OVERVIEW
Third grade math is where students build a strong foundation for abstract thinking and problem-solving. We begin the year by exploring what it means to be a mathematician, learning to make sense of problems and critique the reasoning of others. We then dive into multiplication and division, learning to use patterns to master our facts. Students will expand their understanding of place value up to 10,000 to fluently add and subtract larger numbers. We'll also explore fractions, learning to represent, compare, and find equivalent fractions. Finally, we'll introduce the core concepts of perimeter and area, using hands-on strategies to solve problems. This year is all about building a love for numbers and an understanding of how math is a part of our everyday lives.
Unit 1: Math Is
Learning Targets
Students will learn to make sense of problems and use math to model real-world situations.
Students will construct and defend a mathematical argument.
Students will learn to critique the thinking and reasoning of others.
Students will choose appropriate tools and use precise language when communicating their ideas.
Students will notice patterns and make generalizations about them.
Essential Questions
What does it mean to be a problem solver in math?
How do we explain and justify our thinking to others?
How can we work together to solve a problem?
Questions to Ask at Home
Tell me about a time you used math today.
How did you figure out the answer to that problem? Can you defend your reasoning?
What is one new thing you learned about math today?
What is your math story?
The Boy Who Loved Math by Paul Erdos: This biography of a real-life mathematician shows a young child who is deeply curious about numbers, illustrating that math is about more than just being fast.
What Do You Do with a Problem? by Kobi Yamada: This beautifully illustrated book explores the idea that problems can be opportunities. It encourages children to face their fears and find creative solutions.
Math Curse by Jon Scieszka and Lane Smith: A humorous book that shows how math is all around us in unexpected places, helping children see math as a part of their everyday lives.
Unit 2: Using Place Value to Fluently Add and Subtract within 1,000
Learning Targets
Students will represent 3- and 4-digit numbers in different ways, including expanded form and word form.
Students will add and subtract 3-digit numbers using strategies like decomposing numbers and using partial sums.
Students will solve problems by using compatible numbers to make adding and subtracting easier.
Students will learn to use a letter to represent an unknown in an equation.
Essential Questions
How can we use place value to help us add and subtract?
Why is it helpful to have more than one strategy for solving a problem?
How can a bar diagram help us understand a problem?
Questions to Ask at Home
Can you solve 245+158? What strategy did you use?
We have 560 miles to drive. We have driven 225 miles. How many more miles do we have to go?
How can we use the numbers in 250+75=325 to write a subtraction problem?
What are compatible numbers? Can you give me an example?
The King's Commissioners by Aileen Friedman: This book explains the concept of place value and grouping numbers in a medieval story, a perfect lead-in to adding hundreds.
How Much Is a Million? by David M. Schwartz: This book gives children a sense of the scale of large numbers, which helps them understand place value beyond the hundreds.
Mission: Addition **and Mission: Subtraction by Loreen Leedy: These books provide a clear and fun introduction to addition and subtraction and writing equations from word problems.
Unit 3: Multiplication and Division
Learning Targets
Students will use equal groups and arrays to solve multiplication problems.
Students will understand that multiplication is a fast way to add equal groups.
Students will use equal sharing and equal grouping to solve division problems.
Students will understand the relationship between multiplication and division and will write related equations for a fact family.
Essential Questions
How can we use multiplication and division to solve real-world problems?
How are multiplication and division related?
How can a drawing or a model help us find an answer?
Questions to Ask at Home
We have 4 bags with 3 apples in each bag. How can we write a multiplication problem to find the total?
We have 15 cookies to share among 3 people. How many will each person get?
Can you tell me an array you see in our home?
If you know that 4×5=20, what are two division problems you can write?
The Grapes of Math by Greg Tang: This book presents clever rhymes and visual puzzles that encourage children to see numbers in different ways and look for efficient strategies to add them, which is a great way to introduce repeated addition.
The Doorbell Rang by Pat Hutchins: A great book for introducing the concepts of dividing items into equal shares as more and more friends arrive to share a plate of cookies.
One Hundred Hungry Ants by Elinor J. Pinczes: A great story about 100 ants marching to a picnic that can be used to talk about how a whole group can be broken apart into smaller groups, which is a key concept in division.
Unit 4: Using Patterns to Multiply by 0,1, 2, 5, and 10Â
Learning Targets
Students will use patterns to quickly find the product of a number and 2, 5, and 10.
