OVERVIEW
Fourth grade math is where we 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. We will expand our understanding of place value up to one million to fluently add and subtract larger numbers. We'll also explore fractions and decimals, learning to represent, compare, and perform operations with them. Finally, we'll introduce the core concepts of area and perimeter, 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: Generalize Place-Value Structure
Learning Targets
Students will learn the value of each digit in a multi-digit number, up to the millions place.
Students will read and write numbers in standard form, expanded form, and word form.
Students will use place value to compare multi-digit numbers.
Students will learn to round numbers to any place value.
Essential Questions
How can place value help us understand the value of a large number?
How can we compare two multi-digit numbers?
How can rounding a number help us in real-world situations?
Questions to Ask at Home
Can you read the number 5,234,891? What is the value of the 2?
How would you write 45,678 in expanded form?
Which number is greater: 124,567 or 124,576? How do you know?
If you round 2,489 to the nearest hundred, what number do you get? Why?
On Beyond a Million: An Amazing Math Journey by David M. Schwartz: This book takes children on a visual journey through large numbers, helping them grasp the concept of place value and the scale of millions and beyond.
A Place for Zero: A Math Adventure by Angeline Sparagna LoPresti: A fun story that highlights the importance of the number zero in place value, especially in creating large numbers.
The King's Commissioners by Aileen Friedman: A fun story that explains the concept of place value and grouping numbers in a medieval story.
Unit 3: Addition and Subtraction Strategies and Algorithms
Learning Targets
Students will estimate sums and differences using different strategies, such as rounding.
Students will add multi-digit numbers using a standard algorithm, including problems that require regrouping.
Students will subtract multi-digit numbers using a standard algorithm, including problems that require regrouping.
Students will understand that an algorithm is a set of steps that will always work to solve a problem.
Essential Questions
How can we add and subtract large numbers accurately?
What does it mean to regroup in addition and subtraction?
How can an estimate help us check our work?
Questions to Ask at Home
What is a good estimate for 245+372?
Can you show me how to solve 1,234+5,678 using the algorithm?
Let's say we have 5,000 miles to drive. We have already driven 2,567 miles. How many more miles do we have to go?
How can you tell if an answer is reasonable before you even do the math?
A Million Chameleons by Cara DesJardins: A fun book that illustrates what a million is, which provides a great visual for working with large numbers.
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, a perfect lead-in to adding and subtracting larger numbers.
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 and the need for new strategies to add and subtract.
Unit 4: Multiplication as Comparison
Learning Targets
Students will use additive comparison to solve problems about how much more or less one quantity is than another.
Students will use multiplicative comparison to solve problems about how many times as many one quantity is than another.
Students will write and solve a multiplication equation to represent a comparison.
Students will use bar diagrams to visualize and solve comparison problems.
Essential Questions
How can we use multiplication and addition to compare quantities?
What is the difference between "3 more than" and "3 times as many as"?
How can a drawing help us solve a comparison problem?
Questions to Ask at Home
I have 5 apples. You have 3 times as many as me. How many apples do you have?
How can we write a multiplication sentence to compare the number of wheels on a car and a tricycle?
If a book costs $10 and a magazine costs $2, how can we describe the cost of the book using multiplication?
What is the difference between an additive comparison and a multiplicative comparison?
The Doorbell Rang by Pat Hutchins: A great book for introducing the concepts of dividing items into equal shares, which can be used to set up comparison problems.
The Great Graph Gimmick by Lynne W. Taggart: While a data book, you can use it to create comparison word problems with larger numbers and then subtract to find the difference or use multiplication to compare quantities.
Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells: This book introduces concepts of size and scale, providing a great context for comparing quantities in a fun and engaging way.
Unit 5: Numbers and Number Patterns
Learning Targets
Students will find all the factor pairs for a whole number.
Students will identify a number as either prime or composite.
Students will learn to find the multiples of a given number.
Students will identify the rule of a pattern and use it to continue a sequence.
Students will analyze the features of a pattern that aren't stated in the rule.
Essential Questions
How can we find the factors of a number?
What is the difference between a prime and a composite number?
How can a rule help us create and understand a pattern?
