The
State Education Department /
The University
oF the Curriculum, Instruction, and Instructional Technology Team  Room 320 EB email: emscnysmath@mail.nysed.gov 
Grade 2
Sample Tasks for PreK8, developed by New York State teachers, are clarifications, further explaining the language and intent of the associated Performance Indicators. These tasks are not test items, nor are they meant for students' use.

Students will build new mathematical knowledge through problem solving.
2.PS.1 Explore, examine, and make observations about a social problem or mathematical situation
2.PS.1a
Susan, Mark, Lee, and Sasha have been collecting stickers. Susan has 27, Mark has 18, Lee has 89, and Sasha has 42.
Who has the greatest amount of stickers?
Who has the least amount of stickers?
2.PS.2 Interpret information correctly, identify the problem, and generate possible solutions
2.PS.1b
Gather one crayon, one pencil, one marker, and one straw. Have students place them in length order from least to greatest. Have students choose other items of differing lengths to compare and order.
2.PS.2a
Give each student a group of pattern blocks. Ask the students to show as many different ways as possible to cover a hexagon with pattern blocks.
2.PS.2b
Abe has 26 baseball cards. George has 48 baseball cards. If they put all their cards in one box, how many cards will be in the box? Show two different strategies to solve the problem.
2.PS.2c
Solve the problems below:
Use < , >, or =
Find numbers that will make the number sentence true:
19 > _____
Students will solve problems that arise in mathematics and in other contexts.
2.PS.3 Act out or model with manipulatives activities involving mathematical content from literature and/or story telling
2.PS.3a
Introduce the division concept by reading The Doorbell Rang by Pat Hutchins. Have students model the story with counters.
2.PS.3b
Have students make up stories about Poor Zero, who can never change the value of another addend in an addition sentence. The stories should include examples.
2.PS.3c
Use the story A Doorbell Rang by Pat Hutchins to help students understand division as a process of sharing. The book begins with two children who are about to share 12 cookies. Just as they are about to share the cookies, the doorbell rings and two friends join them. Now there are four children to share 12 cookies. Then two more friends arrive and now there are six children to share the cookies. The doorbell rings again and six more children are there. Now there are 12 children sharing 12 cookies. Have students use their counters to demonstrate each situation.
2.PS.4a
Juice boxes are sold in packages of three. Have students determine how many packages would be needed so that every student in the class of 21 students will get one juice box.
2.PS.4 Formulate problems and solutions from everyday situations e.g., counting the number of children in the class, using the calendar to teach counting).
2.PS.4b
Using a balance scale, have students compare weights of everyday objects. Have students describe their observation using the words heavier and lighter.
Students will apply and adapt a variety of appropriate strategies to solve problems.
2.PS.5 Use informal counting strategies to find solutions
2.PS.5a
Have students work in small groups, and give each group a jar of manipulatives (e.g., bears, buttons). Have students determine the total number of manipulatives in the jar. Encourage students to use the strategy that works best for them.
2.PS.5b
Use a 1100 number chart and have students color in all the even numbers while counting by 2's. Discuss patterns on the number chart.
2.PS.5c
Beginning at 100, verbally count backwards by 10's, using a 1100 number chart.
2.PS.5d
Isaiah was counting and writing down numbers as he counted. Here is part of his paper. What numbers are missing?
_______, 80, _______, 82
2.PS.6 Experience teacherdirected questioning process to understand problems
2.PS.6a
Pose the following problem to students:
Antonio wants to earn an award given to any student who reads at least 30 books during the summer. Will Antonio get an award if he reads 4 books each week for 8 weeks?
Before students try to solve the problem, ask questions such as:
What is the problem?
What information do we need to solve the problem?
What are some strategies we could use to solve the problem?
Can you think of another way to solve it?
2.PS.6b
Ask the students:
What day of the week is the twentyeighth day of this month?
What is the fifteenth letter of the alphabet?
2.PS.7 Compare and discuss ideas for solving a problem with teacher and/or students to justify their thinking
2.PS.7a
Have students think of a strategy to solve the problem below. Have them share possible strategies and discuss whether or not each strategy would work.
Brenda and Carlos are friends. Brenda has saved 45 cents. Her parents will give her five cents a day for feeding the family dog. Carlos has saved 20 cents and he will earn eight cents a day for feeding his dog. Who will have saved a total of one dollar first?
