The
State Education Department /
The University
oF the Curriculum, Instruction, and Instructional Technology Team  Room 320 EB email: emscnysmath@mail.nysed.gov 
Grade 3
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.
3.PS.1 Explore, examine, and make observations about a social problem or mathematical situation
3.PS.1a Using the chart below, determine how many more students ride bus 4 than bus 3. Which buses contain an odd number of students? Explain your answer.
School bus number 
Number of students riding the bus 
1 
31 
2 
28 
3 
27 
4 
33 
3.PS.2 Understand that some ways of representing a problem are more helpful than others
3.PS.2a Use the charts below to discuss the difference in how the data is displayed in the pictograph compared to the same data displayed in the bar graph.
Favorite Lunch Choice in the Third Grade 

Hamburger 
* * * * 
Salad 
* * 
Pizza 
* * * * * * 
* represents two votes 
3.PS.3 Interpret information correctly, identify the problem, and generate possible solutions
Students will solve problems that arise in mathematics and in other contexts.
3.PS.4 Act out or model with manipulatives activities involving mathematical content from literature
3.PS.4a While reading the book Apple Fractions by Jerry Pallotta, use apples to demonstrate the meaning of a numerator and a denominator in the symbolic form of a fraction.
3.PS.5 Formulate problems and solutions from everyday situations
3.PS.5a
Have students create an addition or subtraction problem using the information below:
Joe has collected 113 toy cars.
Ivana has collected 205 toy cars.
3.PS.6 Translate from a picture/diagram to a numeric expression
3.PS.6a The diagram below shows a pizza. What fraction of the pizza is left if Jackie eats her piece of pizza? Write an expression to show your thinking.
3.PS.7 Represent problem situations in oral, written, concrete, pictorial, and graphical forms
3PS7a
Ask the students the following question:
What is your favorite sport?
Have students give their answers orally, write the results in a frequency table, use colored counters to represent each choice, and create a bar graph to display the results of the survey.
3.PS.8 Select an appropriate representation of a problem
3.PS.8a Discuss the appropriateness of using inches, feet, or yards when measuring the length of a football field and measuring yards in a football game
Students will apply and adapt a variety of appropriate strategies to solve problems.
3.PS.9 Use trial and error to solve problems
3.PS.9a Melissa is thinking of a twodigit number. It is an odd number. It has a 2 in the tens place and it is a multiple of 9. What is Melissa’s number
3.PS.10 Use process of elimination to solve problems
3.PS.10a
Which is the best estimate for the capacity of a bathtub?
20 cups
20 pints
20 gallons.
3.PS.11 Make pictures/diagrams of problems
3.PS.11a
Draw a picture to help to solve the problem below:
If 72 third grade students eat lunch in the cafeteria and 8 students can fit at each table, how many tables are needed in the cafeteria for the students?
3.PS.12 Use physical objects to model problems
3.PS.12a
Use cookies or objects to act out the problem below:
Jasmine wants to share 20 cookies with 4 friends. How many cookies will each friend get if each child (including Jasmine) gets an equal amount of cookies?
3.PS.13 Work in collaboration with others to solve problems
3.PS.13a
Have students identify objects where inches would be an appropriate unit to measure the length of the object.
3.PS.14 Make organized lists to solve numerical problems
3.PS.14a
Make an organized list to represent the different combination of coins that can be used to represent 20 cents.
3.PS.15 Make charts to solve numerical problems
3.PS.15a
Make a chart to solve the problem below:
Juan read for 10 minutes on Sunday, 15 minutes on Monday, 20
minutes on
Tuesday, and 25 minutes on Wednesday. If this pattern continues, how many
minutes would he read on Friday?
3.PS.16 Analyze problems by identifying relationships
3.PS.16a
Margo needs to fill a twogallon fish tank with water. She wants to use a onequart jar to fill the tank. How many times must Margo fill the jar in order to fill the fish tank to the top with water?
3.PS.17 Analyze problems by identifying relevant versus irrelevant information
3.PS.17a
Jacques likes to eat a snack before he does his homework. Yesterday he spent 20 minutes doing his homework. Today Jacques has 10 mathematics questions, and he needs to study for his Social Studies test. If Jacques spent one hour today doing his homework, how much more time did he spend today compared to yesterday?