Students will learn the properties of multiplying by 0 and 1.
Students will use equal groups and skip counting to solve multiplication and division problems.
Students will identify the connection between multiplication and division facts.
Essential Questions
How can patterns help us solve multiplication problems?
What happens when you multiply a number by 0 or 1?
How can a related multiplication fact help us solve a division problem?
Questions to Ask at Home
We have 5 people in our family. If everyone has two hands, how many hands is that in all?
What is 7×10? How do you know?
If you have 25 cents, how many nickels do you have?
How are multiplying by 5 and multiplying by 10 similar?
The Best of Times: Math Strategies That Multiply by Greg Tang: This book presents clever rhymes and visual tricks to help children master multiplication facts and see patterns in numbers.
The Hershey's Kisses Multiplication Book by Jerry Pallotta: This book uses a favorite treat to model multiplication and explore the concepts of equal groups and arrays.
Anno's Mysterious Multiplying Jar by Mitsumasa Anno: This beautifully illustrated book takes children on a journey through a multiplying jar, subtly introducing the concept of factorials and repeated multiplication in a creative way.
Unit 5: Using Patterns to Multiply by 3, 4, 6, 7, 8, and 9
Learning Targets
Students will use arrays to visualize how to decompose a factor to find a product.
Students will learn to use facts they already know (like multiplying by 2 or 5) to solve problems with factors of 3, 4, 6, 7, 8, and 9.
Students will learn to double a product to find the answer for a new problem (e.g., 4×8 is double 2×8).
Essential Questions
How can we use multiplication facts we already know to help us solve harder problems?
How can a drawing or array help us break apart a problem?
How can breaking apart a number make a problem easier to solve?
Questions to Ask at Home
We need to figure out 6×7. Can you show me how to decompose that problem?
If you know that 4×6=24, how can you use that to solve 8×6?
Can you show me how to solve 7×8 using a 5s fact?
Why is it helpful to break apart one of the numbers when we multiply?
The Best of Times: Math Strategies That Multiply by Greg Tang: This book presents clever rhymes and visual tricks to help children master multiplication facts and see patterns in numbers.
Amanda Bean's Amazing Dream by Cindy Neuschwander: In this story, a girl who loves to count learns the value of grouping and multiplication as a faster way to find a total.
The Multiplying Menace by Tony Abbott: A fantasy adventure story that weaves multiplication concepts into a fun plot, showing how multiplication can be useful in unexpected ways.
Unit 6: Connect Area and Multiplication
Learning Targets
Students will understand that area is measured in square units and can be found by tiling a shape.
Students will learn how to find the area of a rectangle by multiplying its length and width.
Students will find the area of a composite figure by breaking it into smaller rectangles and adding the areas together.
Students will use the strategy of decomposing a length to find the area of larger rectangles.
Essential Questions
What is area and how do we measure it?
How are multiplication and area related?
How can we find the area of a shape that is not a simple rectangle?
Questions to Ask at Home
Can you find something in our home that is shaped like a rectangle? About how many square tiles would it take to cover it?
If a book is 8 inches long and 5 inches wide, what is its area?
How can we use multiplication to find the area of our placemat?
Why is it helpful to break apart a large shape to find its area?
Spaghetti and Meatballs for All! by Marilyn Burns: This fun story about a family reunion uses a seating arrangement problem to introduce the concepts of area and perimeter in a simple way.
The Best of Times: Math Strategies That Multiply by Greg Tang: This book presents clever rhymes and visual tricks to help children master multiplication facts and see patterns in numbers, which is a great lead-in to understanding how multiplication relates to area.
The Multiplying Menace by Tony Abbott: A fantasy adventure story that weaves multiplication concepts into a fun plot, showing how multiplication can be useful in unexpected ways.
Unit 7: Fractions
Learning Targets
Students will understand that a fraction is a number that represents a certain number of equal parts of a whole.
Students will identify the numerator (the number of parts being used) and the denominator (the total number of parts in the whole).
Students will represent fractions by partitioning shapes into equal parts and plotting them on a number line.
Students will recognize that a fraction with the same numerator and denominator, such as 4/4 is equal to 1.
Students will learn to recognize fractions greater than 1, where the numerator is larger than the denominator.
Essential Questions
What are the parts of a fraction and what do they represent?
How can we show a fraction on a number line?
What does it mean for a fraction to be equal to 1?