2.PS.7b
Cut out shapes (e.g., heart, butterfly, letter A) and fold each shape to show symmetry. Use other shapes that have no line of symmetry (e.g., mitten, sock, letter Z). Have students share other shapes or letters as examples or nonexamples of line symmetry. Compare and discuss.
2.PS.8 Use manipulatives (i.e., tiles, blocks) to model the action in problems
2.PS.8a
Use tiles to model this problem:
Tyrone's remote control car is 16 inches long. Emily's car is 13 inches long. How much longer is Tyrone's car than Emily's car?
2.PS.8b
Have students work with a partner. Have students measure their arm lengths using linking cubes.
2.PS.9 Use drawings/pictures to model the action in problems
2.PS.9a
Draw a picture to solve:
The Garcia family has 2 dogs and 3 cats. Each dog has 2 chew bones and each cat has 3 mouse toys. How many chew bones are in the Garcia home? How many mouse toys are in the home?
2.PS.9b
Make sketches to predict the outcome of sliding, flipping, and turning twodimensional shapes. Verify predictions by tracing slides, flips, and turns.
Students will monitor and reflect on the process of mathematical problem solving.
2.PS.10 Explain to others how a problem was solved, giving strategies and justifications
2.PS.10a
Explain whether or not you would say the number "65" if you were to count backward from 100 by fives.
2.PS.10b
Jasmine earned 3 stickers on Monday and 6 stickers on Tuesday. Chad earned 6 stickers on Monday and some more on Tuesday. Both students earned the same total number of stickers. How many did Chad earn on Tuesday? Explain your answer.
2.RP.1 Understand that mathematical statements can be true or false
2.RP.1a
Brad says that all doubles are even numbers. Explain if this statement is true or false.
2.RP.2 Recognize that mathematical ideas need to be supported by evidence
2.RP.2a
Give students the following problem: Two equalsized brownies are cut as shown in the diagrams. If Jade gets a piece of the first brownie and David gets a piece of the second brownie, will they both have the same amount of brownie or will one have more? Explain your reasoning.
Jade David
2.RP.2b
Gather pairs of classroom items of different masses. Have students lift each and verbally complete the statements:
____ is heavier than _____
____ is lighter than _____
Students will make and investigate mathematical conjectures.
2.RP.3 Investigate the use of knowledgeable guessing as a mathematical tool
2.RP.3a
Show students a footlong ruler and ask the student to estimate the width of the classroom. Measure a distance of 5 feet, and ask if the students would like to revise their first estimate.
2.RP.3b
Have students choose items in the classroom such as a book or a pencil. Have students estimate in inches the length of the object.
2.RP.4 Explore guesses, using a variety of objects and manipulatives
2.RP.4a
Bring in an empty, plastic jar such as a peanut butter jar. Give the jar to a different student each week to bring to school filled with objects (e.g., candy, cereal, pennies, paper clips, keys). Have other students estimate how many objects are in the jar.
2.RP.4b
Display a jar filled with cubes. Have students write estimates on a small piece of paper. Create a class graph of their estimations.
Students will develop and evaluate mathematical arguments and proofs.
2.RP.5 Justify general claims, using manipulatives
2.RP.5a
Have students choose two classroom objects such as a book and a pair of scissors. Have students measure the objects with paper clips. Compare results.
2.RP.5b
Using a hundred chart and colored transparent chips, give the students the first 3 numbers of a pattern, such as 1, 3, 5. Have them put a chip on each of the first 3 numbers of the pattern. Ask students to continue the pattern by placing a chip on the next 3 numbers. Help students verbalize a rule for each pattern.
2.RP.5c
Using attribute blocks have students sort and justify their groupings.
2.RP.6 Develop and explain an argument verbally or with objects
2.RP.6a
Pose the following question to the class:
If an object is bigger than another object, is it always heavier? Explain your answer.
2.RP.7 Listen to and discuss claims other students make
2.RP.7a
Ask the students to explain why there is a zero in the one's place when we write the number ninety.
Students will select and use various types of reasoning and methods of proof.
2.RP.8 Use trial and error strategies to verify claims
2.RP.8a
Find two numbers with a sum of 15 and a difference of 7.
2.RP.8b
Have students put together and take apart tangram pieces to show and name a variety of different shapes.
Students will organize and consolidate their mathematical thinking through communication.