3.PS.18 Analyze problems by observing patterns
3.PS.18a
What shape completes this pattern?
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3.PS.19 State a problem in their own words
3.PS.19a
Have students restate the problem below:
The soccer coach makes the team run for half of the practice time. If the team practices for 60 minutes, how much time do they spend running?
Students will monitor and reflect on the process of mathematical problem solving.
3.PS.20 Determine what information is needed to solve a problem
3.PS.20a
State the additional information that is needed to solve the problem below:
Ricardo's class collected bottles for the bottle drive. Mark's class collected 250 bottles more than Ricardo's class. Victoria's class collected 435 bottles. Which class collected the most bottles?
3.PS.21 Discuss with peers to understand a problem situation
3.PS.21a
A third grade class wants to take a field trip. It will cost the class $100 to go on the field trip. If there are 20 students in the class who want to raise money for the field trip, how much money will each student need to raise, with everyone raising an equal amount of money?
3.PS.22 Discuss the efficiency of different representations of a problem
3.PS.22a
Discuss whether it is more efficient to use a multiplication sentence or to create a chart to solve the problem
below:
A recipe calls for 2 eggs for each dozen cookies. If Judy has 6
eggs, how many
dozen cookies can Judy make?
3.PS.23 Verify results of a problem
3.PS.23a
Have students estimate the length of their pencils to the nearest inch. Then have the students measure their pencils to see how close they were to their estimates.
3.PS.24 Recognize invalid approaches
3.PS.24a
Amelia estimated that there were 20 marshmallows in the Estimation Jar. Amelia tells the class that she measured the height of one marshmallow and she measured the height of the jar. She determined that since one marshmallow is ½ inch tall and the Estimation Jar is 10 inches high, then there must be 20 marshmallows in the jar. Discuss if Amelia's approach to estimation is valid.
3.PS.25 Determine whether a solution is reasonable in the context of the original problem
3.PS.25a
Ella hit the ball 5 times out of 8 times at bat. What fraction of the time at bat did Ella hit the ball? Is it reasonable to say that Ella hit the ball more than half of the time at bat?
3.RP.1 Use representations to support mathematical ideas
3.RP.1a
There are three red cars and two blue cars in a parking lot. Using snap cubes in red and blue, have students represent the five cars by connecting the cubes. Discuss how 3 out of the 5 cubes are red, represented by 3/5.
3.RP.2 Determine whether a mathematical statement is true or false and explain why
3.RP.2a
Using cubes or counters, demonstrate how numbers can be grouped or "associated" with the same result. Show how adding 3 + 2 + 5 is the same as adding 3 + 5 + 2. Write the equation (3 + 2) + 5 = 3 + (2 + 5). Continue demonstrating the concept with different numbers, explaining that you are showing the associative property of addition. Have students provide additional examples.
Students will make and investigate mathematical conjectures.
3.RP.3 Investigate the use of knowledgeable guessing by generalizing mathematical ideas
3.RP.3a
Each jar below contains only 1 blue cube. From which jar do you have the greatest chance of picking the blue cube, Jar 1 or Jar 2? Explain your answer.
3.RP.4 Make conjectures from a variety of representations
3.RP.4a
Show the class a group of paper clips and tell them that there are 20 paper clips in the group. Show the students a group of 100 paper clips, but do not tell them the number of paper clips. Have the class estimate whether the new group contains 40 paper clips or 100 paper clips.
Students will develop and evaluate mathematical arguments and proofs.
3.RP.5 Justify general claims or conjectures, using manipulatives, models, and expressions
3.RP.5a
Have students compare the fractions ½ and ¼ using the symbols <, >, or =, after showing the two comparison models below:
· a piece of string that is ½ inch in length compared to a piece of string that is ¼ inch in length
· two sandwiches of the same size, one cut in half and the other cut in fourths.
3.RP.6 Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms
3.RP.6a
Write the statement below on the board:
The students in this class like chocolate ice cream best.
Have the students survey the class and discuss whether the statement is accurate. Have students display the survey results in a pictograph or bar graph and make a statement about their findings.
3.RP.7 Discuss, listen, and make comments that support or reject claims made by other students
3.RP.7a
Write the statement below on the board:
The students in this class like chocolate ice cream best.
