Category: Grade 3 Math

Attributes of Polygons

Unit description: Students will extend their understanding of polygons as they classify them into categories such as triangles, quadrilaterals, pentagons, and hexagons.  Students will break shapes into fractional parts.  

Download the complete Grade 3  Unit 6 framework to customize for your own planning.

Essential Outcomes of the Unit

Geometry- Reason with shapes and their attributes.

• NY-3.G.1 Recognize and classify polygons based on the number of sides and vertices (triangles, quadrilaterals, pentagons, and hexagons). Identify shapes that do not belong to one of the given subcategories. Note: Include both regular and irregular polygons, however, students need not use formal terms “regular” and “irregular,” e.g., students should be able to classify an irregular pentagon as “a pentagon,” but do not need to classify it as an “irregular pentagon.
• NY-3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

Essential Questions and Big Ideas

How do I identify polygons?

• Polygons are figures with straight lines that are connected.  
• The type of polygon can be determined by counting the sides.

What are common types of polygons?

• A triangle is a shape with three sides and three angles
• A quadrilateral is a shape with four sides and four angles. 
• A pentagon is a shape with five sides and five angles. 
• A hexagon is a shape with six sides and six angles. 

How can shapes be partitioned?  

• A shape can be broken into parts of equal area which represent fractions.  

Download the complete Grade 3  Unit 6 framework to customize for your own planning.

Time, Liquid and Mass Measurement and Graphing

Unit description:  Students will develop an understanding of how to understand and relate time, liquid, and mass in word problems. Students will also build on their ability to create bar and picture graphs with scales other than one. They will also represent data using line plots.

Download the complete Grade 3  Unit 5 framework to customize for your own planning.

Essential Outcomes of the Unit

Measurement and Data- Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

• NY-3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve one-step word problems involving addition and subtraction of time intervals in minutes.

Measurement and Data- Represent and interpret data.

• NY-3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in a scaled picture graph or a scaled bar graph.
• NY-3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

Other Standards Addressed in the Unit

Measurement and Data- Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

• NY-3.MD.2a Measure and estimate liquid volumes and masses of objects using grams (g), kilograms (kg), and liters (l).
  Note: Does not include compound units such as cm3 and finding the geometric volume of a container.
• NY-3.MD.2b Add, subtract, multiply, or divide to solve one-step word problems involving masses or liquid volumes that are given in the same units.Note: Does not include multiplicative comparison problems involving notions of “times as much.”

Essential Questions and Big Ideas

How do I solve word problems involving time?

• There are 60 minutes in an hour.
• Number lines can be used to represent time.

How do I solve word problems involving masses and volumes?

• Mass represents how much matter is in an item (similar to weight).
• Volume represents the amount of space a 3-D shape takes up.

How do I represent data using graphs?

• Graphs can model data using scales besides one.

How do I represent data using a line plot?

• Line plots represent numerical data using Xs.

Download the complete Grade 3  Unit 5 framework to customize for your own planning.

Perimeter and Area

Unit description: In this unit students will deepen their understanding of 2-D shapes by considering area and perimeter.  They will focus on rectangles and how to find their area and perimeter. They will relate area to multiplication and addition. The students will develop arrays of unit squares to solve area and perimeter problems.

Download the complete Grade 3  Unit 4 framework to customize for your own planning.

Essential Outcomes of the Unit

Measurement and Data- Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

• NY-3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
• NY-3.MD.6 Measure areas by counting unit squares. 
• NY-3.MD.7 Relate area to the operations of multiplication and addition. 
• NY-3.MD.7c Use tiling to show in a concrete case that the area of a rectangle with whole-number side length a and side length b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
• NY-3.MD.7d Recognize area as additive. Find areas of figures composed of non-overlapping rectangles, and apply this technique to solve real world problems.

Other Standards Addressed in the Unit

Measurement and Data- Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

• NY-3.MD.5a Recognize a square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
• NY-3.MD.5b Recognize a plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
• NY-3.MD.7a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
• NY-3.MD.7b . Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

Measurement and Data- Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
NY-3.MD.8a Finding the perimeter given the side lengths or find one unknown side length given the perimeter and other side lengths. 

• NY-3.MD.8b Identify rectangles with the same perimeter and different areas or with the same area and different perimeters.