2.CM.1 Understand how to organize their thought processes
2.CM.1a
Help students use logical thinking to solve the following problem:
Five children are standing in line. Jordan is not first, but he is in front of Alex. Ruth is in front of Pat, who is last. Mary is also in line. She is standing in front of Jordan. Decide who is standing first, second, third, fourth, and fifth in line.
2.CM.1b
Have the students fill in the blanks in the statements below. Give clues and visuals as needed.
If you are first in line, and there is one person between you and
your friend, then your friend is _____ in line.
If Sunday is the first of the 7 days in a week, then Thursday is the _____
day.
2.CM.2 Verbally support their reasoning and answer
2.CM.2a
Explain how to use compensation to add 25 + 55.
2.CM.2b
Explain a strategy to a friend for solving the following equation:
8 + 9 =
2.CM.2c
Using geoboards or dot paper, have students make many different triangles. Students should verbally describe why their shapes are all triangles.
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
2.CM.3 Share mathematical ideas
through the manipulation of objects, drawings, pictures, charts, and symbols in
both written and verbal
explanations
2.CM.3a
a Give each student a group of base ten blocks. Ask students to show how to add 40 + 26 or 200 + 115.
Students will analyze and evaluate the mathematical thinking and strategies of others.
2.CM.4 Listen to solutions shared by other students
2.CM.4a
Pose the following problem to each pair of students:
A music lesson starts at 3:00 and lasts for 45 minutes.
Have each group determine what time the music lesson ends. Share the results.
2.CM.4b
In each pair of numbers, which number is greater: 23 or 93, 89 or 98? Explain and justify your response to a friend.
2.CM.5 Formulate mathematically relevant questions
2.CM.5a
Have students brainstorm questions for data collection in their classroom or school.
Students will use the language of mathematics to express mathematical ideas precisely.
2.CM.6 Use appropriate mathematical terms, vocabulary, and language
2.CM.6a
Have students compare numbers using the symbols <, >, and = . Ask the students to read the inequality while using the correct vocabulary:
less than
greater than
equal to
2.CM.6b
Gather or create pictographs. Ask students to formulate questions about the pictographs. Suggest the use of the following vocabulary: most, least, same, differences, greatest difference, or a difference of a given number.
Students will recognize and use connections among mathematical ideas.
2.CN.1 Recognize the connections of patterns in their everyday experiences to mathematical ideas
2.CN.1a
Explore quilt designs. Look for quilt patterns that represent rotating, flipping, or sliding a design.
2.CN.1b
Complete the pattern to 48:
4, 8, 12,…
Explain how you know what comes next. What items in everyday life could you count by 4's?
2.CN.2 Understand and use the connections between numbers and the quantities they represent to solve problems
2.CN.2a
Tom had 12 marbles and was given 4 more marbles. Luis had 4 marbles and bought 12 more. Explain how both students ended up with an equal number of marbles.
2.CN.2b
Using linking cubes, have students demonstrate different ways to represent 82 cubes. Record the results and share.
2.CN.3 Compare the similarities and differences of mathematical ideas
2.CN.3a
Have students examine a nickel and a dime closely. Have students list ways the nickel and dime are similar and different.
2.CN.3b
Using grid paper, have students trace a twodimensional shape. Ask the students to slide, flip, and turn each shape and trace again. Discuss similarities and differences. Repeat the process with other twodimensional shapes.
Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
2.CN.4 Understand how models of situations involving objects, pictures, and symbols relate to mathematical ideas
2.CN.4a
Give each group of students a balance scale. Choose two classroom objects such as a small book or a pair of scissors. Have students use the scale to weigh the objects and explain which object is heavier.
2.CN.4b
On a blank number chart set up as a 12 X 3 array, write the numbers 136 with the numbers 1, 2, 3 across the first row and continuing on to 36, highlighting the last number in each row. Discuss the number pattern in the last row.
2.CN.5 Understand meanings of operations and how they relate to one another
2.CN.5a
Use objects such as counters, buttons, or cubes to model addition/subtraction fact families. Have students write the corresponding number sentences.
2.CN.5b
Solve the
problem below:
Explain how to solve these equations.
2.CN.6 Understand how mathematical models represent quantitative relationships
2.CN.6a
Explore the following doubling problem with students and represent information on a chart:
Joshua puts one cent in a bank on the first day, two cents on the second day, and on the third day he puts four cents in the bank. How long would it take Joshua to save enough money to buy a toy that costs one dollar?