Questions to Ask at Home
If we cut a pizza into 8 slices, and we eat 3 of them, what fraction of the pizza did we eat?
Can you show me what one-half of this sandwich looks like?
How can we use a ruler to show one-fourth?
If a whole pie is cut into 6 equal parts, what is the unit fraction for each part?
Eating Fractions by Bruce McMillan: This book uses vibrant photos of food to illustrate simple fractions, including halves and fourths.
Give Me Half! by Stuart J. Murphy: This book uses a fun story about a brother and sister sharing a pizza and a cake to introduce the concept of halves. It clearly explains why the pieces must be equal.
Full House: An Invitation to Fractions by Dayle Ann Dodds: A humorous story about a woman who owns a gingerbread factory and has to divide her gingerbread into different equal parts. This is a great way to talk about equal shares and simple fractions.
Unit 8: Fraction Equivalence and Comparison
Learning Targets
Students will understand that fractions can only be compared when the wholes are the same size.
Students will identify and create equivalent fractions, such as 1/2 and 2/4.
Students will compare fractions with the same denominator by looking at the numerator.
Students will compare fractions with the same numerator by looking at the denominator.
Essential Questions
How can we tell if two fractions are the same size?
When we compare fractions, what does the denominator tell us? What does the numerator tell us?
How can a number line or a drawing help us compare fractions?
Questions to Ask at Home
Would you rather have 1/2 of a small cookie or 1/2 of a large cookie? Why?
How can we use two halves of a sandwich to show that 1/2 is the same as 2/4?
If we cut two identical pizzas, one into 6 slices and one into 8 slices, which has bigger slices?
Is 3/4 of a candy bar more or less than 2/4 of the same candy bar? How do you know?
Full House: An Invitation to Fractions by Dayle Ann Dodds: A humorous story about a woman who owns a gingerbread factory and has to divide her gingerbread into different equal parts. This is a great way to talk about equal shares and simple fractions.
Jump, Kangaroo, Jump! by Stuart J. Murphy: This book uses a tug-of-war game to introduce the concept of equal groups, which is a great lead-in to talking about fractions.
The Hershey's Milk Chocolate Bar Fractions Book by Jerry Pallotta: This book uses a chocolate bar to show different fractions and equivalent fractions in a delicious and memorable way.
Unit 9: Use Multiplication to Divide
Learning Targets
Students will use a related multiplication fact to find the quotient in a division problem.
Students will learn to identify the dividend, divisor, and quotient in a division equation.
Students will use fact triangles and multiplication tables to find missing numbers in multiplication and division equations.
Students will solve for a missing unknown in an equation.
Essential Questions
How can a multiplication fact help us solve a division problem?
What are the parts of a division problem?
How can a fact triangle help us remember related facts?
Questions to Ask at Home
What is 40÷5? How can a multiplication fact help you find the answer?
If you know that 7×8=56, what are two division problems you can write using those numbers?
Can you tell me what the dividend, divisor, and quotient are in the problem 12÷3=4?
Let's say we have 27 cookies. If we give 3 to each person, how many people can we give cookies to?
The Best of Times: Math Strategies That Multiply by Greg Tang: This book presents clever rhymes and visual tricks to help children master multiplication facts and see how they are connected to each other.
The Doorbell Rang by Pat Hutchins: A great book for introducing the concepts of dividing items into equal shares, which is a key concept in division.
The Multiplying Menace by Tony Abbott: A fantasy adventure story that weaves multiplication concepts into a fun plot, showing how multiplication can be useful in unexpected ways.
Unit 10: Use Properties and Strategies to Multiply and Divide
Learning Targets
Students will use patterns on the multiplication fact table to solve problems.
Students will learn that when multiplying three factors, the grouping doesn't change the product.
Students will find the product of a one-digit number and a multiple of 10.
Students will solve two-step word problems involving any of the four operations (addition, subtraction, multiplication, and division).
Students will use a letter to represent the unknown in an equation.
Essential Questions
How can patterns help us solve multiplication problems?
How can we use the strategies we've learned to solve problems with bigger numbers?
How do we break a two-step word problem into smaller parts?
Questions to Ask at Home
What is a quick way to solve 4×30?
Can you solve 2×3×5? What if you group the numbers differently?
I have 4 bags of apples with 6 apples in each bag. I gave 5 apples to our neighbor. How many apples do I have left?