Essential Questions and Big Ideas

What is area?

Area is the amount of space a shape covers, or the measure of the inside of shape.

What is perimeter?

Perimeter is the distance around the outside of a shape.

How do we solve area and perimeter problems with rectangles? 

The area of a rectangle can be determined using L x W. 

The perimeter of a rectangle can be determined by using the formula 2L + 2W.

How do we find the area of a shape made of multiple rectangles?

The area of a shape made of multiple rectangles can be determined by finding the area of each rectangle using L x W and adding the total of all areas within the larger shape.

Download the complete Grade 3  Unit 4 framework to customize for your own planning.

Understand Fractions

Unit description: Students will deepen their understanding of parts and wholes.  They will begin to learn about unit fractions and non-unit fractions and how to represent them and compare them.  They will also start thinking about equivalent fractions.  

Download the complete Grade 3 Math Unit 3 framework to customize for your own planning.

Essential Outcomes

Number & Operations – Fractions 

NY-3.NF.1 Understand a unit fraction, 1b, is the quantity formed by 1 part when a whole is partitioned into b equal parts. Understand a fraction abis the quantity formed by a parts of size 1b. Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.

NY-3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line. Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.

NY-3.NF.2a Represent a fraction 1bon a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1band that the endpoint of the part starting at 0 locates the number 1b on the number line.

NY-3.NF.2b Represent a fraction ab on a number line by marking off a lengths 1b from 0. Recognize that the resulting interval has size aband that its endpoint locates the number abon the number line.

NY-3.NF.3 Explain equivalence of fractions and compare fractions by reasoning about their size.

Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.

NY-3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

NY-3.NF.3b Recognize and generate equivalent fractions. e.g., 12= 24; 46= 23. Explain why the fractions are equivalent. e.g., using a visual fraction model.

NY-3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. e.g., Express 3 in the form 3 = 31, recognize that 63= 2, and locate 44and 1 at the same point on a number line.

NY-3.NF.3d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions. e.g., using a visual fraction model.

NY-3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. e.g., Partition a shape into 4 parts with equal area, and describe the area of each part as 14 of the area of the shape.

Essential Questions and Big Ideas

What is a fraction?  What is a unit fraction? 

• A fraction represents a part of a whole.  
• A unit fraction represents one part of a whole broken into equal parts.  

How can a fraction be represented on a number line?  

• The number one represents one whole.  
• To represent a fraction on a number line, break the whole (1) into the number of parts.  

What are equivalent fractions?  

• Equivalent fractions are equal.  
• A whole can be broken in different ways that create equal amounts.  

How can I compare fractions?  

• Fractions can be compared by comparing the size of the parts.  
• Fractions can be compared by comparing the number of parts.  
• Fraction bars can be used to compare fractions.  
• Number lines can be used to compare fractions.  

Prerequisite Skills

• NY-1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
• NY-2.MD.6 Represent whole numbers as lengths from 0 on a number line with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line.
• NY-2.G.3 Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, etc. Describe the whole as two halves, three thirds, four fourths.

Download the complete Grade 3 Math Unit 3 framework to customize for your own planning.

Addition and Subtraction within 1,000

Students will develop deeper understandings of the base ten number system, which will strengthen their abilities to round as well as add and subtract numbers.

Note: Lessons will vary in length, depending on the amount of time you have with students, the resources that you choose to accompany the unit, the level of rigor within each learning target, and any other factors that may contribute to the pacing of your learning progressions. It is recommended that you adjust the pace and length of each learning progression(s) accordingly in response to these factors.

These learning progressions were developed using Next Generation Learning Standards and were cross-walked with the Common Core Standards.

Download the complete Grade 3  Unit 2 framework to customize for your own planning.

Essential Outcomes

Numbers in Base Ten

• 3-NY-NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
• 3-NY-NBT.2: Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Operations and Algebraic Thinking

• NY-3.OA.8: Solve two-step word problems posed with whole numbers and having whole-number answers using the four operations.

Other Standards Addressed in this Unit

Numbers in Base Ten

• NY-3.NBT.4a: Understand that the digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones. e.g., 3,245 equals 3 thousands, 2 hundreds, 4 tens, and 5 ones.
• NY-3.NBT.4b: Read and write four-digit numbers using base-ten numerals, number names, and expanded form. e.g., The number 3,245 in expanded form can be written as 3,245= 3,000 + 200 + 40 + 5.