2.CN.6b
Write the numeral to represent 11 tens. Verify with base ten blocks.
Students will recognize and apply mathematics in contexts outside of mathematics.
2.CN.7 Recognize the presence of mathematics in their daily lives
2.CN.7a
Investigate the number of players on different sports teams such as baseball, basketball, and soccer. Display the information in a pictograph or bar graph.
2.CN.7b
Count the value of 20 nickels by skip counting.
2.CN.7c
Using an analog clock, display a time to the half hour or five minute increments. Show students an analog clock and have students write a corresponding digital display.
2.CN.8 Recognize and apply mathematics to solve problems
2.CN.8a
Jack is helping his mother make brownies for a soccer party. One batch makes 24 brownies. If Jack and his mom make 2 batches of brownies, will they have enough brownies so that each of the 50 players can have one brownie?
2.CN.8b
What pattern in addition sentences can you find when double numbers are in the ten's place and zeros are in the one's place?
2.CN.9 Recognize and apply mathematics to objects, pictures and symbols
2.CN.9a
Give students pictures of insects. Ask students to find a picture of an insect whose body is symmetrical. Ask the students to draw a picture of their insect, indicating the line of symmetry and labeling with the insect's name.
2.CN.9b
Given a visual of a dollar bill, have students write the appropriate money notation.
Students will create and use representations to organize, record, and communicate
mathematical ideas.
2.R.1 Use multiple representations, including verbal and written language, acting out or modeling a situation, drawings, and/or symbols as representations
2.R.1a
Give each pair of students a box of manipulatives. Have students create groups of manipulatives and explain whether the group of manipulatives is an odd or even number.
2.R.1b
Give students a specified number of tiles (e.g., 18 tiles). Have them make as many rectangles as possible and record each on graph paper. Have students note the number of rows and columns for each rectangle to discover all the facts for the given number. For example, for 3 rows of 6, the student could record 6 + 6 + 6 = 18 and 3 x 6 = 18.
2.R.2 Share mental images of mathematical ideas and understandings
2.R.2a
Ask children to close their eyes and visualize geometric figures such as:
· a circle on top of a square
· twice as many triangles as rectangles
· a square between two triangles
2.R.2b
Solve mentally using compensation:
36 + 29 =
Possible solution:
36 + 30 = 66 (Add one to 29)
66  1 = 65 (Subtract one to compensate)
2.R.3 Use standard and nonstandard representations
2.R.3a
Give students a collection of shells (or other objects that lend well to sorting). Ask the students to sort the shells by categories or characteristics. Introduce a bar graph or pictograph and ask the students to represent the same information using a graph.
2.R.3b
Have students conduct a classroom survey about their favorite subject. Have student record results on a tally chart and then create a pictograph for the results.
Students will select, apply, and translate among mathematical representations to solve problems.
2.R.4 Connect mathematical representations with problem solving
2.R.4a
After first solving addition and subtraction problems using manipulatives and drawings, model how the problem can be represented and solved using a number sentence.
Students will use representations to model and interpret physical, social, and mathematical phenomena.
2.R.5 Use mathematics to show and understand physical phenomena (i.e., estimate and represent the number of apples in a tree)
2.R.5a
Estimate, measure and represent the growth of a plant.
2.R.5b
Have students arrange each kind of coin from least to greatest for monetary value. Have students state what each coin represents.
2.R.6 Use mathematics to show and understand social phenomena (i.e., count and represent sharing cookies between friends)
2.R.6a
A group of nine friends is going sledding. If each sled can hold 3 children, how many sleds will the friends need?
2.R.6b
Have students measure their heights using feet and inches. Record results on chart paper.
2.R.7 Use mathematics to show and understand mathematical phenomena (i.e., draw pictures to show a story problem or show number value using fingers on your hand)
2.R.7a
Draw a picture to solve. Renee has 6 stickers. Maria has twice as many stickers as Renee. How many stickers do they have together?
2.R.7b
Have students bundle 105 craft sticks into 10 groups of ten. (There will be five left over. )Together count the 10 bundles and put them together to make a one hundred bundle. Place the one hundred bundle in the hundreds pocket in a place value pocket chart. Then put the 5 remaining single sticks in the ones pocket. Point out that the tens pocket is empty because there are not enough single sticks to make a bundle of ten. Ask students how the number one hundred five should be written. Guide them to write 105 and discuss that zero represents no tens and that zero needs to be in tens place. Repeat the process with 120.