Have the students survey the class and discuss whether the statement is accurate. Have students display the survey results in a pictograph or bar graph and make a statement about their findings.
Encourage students to listen and discuss the observations of other students.
Students will select and use various types of reasoning and methods of proof.
3.RP.8 Justify an argument by trying many cases
3.RP.8a
Present the following information to students:
Justin has 2 tens blocks and Kirsten has 20 ones blocks. Kirsten says her blocks represent a larger number than Justin’s blocks. Is she correct?
Have students provide other examples where the same amount is represented in two different ways. Have the students use place value blocks to check their work.
Students will organize and consolidate their mathematical thinking through communication.
3.CM.1 Understand and explain how to organize their thought process
3.CM.1a
Have students choose a strategy to solve the problem below and then explain how they arrived at a solution.
Four children line up at the door for lunch. Jackie is in front of Lynn, Mohammed is the last in line, and Fred is not standing next to Jackie. Who is the first in line?
3.CM.2 Verbally explain their rationale for strategy selection
3.CM.2a
Have students describe their reasons for choosing the strategy they used to solve the problem below:
Four children line up at the door for lunch. Jackie is in front of Lynn, Mohammed is the last in line, and Fred is not standing next to Jackie. Who is the first in line?
3.CM.3 Provide reasoning both in written and verbal form
3.CM.3a
Have students write an explanation for the strategy they chose to solve the problem below:
Four children line up at the door for lunch. Jackie is in front of Lynn, Mohammed is the last in line and Fred is not standing next to Jackie. Who is the first in line?
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
3.CM.4 Organize and accurately label work
3.CM.4a
Provide a set of data and have students create a pictograph and bar graph. Review the parts of the pictographs and bar graphs. Stress the importance of giving both graphs a title, choosing an appropriate scale, labeling the xaxis and yaxis on the bar graph, and using a key on the pictograph.
3.CM.5 Share organized mathematical ideas through the manipulation of objects, drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form
3.CM.5a
Provide a set of data and have students create a pictograph and a bar graph. Review the parts of a line graph, pictograph and a bar graph. Stress the importance of giving the graphs a title, choosing an appropriate scale, labeling the xaxis and yaxis on the bar graph, and using a key on the pictograph. Have students discuss the data displayed in the graphs.
3.CM.6 Answer clarifying questions from others
3.CM.6a
Provide a set of data and have students create graphs. Once students have presented an argument about the graphs that they have prepared, encourage students from the class to ask questions about the argument.
Students will analyze and evaluate the mathematical thinking and strategies of others.
3.CM.7 Listen for understanding of mathematical solutions shared by other students
3.CM.7a
Have a student use addition to solve the multiplication fact 5 x 3. Have the student present the process and solution to the class. Assign a multiplication problem to each student and ask them to solve it in the same manner.
3.CM.8 Consider strategies used and solutions found in relation to their own work
3.CM.8a
Have students describe a strategy that they can use to determine if 5 is an even or odd number. Have students share strategies and apply those strategies to determine if 24 is an even or odd number.
Students will use the language of mathematics to express mathematical ideas precisely
3.CM.9 Increase their use of mathematical vocabulary and language when communicating with others
3.CM.9a
Have students state the attributes of a cube, cylinder, sphere, prism, and cone using the words face(s), vertices, and edge(s).
3.CM.10 Describe objects, relationships, solutions, and rationale using appropriate vocabulary
3.CM.10a
Have students sort the following shapes based on the number of sides or angles of each shape: triangle, square, rectangle, rhombus, trapezoid and hexagon.
3.CM.11 Decode and comprehend mathematical visuals and symbols to construct meaning
3.CM.11a
Have students write the number represented by the following base 10 blocks:
2 hundreds blocks, 3 tens blocks, and 6 ones blocks
Students will recognize and use connections among mathematical ideas.
3.CN.1 Recognize, understand, and make connections in their everyday experiences to mathematical ideas
3.CN.1a
Have students relate their knowledge of ½ and ¼ of a whole to the face of the clock. Discuss how the whole face of the clock is equivalent to 60 minutes. Then discuss how ½ of the face would equal 30 minutes and ¼ of the face would equal 15 minutes. Connect these mathematical ideas to the telling of time (e.g., quarter after two equals 2:15).