Questions to Ask at Home
Can you tell me all the factors of 12?
Is the number 7 prime or composite? How do you know?
What are the first five multiples of 6?
What is the rule for this pattern: 3, 6, 9, 12...?
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 patterns.
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. It's a perfect book for discussing factors and multiples.
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 6: Multiplication Strategies with Multi-Digit Numbers
Learning Targets
Students will use patterns and basic facts to multiply by multiples of 10, 100, and 1,000.
Students will estimate products using compatible numbers.
Students will use the Distributive Property of Multiplication to break apart problems.
Students will multiply a whole number of up to four digits by a one-digit number.
Students will multiply two two-digit numbers using the method of partial products.
Essential Questions
How can we use multiplication properties to help us solve problems?
How can an estimate help us check if an answer is reasonable?
How can we multiply multi-digit numbers?
Questions to Ask at Home
What is a good estimate for 31×48?
Can you solve 6×400? How do you know?
How can we use the Distributive Property to solve 12×7?
Can you show me how to solve 18×27 using the partial products method?
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. This helps reinforce the idea of breaking numbers into smaller parts.
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.
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 repeated multiplication in a creative way.
Unit 7: Division Strategies with Multi-Digit Dividends and 1-Digit Divisors
Learning Targets
Students will use patterns and basic facts to divide multiples of 10, 100, and 1,000.
Students will estimate quotients using compatible numbers.
Students will use the partial quotients method to divide two- and three-digit dividends by one-digit divisors.
Students will learn to interpret the meaning of a remainder in a division problem.
Essential Questions
How can an estimate help us check if an answer is reasonable?
How can we break down a large division problem into smaller, easier steps?
What does a remainder tell us about a problem?
Questions to Ask at Home
What is a good estimate for 5,000÷8?
Can you show me how to solve 72÷3 using the partial quotients method?
We have 50 cookies to put into bags, with 6 cookies in each bag. How many bags can we fill? How many cookies will be left over?
How can you tell if an answer is reasonable before you even do the math?
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.
A Remainder of One by Elinor J. Pinczes: A story about a soldier ant who is always left out when the troops are arranged in lines. It's a great book for talking about even and odd numbers and remainders in a simple context.
Divide and Ride by Stuart J. Murphy: Ten friends want to go on a ride, but it can only hold two people at a time. This book uses a fun story to illustrate simple division and the concept of equal groups.
Unit 8: Fraction Equivalence
Learning Targets
Students will identify and generate equivalent fractions by multiplying or dividing the numerator and denominator by the same number.
Students will use benchmark fractions like 1/2 and 1 to compare other fractions.
Students will use number lines to visualize and compare fractions.
Students will compare fractions with like and unlike numerators and denominators.
Essential Questions
How can we tell if two fractions are equivalent?
How can a benchmark fraction help us compare other fractions?
How does the size of the denominator affect the size of the fractional parts?
Questions to Ask at Home
Can you show me with a pizza that 1/2 is the same as 2/4?
Is 3/5 greater or less than 1/2? How do you know?
Which is bigger: 3/8 or 3/10? Why?
How can we show that 1/3 and 2/6 are the same using a piece of paper?
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.
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.
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, which can be extended to discuss how fractions are related to parts of a whole.
Unit 9: Addition and Subtraction Meanings and Strategies with Fractions
Learning Targets
Students will learn to compose fractions by adding parts together.
Students will learn to decompose fractions by breaking them into smaller parts.
Students will add and subtract fractions that have like denominators.
Students will use different visual models to add and subtract fractions.
Essential Questions
How can we add and subtract fractions?
What happens to the numerator and denominator when we add or subtract fractions?
How can a visual model help us understand fraction operations?
Questions to Ask at Home
If we have a pizza cut into 8 slices, and we eat 3 of them, what fraction of the pizza is left?
Can you show me with a drawing how to solve 2/5+1/5?
How can we decompose the fraction 4/6?
If we need to add fractions, why is it important that they have the same denominator?
The Multiplying Menace Divides by Pam Calvert: This sequel to a previous recommendation continues the adventure, but this time with a focus on division, showing how the two operations are related in a fun and exciting story.