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Systems
2.N.1 Skip count to 100 by 2's, 5's, 10's
2.N.1a
Use a 1100 number chart and have students color in all the even numbers while counting by 2's. Discuss patterns on the number chart.
2.N.2 Count back from 100 by 1's, 5's, 10's using a number chart
2.N.2a
Beginning at 100, verbally count backwards by 10's, using a 1100 number chart.
2.N.2b
Explain whether or not you would say the number "65" if you were to count backward from 100 by fives.
2.N.3 Skip count by 3's to 36 for multiplication readiness
2.N.3a
Juice boxes are sold in packages of three. Have students determine how many packages would be needed so that every student in the class of 21 students will get one juice box.
2.N.3b
On a blank number chart set up as a 12 X 3 array, write the numbers 136 with the numbers 1, 2, 3 across the first row and continuing on to 36, highlighting the last number in each row. Discuss the number pattern in the last row.
2.N.4 Skip count by 4's to 48 for multiplication readiness
2.N.4a
Pose the following problem to students:
Antonio wants to earn an award given to any student who reads at least 30 books during the summer. Will Antonio get an award if he reads 4 books each week for 8 weeks?
Before students try to solve the problem, ask questions such as:
What is the problem?
What information do we need to solve the problem?
What are some strategies we could use to solve the problem?
Can you think of another way to solve it?
2.N.4b
Complete the pattern to 48:
4, 8, 12,…
Explain how you know what comes next. What items in everyday life could you count by 4's?
2.N.5 Compare and order numbers to 100
2.N.5a
Susan, Mark, Lee, and Sasha have been collecting stickers. Susan has 27, Mark has 18, Lee has 89, and Sasha has 42.
Who has the greatest amount of stickers?
Who has the least amount of stickers?
2.N.5b
In each pair of numbers, which number is greater: 23 or 93, 89 or 98? Explain and justify your response to a friend.
2.N.6 Develop an understanding of the base ten system:
10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand
2.N.6a
Give each student a group of base ten blocks. Ask students to show how to add 40 + 26 or 200 + 115.
2.N.6b
Write the numeral to represent 11 tens. Verify with base ten blocks.
2.N.7 Use a variety of strategies to compose and decompose twodigit numbers
2.N.7a
Have students work in small groups, and give each group a jar of manipulatives (e.g., bears, buttons). Have students determine the total number of manipulatives in the jar. Encourage students to use the strategy that works best for them.
2.N.7b
Using linking cubes, have students demonstrate different ways to represent 82 cubes. Record the results and share.
2.N.8 Understand and use the commutative property of addition
2.N.8a
Jasmine earned 3 stickers on Monday and 6 stickers on Tuesday. Chad earned 6 stickers on Monday and some more on Tuesday. Both students earned the same total number of stickers. How many did Chad earn on Tuesday? Explain your answer.
2.N.8b
Tom had 12 marbles and was given 4 more marbles. Luis had 4 marbles and bought 12 more. Explain how both students ended up with an equal number of marbles.
2.N.9 Name the number before and the number after a given number, and name the number(s) between two given numbers up to 100 (with and without the use of a number line or a hundreds chart)
2.N.9a
Isaiah was counting and writing down numbers as he counted. Here is part of his paper. What numbers are missing?
_______, 80, _______, 82
2.N.10 Use and understand verbal ordinal terms
2.N.10a
Ask the students:
What day of the week is the twentyeighth day of this month?
What is the fifteenth letter of the alphabet?
2.N.10b
Help students use logical thinking to solve the following problem:
Five children are standing in line. Jordan is not first, but he is in front of Alex. Ruth is in front of Pat, who is last. Mary is also in line. She is standing in front of Jordan. Decide who is standing first, second, third, fourth, and fifth in line.
2.N.11 Read written ordinal terms (first through ninth) and use them to represent ordinal relations
2.N.11a
Have the students fill in the blanks in the statements below. Give clues and visuals as needed.
If you are first in line, and there is one person between you and your friend,
then your friend is _____ in line.
If Sunday is the first of the 7 days in a week, then Thursday is the_____ day.