3.CN.2 Compare and contrast mathematical ideas
3.CN.2a
Identify and discuss symmetry found in nature and compare and contrast them to lines of symmetry of geometric figures.
3.CN.3 Connect and apply mathematical information to solve problems
3.CN.3a
Have students discuss the following question:
What threedimensional figure can be constructed using the three twodimensional shapes below?
Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
3.CN.4 Understand multiple representations and how they are related
3.CN.4a
Represent the number 536 multiple ways (e.g., 5 hundreds, 3 tens, 6 ones or 500 + 30 + 6).
3.CN.5 Model situations with objects and representations and be able to make observations
3.CN.5a
Have students use blocks or counters to complete the sentences below:
The sum of two even numbers is always __________.
The sum of two odd numbers is always ___________.
The sum of an odd number and an even number is always __________.
Students will recognize and apply mathematics in contexts outside of mathematics.
3.CN.6 Recognize the presence of mathematics in their daily lives
3.CN.6a
Have students discuss the importance of being able to tell time and how this skill is used by everyone throughout the day.
3.CN.7 Apply mathematics to solve problems that develop outside of mathematics
3.CN.7a
Dolores wants to buy a present that costs $6.00. She has many quarters in her piggy bank. She does not want to carry the whole piggy bank to the store. How many quarters does she need to pay for the present?
3.CN.8 Recognize and apply mathematics to other disciplines
3.CN.8a
In science class, Josephina needs to make a structure that could support one pound. To test her structure, she has to weigh a variety of objects to find something that weighs close to one pound. What objects can she weigh? Choose some objects around the room and weigh them.
Students will create and use representations to organize, record, and communicate mathematical ideas.
3.R.1 Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations
3.R.1a
Have students use fraction strips to explore the concept of equivalent fractions. Have them create a list, writing the fractions in symbolic form. From the list, students can create a chart displaying the information.
3.R.2 Share mental images of mathematical ideas and understandings
3.R.2a
Have the class envision adding 2 cookies to a plate that already contains 3 cookies. Ask them how many total cookies they picture on the plate. Then have them envision adding 3 cookies to a plate that already contains 2 cookies. Again, ask them how many cookies they picture on the plate. Explain the commutative property and discuss other situations using the commutative property. Have students state the definition of the commutative property. Apply this property to multiplication (e.g., adding 2 objects 4 times compared to adding 4 objects 2 times). Discuss how the commutative property only applies to addition and multiplication and not subtraction and division.
3.R.3 Recognize and use external mathematical representations
3.R.3a
Describe to students a ruler as a type of number line. Use the ruler to locate, compare, and order unit fractions.
3.R.4 Use standard and nonstandard representations with accuracy and detail
3.R.4a
Discuss with the class that the distance from one knuckle to the other knuckle on their pointer finger is approximately one inch and the distance from their elbow to their wrist is approximately one foot. Using these nonstandard tools, estimate the length of various objects throughout the room. Then have the students use a ruler to measure the lengths of the objects. Compare the two measurements.
Students will select, apply, and translate among mathematical representations to solve problems.
3.R.5 Understand similarities and differences in representations.
3.R.5a
Share the three representations below. Compare the similarities and differences.
3.R.6 Connect mathematical representations with problem solving
3.R.6a
How much money did Jill spend at the store if she spent $3.99 on Friday, $2.32 on Saturday, and $6.75 on Sunday?
3.R.7 Construct effective representations to solve problems
3.R.7a
Lauren bought a large cookie to share with two of her friends. Draw a picture of how Lauren could cut the cookie so that she and her two friends would each get an equal part of the whole cookie. What fraction does each part represent?
Students will use representations to model and interpret physical, social, and mathematical phenomena.
3.R.8 Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)
3.R.9 Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a field trip)
3.R.10 Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems)
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Systems
3.N.1 Skip count by 25's, 50's, 100's to 1,000
3.N.1a
Dolores wants to buy a present that costs $6.00. She has many quarters in her piggy bank. She does not want to carry the whole piggy bank to the store. How many quarters does she need to pay for the present?
3.N.2 Read and write whole numbers to 1,000
3.N.2a
Have students write the number represented by the following base 10 blocks:
2 hundreds blocks, 3 tens blocks, and 6 ones blocks.