What is the difference between a factor and a multiple?
The Best of Times: Math Strategies That Multiply by Greg Tang: This book presents clever rhymes and visual tricks to help children master multiplication facts and see patterns in numbers.
Amanda Bean's Amazing Dream by Cindy Neuschwander: In this story, a girl who loves to count learns the value of grouping and multiplication as a faster way to find a total.
The Multiplying Menace by Tony Abbott: A fantasy adventure story that weaves multiplication concepts into a fun plot, showing how multiplication can be useful in unexpected ways.
Unit 11: Perimeter
Learning Targets
Students will find the perimeter of a shape by adding all of its side lengths.
Students will learn to use multiplication as a faster way to find the perimeter of certain shapes, like squares and rectangles.
Students will solve for an unknown side length of a figure when given its perimeter and the lengths of the other sides.
Students will understand that figures can have the same area but different perimeters, or the same perimeter but different areas.
Essential Questions
How can we measure the distance around a shape?
What is the difference between perimeter and area?
How can knowing the perimeter help us find a missing side length?
Questions to Ask at Home
How can we find the perimeter of the dining table?
If a picture frame is a square with sides of 10 inches, what is its perimeter?
A garden has a perimeter of 24 feet. What could the side lengths be? Can you think of another possible shape for the garden?
Why can two different shapes have the same area but different perimeters?
Perimeter, Area, and Volume: A Monster Book of Math by David A. Adler: This book uses fun monster illustrations to introduce and explain the concepts of perimeter, area, and volume in a clear and engaging way.
Spaghetti and Meatballs for All! by Marilyn Burns: This fun story about a family reunion uses a seating arrangement problem to introduce the concepts of area and perimeter in a simple way.
The Greedy Triangle by Marilyn Burns: A triangle decides he wants more sides and transforms into different shapes. This is a great story for talking about how the number of sides and shape relate to a figure's perimeter.
Unit 12: Measurement and Data
Learning Targets
Students will estimate and measure liquid volume in liters and milliliters.
Students will learn to measure the mass of objects in grams and kilograms.
Students will tell time to the nearest minute.
Students will create and interpret scaled picture graphs using a key.
Students will also learn to interpret bar graphs and line plots.
Essential Questions
How can we measure the amount of liquid or the weight of an object?
What are different ways to tell time?
How can a graph help us organize and understand data?
Questions to Ask at Home
What time is it right now? How many minutes until the next hour?
Let's look at the label on this soda bottle. How many liters or milliliters of liquid are in it?
Do you think a pencil has a mass of about 1 gram or 1 kilogram? Why?
Can you tell me what the key on a graph is for?
The Go-Around Dollar by Barbara Johnston Adams: This book follows a dollar bill as it is used and reused, showing how money circulates and can be counted and organized.
The Great Graph Gimmick by Lynne W. Taggart: A fun story that shows how to use a simple graph to organize information, from what different pets eat to how many socks are in a drawer.
A Second Is a Hiccup: A Child's Book of Time by Hazel-Grace: This book breaks down the concepts of time into relatable examples, helping children understand what a second, minute, and hour feel like.
Unit 13: Describe and Analyze 2-Dimensional Shapes
Learning Targets
Students will recognize and name polygons with up to eight sides, including triangles, quadrilaterals, pentagons, hexagons, and octagons.
Students will identify a right angle as a square corner.
Students will classify quadrilaterals based on their attributes, distinguishing between a rhombus, a rectangle, and a square.
Students will learn to use a shape's attributes (sides, angles, parallel lines) to identify it.
Essential Questions
How can we use the attributes of a shape to describe it?
What are the different types of polygons?
What makes a square a special kind of rectangle and rhombus?
Questions to Ask at Home
Can you find a quadrilateral in our home? How do you know it's a quadrilateral?
Let's look at the tiles on the floor. What kind of shapes are they?
Can you draw a pentagon? How many sides does it have?
How can you tell if an angle is a right angle?
The Greedy Triangle by Marilyn Burns: A triangle decides he wants more sides and transforms into different shapes. This is a great story for talking about how shapes change based on their features.
Sir Cumference and All the King's Tens by Cindy Neuschwander: This book explains the concept of place value and grouping numbers in a medieval story.
If You Were a Polygon by Trisha Speed Shaskan: A fun book that uses simple language and illustrations to describe different types of polygons based on their number of sides and corners.