2.N.12 Use zero as the identity element for addition
2.N.12a
Have students make up stories about Poor Zero, who can never change the value of another addend in an addition sentence. The stories should include examples.
2.N.13 Recognize the meaning of zero in the place value system (0100)
2.N.13a
Ask the students to explain why there is a zero in the one's place when we write the number ninety.
2.N.13b
Have students bundle 105 craft sticks into 10 groups of ten. (There will be five left over. )Together count the 10 bundles and put them together to make a one hundred bundle. Place the one hundred bundle in the hundreds pocket in a place value pocket chart. Then put the 5 remaining single sticks in the ones pocket. Point out that the tens pocket is empty because there are not enough single sticks to make a bundle of ten. Ask students how the number one hundred five should be written. Guide them to write 105 and discuss that zero represents no tens and that zero needs to be in tens place. Repeat the process with 120.
Number Theory
2.N.14 Use concrete materials to justify a number as odd or even
2.N.14a
Brad says that all doubles are even numbers. Explain if this statement is true or false.
2.N.14b
Give each pair of students a box of manipulatives . Have students create groups of manipulatives and explain whether the group of manipulatives is an odd or even number.
Operations
2.N.15 Determine sums and differences of number sentences by various means (e.g., families, related facts, inverse operations, addition doubles, and doubles plus one)
2.N.15a
Explain a strategy to a friend for solving the following equation:
8 + 9 =
2.N.15b
Use objects such as counters, buttons, or cubes to model addition/subtraction fact families. Have students write the corresponding number sentences.
2.N.16 Use a variety of strategies to solve addition and subtraction problems using one and twodigit numbers with and without regrouping
2.N.16a
Abe has 26 baseball cards. George has 48 baseball cards. If they put all their cards in one box, how many cards will be in the box? Show two different strategies to solve the problem.
2.N.16b
After first solving addition and subtraction problems using manipulatives and drawings, model how the problem can be represented and solved using a number sentence.
2.N.16c
Draw a picture to solve. Renee has 6 stickers. Maria has twice as many stickers as Renee. How many stickers do they have together?
2.N.17 Demonstrate fluency and apply addition and subtraction facts up to and including 18
2.N.17a
Solve the problem below:
Explain how to solve these equations.
2.N.18 Use doubling to add 2digit numbers
2.N.18a
Jack is helping his mother make brownies for a soccer party. One batch makes 24 brownies. If Jack and his mom make 2 batches of brownies, will they have enough brownies so that each of the 50 players can have one brownie?
2.N.18b
What pattern in addition sentences can you find when double numbers are in the ten's place and zeros are in the one's place?
2.N.19 Use compensation to add 2digit numbers
2.N.19a
Explain how to use compensation to add 25 + 55.
2.N.19b
Solve mentally using compensation:
36 + 29 =
Possible solution:
36 + 30 = 66 (Add one to 29)
66  1 = 65 (Subtract one to compensate)
2.N.20 Develop readiness for multiplication by using repeated addition
2.N.20a
Draw a picture to solve:
The Garcia family has 2 dogs and 3 cats. Each dog has 2 chew bones and each cat has 3 mouse toys. How many chew bones are in the Garcia home? How many mouse toys are in the home?
2.N.20b
Give students a specified number of tiles (e.g., 18 tiles). Have them make as many rectangles as possible and record each on graph paper. Have students note the number of rows and columns for each rectangle to discover all the facts for the given number. For example, for 3 rows of 6, the student could record 6 + 6 + 6 = 18 and 3 x 6 = 18.
2.N.21 Develop readiness for division by using repeated subtraction, dividing objects into groups (fair share)
2.N.21a
Introduce the division concept by reading The Doorbell Rang by Pat Hutchins. Have students model the story with counters.
2.N.21b
Use the story A Doorbell Rang by Pat Hutchins to help students understand division as a process of sharing. The book begins with two children who are about to share 12 cookies. Just as they are about to share the cookies, the doorbell rings and two friends join them. Now there are four children to share 12 cookies. Then two more friends arrive and now there are six children to share the cookies. The doorbell rings again and six more children are there. Now there are 12 children sharing 12 cookies. Have students use their counters to demonstrate each situation.
2.N.21c
A group of nine friends is going sledding. If each sled can hold 3 children, how many sleds will the friends need?
Students will compute accurately and make reasonable estimates.