3.N.2b
Represent the number 536 multiple ways (e.g., 5 hundreds, 3 tens, 6 ones or 500 + 30 + 6).
3.N.3 Compare and order numbers to 1,000
3.N.3a
State the additional information that is needed to solve the problem below:
Ricardo's class collected bottles for the bottle drive. Mark's class collected 250 bottles more than Ricardo's class. Victoria's class collected 435 bottles. Which class collected the most bottles?
3.N.4 Understand the place value
structure of the base ten number system: 10 ones = 1 ten
10 tens = 1 hundred 10 hundreds = 1 thousand
3.N.4a
Melissa is thinking of a twodigit number. It is an odd number. It has a 2 in the tens place and it is a multiple of 9. What is Melissa's number?
3.N.4b
Present the following information to students:
Justin has 2 tens blocks and Kirsten has 20 ones blocks. Kirsten says her blocks represent a larger number than Justin's blocks. Is she correct?
Have students provide other examples where the same amount is represented in two different ways. Have the students use place value blocks to check their work.
3.N.4c
Have students write the number represented by the following base 10 blocks:
2 hundreds blocks, 3 tens blocks, and 6 ones blocks.
3.N.5 Use a variety of strategies to compose and decompose threedigit numbers
3.N.6 Use and explain the commutative property of addition and multiplication
3.N.6a
Have the class envision adding 2 cookies to a plate that already contains 3 cookies. Ask them how many total cookies they picture on the plate. Then have them envision adding 3 cookies to a plate that already contains 2 cookies. Again, ask them how many cookies they picture on the plate. Explain the commutative property and discuss other situations using the commutative property. Have students state the definition of the commutative property. Apply this property to multiplication (e.g., adding 2 objects 4 times compared to adding 4 objects 2 times). Discuss how the commutative property only applies to addition and multiplication and not subtraction and division.
3.N.7 Use 1 as the identity element for multiplication
3.N.8 Use the zero property of multiplication
3.N.9 Understand and use the associative property of addition
3.N.9a
Using cubes or counters, demonstrate how numbers can be grouped or "associated" with the same result. Show how adding 3 + 2 + 5 is the same as adding 3 + 5 + 2. Write the equation (3 + 2) + 5 = 3 + (2 + 5). Continue demonstrating the concept with different numbers, explaining that you are showing the associative property of addition. Have students provide additional examples.
3.N.10 Develop an understanding of fractions as part of a whole unit and as parts of a collection
3.N.10a
Ella hit the ball 5 times out of 8 times at bat. What fraction of the time at bat did Ella hit the ball? Is it reasonable to say that Ella hit the ball more than half of the time at bat?
3.N.10b
There are three red cars and two blue cars in a parking lot. Using snap cubes in red and blue, have students represent the five cars by connecting the cubes. Discuss how 3 out of the 5 cubes are red, represented by 3/5.
3.N.11 Use manipulatives, visual models, and illustrations to name and represent unit fractions (1/2, 1/3, 1/4, 1/5, 1/6, and 1/10) as part of a whole or a set of objects
3.N.11a
The diagram below shows a pizza. What fraction of the pizza is left if Jackie eats her piece of pizza? Write an expression to show your thinking.
3.N.11b
Lauren bought a large cookie to share with two of her friends. Draw a picture of how Lauren could cut the cookie so that she and her two friends would each get an equal part of the whole cookie. What fraction does each part represent?
3.N.12 Understand and recognize the meaning of numerator and denominator in the symbolic form of a fraction
3.N.12a
While reading the book Apple Fractions by Jerry Pallotta, use apples to demonstrate the meaning of a numerator and a denominator in the symbolic form of a fraction.
3.N.13 Recognize fractional numbers as equal parts of a whole
3.N.13a
Lauren bought a large cookie to share with two of her friends. Draw a picture of how Lauren could cut the cookie so that she and her two friends would each get an equal part of the whole cookie. What fraction does each part represent?
3.N.14 Explore equivalent fractions (½, ⅓, ¼)
3.N.14a
Have students use fraction strips to explore the concept of equivalent fractions. Have them create a list, writing the fractions in symbolic form. From the list, students can create a chart displaying the information.
