pieces would be needed to make 4/4).
- Using same-size fraction pieces from a region/area model, count by unit fractions up to two wholes (for example, zero one-fourths, one one-fourth, two one-fourths, three one-fourths, four one-fourths, five one-fourths; or zero-fourths, one-fourth, two-fourths, three-fourths, four-fourths, five-fourths).
- Given a context, represent, name, and write fractional parts of a whole for halves, fourths, eighths, thirds, and sixths using:
- Region/area models (like pie pieces, pattern blocks, geoboards)
- Length models (like paper fraction strips, fraction bars, rods, number lines)
- Set models (like chips, counters, cubes)

- Compare unit fractions for halves, fourths, eighths, thirds, and sixths using words (greater than, less than, or equal to) and symbols (>, <, =) with region/area and length models.

**Students will:**

- Use strategies (like rounding to the nearest 10, using compatible numbers, and other number relationships) to estimate the answer for single-step addition or subtraction problems, including real-life situations, where the numbers do not exceed 100.
- Use strategies (like concrete and pictorial models, place value, properties of addition, and the relationship between addition and subtraction) to find the sum or difference of two whole numbers where the numbers do not exceed 100.
- Show, solve, and explain solutions to single-step and multistep real-life problems (like joining, separating, part-part-whole, and comparison) involving addition or subtraction of whole numbers where the numbers do not exceed 100.
- Quickly recall addition and subtraction facts within 20.
- Organize and represent a data set using a bar graph with a title and labeled axes (limited to 25 or fewer data points for up to six categories, and limit increments of scale to multiples of 1 or 2).
- Analyze data represented in pictographs and bar graphs and communicate results:
- Ask and answer questions about the data represented in pictographs and bar graphs (like the total number of data points, how many are in each category, and how many more or less are in one category than another). Pictograph keys will be limited to symbols representing 1, 2, 5, or 10 pieces of data and bar graphs will be limited to scales with increments in multiples of 1, 2, 5, or 10.
- Draw conclusions about the data and make predictions based on what you see.

- Identify and describe repeating and increasing patterns.
- Create a repeating or increasing pattern using different representations (like objects, pictures, or numbers).
- Change a given repeating or increasing pattern from one form to another (like objects, pictures, or numbers) and explain how the two patterns are connected.

## Virginia Department of Education Resources

## Assessments

Student assessments are part of the teaching and learning process.

- Teachers give assessments to students on an ongoing basis to
- Check for understanding
- Gather information about students' knowledge or skills.

- Assessments provide information about a child's development of knowledge and skills that can help families and teachers better plan for next steps in instruction.

For testing questions or additional information about how schools and teachers use test results to support student success, families can contact their children's schools.

In Fairfax County Public Schools (FCPS), second grade tests focus on basic literacy and numeracy development.