Essential Questions and Big Ideas

• How does understanding place value help you to better understand numbers?
  • The base ten number system determines the value of the digits within numbers.
  • Numbers are broken into places which are based on powers of 10.
  • Rounding numbers shows about how much of a certain place value they hold.
  • Expanded form is a way to write numbers broken into the values of each place value.
• What are efficient strategies to add multi digit whole numbers?
  • Digits in a number can be added based on place value.
  • Add like place values.
  • Only 9 of a place can fit in each place.
  • Ten of one place makes one of the next largest place value.
• What are efficient strategies to subtract multi digit whole numbers?
  • Digits in a number can be subtracted based on place value.
  • Subtract like place values.
  • If you do not have enough of a place value, regroup one of the next largest place value to create ten more of that place value.
  • Subtraction is the inverse to addition.
  • Adding on can be used to find a difference.
• How can I solve two-step word problems with addition and subtraction?
  • When a word problem has more than one unknown, there is more than one step.
  • Finding a difference or comparing requires subtraction.
  • Finding a total or combining amounts requires addition.
  • Finding a missing part requires subtraction.

Download the complete Grade 3  Unit 2 framework to customize for your own planning.

Understanding Multiplication and Division

Students will develop an understanding of multiplication and division and their relationship. Students will develop strategies to solve single digit multiplication number sentences. Students will develop strategies to solve division number sentences. Students will relate multiplication and division to equal groups story problems.

Download the complete Grade 3 Math Unit 1 framework to customize for your own planning.

Essential Outcomes

Operations and Algebraic Thinking

• NY-3.OA.3 – Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. e.g., using drawings and equations with a symbol for the unknown number to represent the problem.
• NY-3.OA.1 – Interpret products of whole numbers.e.g., Interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. Describe a context in which a total number of objects can be expressed as 5 × 7.
• NY-3.OA.2 – Interpret whole-number quotients of whole numbers. e.g., Interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
• NY-3.OA.4 – Determine the unknown whole number in a multiplication or division equation relating three whole numbers. e.g., Determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.
• NY-3.OA.5 – Apply properties of operations as strategies to multiply and divide. E.g.,
  • If 6×4=24 is known,then 4×6 = 24 is also known. (Commutative property of multiplication)
  • 3×5×2 can be found by 3×5=15, then 15×2=30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication)
  • Knowing that 8×5=40 and 8×2=16, one can find 8×7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property)
    Note: Students need not use formal terms for these properties.
    Note: A variety of representations can be used when applying the properties of operations, which may or may not include parentheses.
• NY-3.OA.6 – Understand division as an unknown-factor problem. e.g., Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
• NY-3.OA.7a – Fluently solve single-digit multiplication and related divisions, using strategies such as the relationship between multiplication and division or properties of operations. e.g., Knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8.
• NY-3.OA.7b – Know from memory all products of two one-digit numbers.
• NY-3.OA.9 – Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table).

Number and Operations in Base Ten

• NY-3.NBT.3 – Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations. e.g., 9 × 80, 5 × 60

Essential Questions and Big Ideas

• What is multiplication?
  • Multiplication represents finding a total made from equal groups.
  • A x B represents A groups of the number B.
• What is division?
  • Division represents splitting a total into equal groups.
  • B ÷ A can represents a total B split into A groups or a total B split into groups of size A.
• How are multiplication and division related?
  • Multiplication and division are inverse operations.
  • Factors are multiplied to create a product.
  • An unknown factor can be found through division.
  • A dividend is divided by a divisor to find a quotient.
  • An unknown dividend can be found through multiplication.
• What are strategies that can be used to efficiently multiply or divide?
  • Skip counting can be used to solve multiplication and division problems.
  • Known multiplication facts can be used to solve division problems.
  • Factors can be rearranged to solve multiplication problems.
  • A factor can be broken up into smaller pieces to find known products.
  • Memorizing multiplication facts can support more fluent solving.
  • Multiplying by multiples of 10 can be thought of as by multiplying a digit and 10, ex. 3 x 20 = 3 x 2 x 10.

Download the complete Grade 3 Math Unit 1 framework to customize for your own planning.