3.N.15 Compare and order unit fractions (½, ⅓, ¼) and find their approximate locations on a number line
3.N.15a
Describe to students a ruler as a type of number line. Use the ruler to locate, compare, and order unit fractions.
Number Theory
3.N.16 Identify odd and even numbers
3.N.16a
Using the chart below, determine how many more students ride bus 4 than bus 3. Which buses contain an odd number of students? Explain your answer.
School bus number 
Number of students riding the bus 
1 
31 
2 
28 
3 
27 
4 
33 
3.N.16b
Melissa is thinking of a twodigit number. It is an odd number. It has a 2 in the tens place and it is a multiple of 9. What is Melissa's number?
3.N.16c
Have students describe a strategy that they can use to determine if 5 is an even or odd number. Have students share strategies and apply those strategies to determine if 24 is an even or odd number.
3.N.17 Develop an understanding of the properties of odd/even numbers as a result of addition or subtraction
3.N.17a
Have students use blocks or counters to complete the sentences below:
The sum of two even
numbers is always __________.
The sum of two odd numbers is always ___________.
The sum of an odd number and an even number is always __________.
Students will understand meanings of operations and procedures, and how they relate to one another.
Operations
3.N.18 Use a variety of strategies to add and subtract 3digit numbers (with and without regrouping)
3.N.18a
Have students create an addition or subtraction problem using the information below:
Joe has collected 113 toy cars.
Ivana has collected 205 toy cars.
3.N.19 Develop fluency with singledigit multiplication facts
3.N.19a
Melissa is thinking of a twodigit number. It is an odd number. It has a 2 in the tens place and it is a multiple of 9. What is Melissa's number?
3.N.20 Use a variety of strategies to solve multiplication problems with factors up to 12 x 12
3.N.20a
Have a student use addition to solve the multiplication fact 5 x 3. Have the student present the process and solution to the class. Assign a multiplication problem to each student and ask them to solve it in the same manner.
3.N.21 Use the area model, tables, patterns, arrays, and doubling to provide meaning for multiplication
3.N.21a
Discuss whether it is more efficient to use a multiplication sentence or to create a chart to solve the problem below:
A recipe calls for 2 eggs for each dozen cookies. If Judy has 6 eggs, how many dozen cookies can Judy make?
3.N.22 Demonstrate fluency and apply singledigit division facts
3.N.22a
Draw a picture to help to solve the problem below:
If 72 third grade students eat lunch in the cafeteria and 8 students can fit at each table, how many tables are needed in the cafeteria for the students?
3.N.23 Use tables, patterns, halving, and manipulatives to provide meaning for division
3.N.23
Use cookies or objects to act out the problem below:
Jasmine wants to share 20 cookies with 4 friends. How many cookies will each friend get if each child (including Jasmine) gets an equal amount of cookies?
3.N.24 Develop strategies for selecting the appropriate computational and operational method in problem solving situations
3.N.24a
A third grade class wants to take a field trip. It will cost the class $100 to go on the field trip. If there are 20 students in the class who want to raise money for the field trip, how much money will each student need to raise, with everyone raising an equal amount of money?
3.N.25 Estimate numbers up to 500
3.N.25a
Show the class a group of paper clips and tell them that there are 20 paper clips in the group. Show the students a group of 100 paper clips, but do not tell them the number of paper clips. Have the class estimate whether the new group contains 40 paper clips or 100 paper clips.
3.N.26 Recognize real world situations in which an estimate (rounding) is more appropriate
3.N.26a
Amelia estimated that there were 20 marshmallows in the Estimation Jar. Amelia tells the class that she measured the height of one marshmallow and she measured the height of the jar. She determined that since one marshmallow is ½ inch tall and the Estimation Jar is 10 inches high, then there must be 20 marshmallows in the jar. Discuss if Amelia's approach to estimation is valid.
3.N.27 Check reasonableness of an answer by using estimation
3.N.27a
Ella hit the ball 5 times out of 8 times at bat. What fraction of the time at bat did Ella hit the ball? Is it reasonable to say that Ella hit the ball more than half of the time at bat?
Students will perform algebraic procedures accurately.