Estimation
2.N.22 Estimate the number in a collection to 100 and then compare by counting the actual items in the collection
2.N.22a
Bring in an empty, plastic jar such as a peanut butter jar. Give the jar to a different student each week to bring to school filled with objects (e.g., candy, cereal, pennies, paper clips, keys). Have other students estimate how many objects are in the jar.
2.N.22b
Display a jar filled with cubes. Have students write estimates on a small piece of paper. Create a class graph of their estimations.
Students will perform algebraic procedures accurately.
Equations and Inequalities
2.A.1 Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers up to 100
2.A.1a
Solve the problems below:
Use < , >, or =
Find numbers that will make the number sentence true:
19 > _____
2.A.1b
Have students compare numbers using the symbols <, >, and = . Ask the students to read the inequality while using the correct vocabulary:
less than
greater than
equal to
Students will recognize, use, and represent algebraically patterns, relations, and functions.
Patterns, Relations and Functions
2.A.2 Describe and extend increasing or decreasing (+,) sequences and patterns (numbers or objects up to 100)
2.A.2a
Using a hundred chart and colored transparent chips, give the students the first 3 numbers of a pattern, such as 1, 3, 5. Have them put a chip on each of the first 3 numbers of the pattern. Ask students to continue the pattern by placing a chip on the next 3 numbers. Help students verbalize a rule for each pattern.
2.A.2b
Explore the following doubling problem with students and represent information on a chart:
Joshua puts one cent in a bank on the first day, two cents on the second day, and on the third day he puts four cents in the bank. How long would it take Joshua to save enough money to buy a toy that costs one dollar?
Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
Shapes
2.G.1 Experiment with slides, flips, and turns to compare twodimensional shapes
2.G.1a
Using grid paper, have students trace a twodimensional shape. Ask the students to slide, flip, and turn each shape and trace again. Discuss similarities and differences. Repeat the process with other twodimensional shapes.
2.G.2 Identify and appropriately name twodimensional shapes: circle, square, rectangle, and triangle (both regular and irregular)
2.G.2a
Using geoboards or dot paper, have students make many different triangles. Students should verbally describe why their shapes are all triangles.
2.G.2b
Ask children to close their eyes and visualize geometric figures such as:
· a circle on top of a square
· twice as many triangles as rectangles
· a square between two triangles
2.G.3
2.G.3a
Give each student a group of pattern blocks. Ask the students to show as many different ways as possible to cover a hexagon with pattern blocks.
2.G.3b
Give students the following problem: Two equalsized brownies are cut as shown in the diagrams. If Jade gets a piece of the first brownie and David gets a piece of the second brownie, will they both have the same amount of brownie or will one have more? Explain your reasoning.
Jade David






2.G.3c
Have students put together and take apart tangram pieces to show and name a variety of different shapes.
Students will identify and justify geometric relationships, formally and informally.
Geometric Relationships
2.G.4 Group objects by like properties
2.G.4a
Using attribute blocks have students sort and justify their groupings.
2.G.4b
Give students a collection of shells (or other objects that lend well to sorting). Ask the students to sort the shells by categories or characteristics. Introduce a bar graph or pictograph and ask the students to represent the same information using a graph.
Students will apply transformations and symmetry to analyze problem solving situations.
Transformational Geometry
2.G.5 Explore and predict the outcome of slides, flips, and turns of twodimensional shapes
2.G.5a
Make sketches to predict the outcome of sliding, flipping, and turning twodimensional shapes. Verify predictions by tracing slides, flips, and turns.
2.G.5b
Explore quilt designs. Look for quilt patterns that represent rotating, flipping, or sliding a design.
2.G.6 Explore line symmetry
2.G.6a
Cut out shapes (e.g., heart, butterfly, letter A) and fold each shape to show symmetry. Use other shapes that have no line of symmetry (e.g., mitten, sock, letter Z). Have students share other shapes or letters as examples or nonexamples of line symmetry. Compare and discuss.
2.G.6b
Give students pictures of insects. Ask students to find a picture of an insect whose body is symmetrical. Ask the students to draw a picture of their insect, indicating the line of symmetry and labeling with the insect's name.
Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
2.M.1 Use nonstandard and standard units to measure both vertical and horizontal lengths
2.M.1a
Have students work with a partner. Have students measure their arm lengths using linking cubes.