Equations and Inequalities
3.A.1 Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers and unit fractions (1/2, 1/3, 1/4, 1/5, 1/6, and 1/10)
3.A.1a
Have students compare the fractions ½ and ¼ using the symbols <, >, or =, after showing the two comparison models below:
· a piece of string that is ½ inch in length compared to a piece of string that
is ¼ inch in length
· two sandwiches of the same size, one cut in half and the other cut in fourths
Students will recognize, use, and represent algebraically patterns, relations, and functions.
Patterns, Relations, and Functions
3.A.2 Describe and extend numeric (+, ) and geometric patterns
3.A.2a
Make a chart to solve the problem below:
Juan read for 10 minutes on Sunday, 15 minutes on Monday, 20 minutes on Tuesday, and 25 minutes on Wednesday. If this pattern continues, how many minutes would he read on Friday?
3.A.2b
What shape completes this pattern?
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Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
Shapes
3.G.1 Define and use correct terminology when referring to shapes (circle, triangle, square, rectangle, rhombus, trapezoid, and hexagon)
3.G.1a
Have students sort the following shapes based on the number of sides or angles of each shape: triangle, square, rectangle, rhombus, trapezoid and hexagon.
3.G.2 Identify congruent and similar figures
3.G.3 Name, describe, compare, and sort threedimensional shapes: cube, cylinder, sphere, prism, and cone
3.G.3a
Have students state the attributes of a cube, cylinder, sphere, prism, and cone using the words face(s), vertices, and edge (s).
3.G.4 Identify the faces on a threedimensional shape as twodimensional shapes
3.G.4a
Have students discuss the following question:
What threedimensional figure can be constructed using the three twodimensional shapes below?
Students will apply transformations and symmetry to analyze problem solving situations.
Transformational Geometry
3.G.5 Identify and construct lines of symmetry
3.G.5a
Identify and discuss symmetry found in nature and compare and contrast them to lines of symmetry of geometric figures.
Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
3.M.1 Select tools and units (customary) appropriate for the length measured
3.M.1a
Discuss the appropriateness of using inches, feet, or yards when measuring the length of a football field and measuring yards in a football game.
3.M.1b
Have students identify objects where inches would be an appropriate unit to measure the length of the object.
3.M.2 Use a ruler/yardstick to measure to the nearest standard unit (whole and ½ inches, whole feet, and whole yards)
3.M.2a
Have students estimate the length of their pencils to the nearest inch. Then have the students measure their pencils to see how close they were to their estimates.
3.M.3 Measure objects, using ounces and pounds
3.M.3a
In science class, Josephina needs to make a structure that could support one pound. To test her structure, she has to weigh a variety of objects to find something that weighs close to one pound. What objects can she weigh? Choose some objects around the room and weigh them.
3.M.4 Recognize capacity as an attribute that can be measured
3.M.4a
Margo needs to fill a twogallon fish tank with water. She wants to use a onequart jar to fill the tank. How many times must Margo fill the jar in order to fill the fish tank to the top with water?
3.M.5 Compare capacities (e.g., Which contains more? Which contains less?)
3.M.6 Measure capacity, using cups, pints, quarts, and gallons
Students will use units to give meaning to measurements.
Units
3.M.7 Count and represent combined coins and dollars, using currency symbols ($0.00)
3.M.7a
Harry bought a book at the bookstore that cost $4.75. What coins and bills could he use to pay for the book if he wants to use exact change?
3.M.7b
Make an organized list to represent the different combination of coins that can be used to represent 20 cents.
3.M.7c
Dolores wants to buy a present that costs $6.00. She has many quarters in her piggy bank. She does not want to carry the whole piggy bank to the store. How many quarters does she need to pay for the present?
3.M.7d
How much money did Jill spend at the store if she spent $3.99 on Friday, $2.32 on Saturday, and $6.75 on Sunday?
3.M.8 Relate unit fractions to the face of the clock:
Whole = 60 minutes
½ = 30 minutes
¼ = 15 minutes
3.M.8a
Have students restate the problem below:
The soccer coach makes the team run for half of the practice time. If the team practices for 60 minutes, how much time do they spend running?
3.M.8b
Have students relate their knowledge of ½ and ¼ of a whole to the face of the clock. Discuss how the whole face of the clock is equivalent to 60 minutes. Then discuss how ½ of the face would equal 30 minutes and ¼ of the face would equal 15 minutes. Connect these mathematical ideas to the telling of time (e.g., quarter after two equals 2:15).