2.M.1b
Have students choose two classroom objects such as a book and a pair of scissors. Have students measure the objects with paper clips. Compare results.
2.M.1c
Estimate, measure and represent the growth of a plant.
2.M.2 Use a ruler to measure standard units (including whole inches and whole feet)
2.M.2a
Show students a footlong ruler and ask the student to estimate the width of the classroom. Measure a distance of 5 feet, and ask if the students would like to revise their first estimate.
2.M.2b
Have students measure their heights using feet and inches. Record results on chart paper.
2.M.3 Compare and order objects according to the attribute of length
2.M.3a
Gather one crayon, one pencil, one marker, and one straw. Have students place them in length order from least to greatest. Have students choose other items of differing lengths to compare and order.
2.M.3b
Use tiles to model this problem:
Tyrone's remote control car is 16 inches long. Emily's car is 13 inches long. How much longer is Tyrone's car than Emily's car?
2.M.4 Recognize mass as a qualitative measure (e.g., Which is heavier? Which is lighter?)
2.M.4a
Gather pairs of classroom items of different masses. Have students lift each and verbally complete the statements:
____ is heavier than _____
____ is lighter than _____
2.M.4b
Give each group of students a balance scale. Choose two classroom objects such as a small book or a pair of scissors. Have students use the scale to weigh the objects and explain which object is heavier.
2.M.5 Compare and order objects, using lighter than and heavier than
2.M.5a
Using a balance scale, have students compare weights of everyday objects. Have students describe their observation using the words heavier and lighter.
2.M.5b
Pose the following question to the class:
If an object is bigger than another object, is it always heavier? Explain your answer.
Students will use units to give meaning to measurements.
Units
2.M.6 Know and recognize coins (penny, nickel, dime, quarter) and bills ($1, $5, $10, and $20)
2.M.6a
Have students examine a nickel and a dime closely. Have students list ways the nickel and dime are similar and different.
2.M.6b
Have students arrange each kind of coin from least to greatest for monetary value. Have students state what each coin represents.
2.M.7 Recognize the whole dollar notation as $1, etc.
2.M.7a
Given a visual of a dollar bill, have students write the appropriate money notation.
2.M.8 Identify equivalent combinations to make one dollar
2.M.8a
Have students think of a strategy to solve the problem below. Have them share possible strategies and discuss whether or not each strategy would work.
Brenda and Carlos are friends. Brenda has saved 45 cents. Her parents will give her five cents a day for feeding the family dog. Carlos has saved 20 cents and he will earn eight cents a day for feeding his dog. Who will have saved a total of one dollar first?
2.M.8b
Count the value of 20 nickels by skip counting.
2.M.9 Tell time to the half hour and five minutes using both digital and analog clocks
2.M.9a
Pose the following problem to each pair of students:
A music lesson starts at 3:00 and lasts for 45 minutes.
Have each group determine what time the music lesson ends. Share the results.
2.M.9b
Using an analog clock, display a time to the half hour or five minute increments. Show students an analog clock and have students write a corresponding digital display.
Students will develop strategies for estimating measurements.
Estimation
2.M.10 Select and use standard (customary) and nonstandard units to estimate measurements
2.M.10a
Have students choose items in the classroom such as a book or a pencil. Have students estimate in inches the length of the object.
Students will collect, organize, display, and analyze data.
Collection of Data
2.S.1 Formulate questions about themselves and their surroundings
2.S.1a
Have students brainstorm questions for data collection in their classroom or school.
2.S.2 Collect and record data (using tallies) related to the question
Organization and Display of Data
2.S.3 Display data in pictographs and bar graphs using concrete objects or a representation of the object
2.S.3a
Investigate the number of players on different sports teams such as baseball, basketball, and soccer. Display the information in a pictograph or bar graph.
2.S.3b
Have students conduct a classroom survey about their favorite subject. Have student record results on a tally chart and then create a pictograph for the results.
Analysis of Data
2.S.4 Compare and interpret data in terms of describing quantity (similarity or differences)
2.S.4a
Gather or create pictographs. Ask students to formulate questions about the pictographs. Suggest the use of the following vocabulary: most, least, same, differences, greatest difference, or a difference of a given number.
Students will make predictions that are based upon data analysis.
Predictions from Data
2.S.5 Discuss conclusions and make predictions from graphs