Students will develop strategies for estimating measurements.
Estimation
3.M.9 Tell time to the minute, using digital and analog clocks
3.M.9a
Have students discuss the importance of being able to tell time and how this skill is used by everyone throughout the day.
3.M.10 Select and use standard (customary) and nonstandard units to estimate measurements
3.M.10a
Which is the best estimate for the capacity of a bathtub?
20 cups
20 pints
20 gallons.
3.M.10b
Margo needs to fill a twogallon fish tank with water. She wants to use a onequart jar to fill the tank. How many times must Margo fill the jar in order to fill the fish tank to the top with water?
3.M.10c
Discuss with the class that the distance from one knuckle to the other knuckle on their pointer finger is approximately one inch and the distance from their elbow to their wrist is approximately one foot. Using these nonstandard tools, estimate the length of various objects throughout the room. Then have the students use a ruler to measure the lengths of the objects. Compare the two measurements.
Students will collect, organize, display, and analyze data.
Collection of Data
3.S.1 Formulate questions about themselves and their surroundings
3.S.2 Collect data using observation and surveys, and record appropriately
3.S.2a
Ask the students the following question:
What is your favorite sport?
Have students give their answers orally, write the results in a frequency table, use colored counters to represent each choice, and create a bar graph to display the results of the survey.
3.S.2b
Write the statement below on the board:
The students in this class like chocolate ice cream best.
Have the students survey the class and discuss whether the statement is accurate. Have students display the survey results in a pictograph or bar graph and make a statement about their findings.
Organization and Display of Data
3.S.3 Construct a frequency table to represent a collection of data
3.S.3a
Ask the students the following question:
What is your favorite sport?
Have students give their answers orally, write the results in a frequency table, use colored counters to represent each choice, and create a bar graph to display the results of the survey.
3.S.4 Identify the parts of pictographs and bar graphs
3.S.4a
Provide a set of data and have students create a pictograph and bar graph. Review the parts of the pictographs and bar graphs. Stress the importance of giving both graphs a title, choosing an appropriate scale, labeling the xaxis and yaxis on the bar graph, and using a key on the pictograph.
3.S.5 Display data in pictographs and bar graphs
3.S.5a
Ask the students the following question:
What is your favorite sport?
Have students give their answers orally, write the results in a frequency table, use colored counters to represent each choice, and create a bar graph to display the results of the survey.
3.S.5b
Provide a set of data and have students create a pictograph and bar graph. Review the parts of the pictographs and bar graphs. Stress the importance of giving both graphs a title, choosing an appropriate scale, labeling the xaxis and yaxis on the bar graph, and using a key on the pictograph.
3.S.6 State the relationships between pictographs and bar graphs
3.S.6a
Use the charts below to discuss the difference in how the data is displayed in the pictograph compared to the same data displayed in the bar graph.
Favorite Lunch Choice in the Third Grade  
Hamburger  ****  
Salad  **  
Pizza  ******  
* represents two votes  
Analysis of Data
3.S.7 Read and interpret data in bar graphs and pictographs
3.S.7a
Provide a set of data and have students create a pictograph and a bar graph. Review the parts of a line graph, pictograph and a bar graph. Stress the importance of giving the graphs a title, choosing an appropriate scale, labeling the xaxis and yaxis on the bar graph, and using a key on the pictograph. Have students discuss the data displayed in the graphs.
Students will make predictions that are based upon data analysis.
Predictions from Data
3.S.8 Formulate conclusions and make predictions from graphs
3.S.8a
Write the statement below on the board:
The students in this class like chocolate ice cream best.
Have the students survey the class and discuss whether the statement is accurate. Have students display the survey results in a pictograph or bar graph and make a statement about their findings.
Encourage students to listen and discuss the observations of other students.
3.S.8b
Provide a set of data and have students create a pictograph and a bar graph. Review the parts of a line graph, pictograph and a bar graph. Stress the importance of giving the graphs a title, choosing an appropriate scale, labeling the xaxis and yaxis on the bar graph, and using a key on the pictograph. Have students discuss the data displayed in the graphs.