Jump, Kangaroo, Jump! by Stuart J. Murphy: This book uses a fun tug-of-war game to introduce the concept of equal groups, which is a great lead-in to talking about how parts can be added and subtracted.
Go, Fractions! by Jennifer S. York: A fun book that uses simple language and illustrations to describe different types of fractions and what happens when they are combined.
Unit 10: Addition and Subtraction Strategies with Mixed Numbers
Learning Targets
Students will learn to decompose mixed numbers into whole-number and fractional parts.
Students will use a number line or fraction tiles to model the addition and subtraction of mixed numbers.
Students will add and subtract mixed numbers by combining the whole numbers and fractions separately.
Students will convert mixed numbers to equivalent fractions to add and subtract them.
Essential Questions
How can we represent a mixed number in different ways?
What are different strategies we can use to add and subtract mixed numbers?
How can a number line or drawing help us solve a problem with mixed numbers?
Questions to Ask at Home
Can you show me what the mixed number 2 1/2 looks like using these two-and-a-half cookies?
Let's say we have 1 1/4 pizzas and you bring over another 1 1/4 pizzas. How many pizzas do we have now?
Can you show me how to subtract 1 1/4 from 3 3/4 using a drawing?
What is the difference between a fraction and a mixed number?
The Hershey's Milk Chocolate Bar Fractions Book by Jerry Pallotta: This book uses a chocolate bar to show different fractions, including how they can be combined to make a whole and a fraction, which is a key concept for mixed numbers.
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, which can be extended to discuss how fractions are related to parts of a whole and mixed numbers.
The Doorbell Rang by Pat Hutchins: A great book for introducing the concepts of dividing items into equal shares, which can be extended to problems that result in mixed numbers.
Unit 11: Multiply Fractions by Whole Numbers
Learning Targets
Students will multiply a fraction by a whole number.
Students will use a number line to model the multiplication of a fraction by a whole number.
Students will multiply a mixed number by a whole number using decomposition.
Students will solve real-world problems that involve multiplying fractions and mixed numbers by whole numbers.
Essential Questions
How can we use a number line to show multiplication with fractions?
What happens when you multiply a whole number by a unit fraction?
How can we break apart a problem to make it easier to solve?
Questions to Ask at Home
We have 3 friends. If each of them eats 1/4 of a pizza, how much pizza did they eat in total?
Can you show me with a drawing how to solve 4×1/2?
How can you use decomposition to solve 2×3 1/2?
If you have 5 plates, and each has 1/3 of a sandwich, how many sandwiches are there in all?
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 can be extended to multiplying fractions by asking, "What if we have 3 times as much dough? How many full cakes can we make?"
Inchworm and a Half by Elinor J. Pinczes: An inchworm's measuring adventure gets more complex when it can't find the exact length of an object. The story introduces a half-inchworm and other fractional parts to solve the problem, which can be a great way to talk about multiplying fractions.
The Doorbell Rang by Pat Hutchins: A great book for introducing the concepts of dividing items into equal shares, which is a great lead-in to talking about multiplying fractions by thinking about how many total items you would need if you had a certain number of groups.
Unit 12: Decimal Fractions
Learning Targets
Students will represent tenths and hundredths as both fractions and decimals.
Students will understand that 10 hundredths is the same as 1 tenth.
Students will compare two decimals using number lines or visual models.
Students will add fractions with denominators of 10 and 100 by converting them to have the same denominator.
Essential Questions
How are fractions and decimals related?
How can we compare two decimals?
How can a grid or number line help us understand decimals?
Questions to Ask at Home
Can you tell me what the decimal point on the price tag at the grocery store means?
Which is a larger number, 0.5 or 0.45? How do you know?
If we have a dollar, how can we use fractions to show how much a dime is worth? How about a penny?
Can you show me with a drawing how to add 3/10 and 20/100?
Pieces of the Whole: A Whole-Brain Approach to Fractions and Decimals by Rebecca Klemm: This book uses a fun, visual approach to help children see the relationship between fractions and decimals.
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 can be extended to decimals by talking about what part of a whole is left.
The Cheerios Counting Book by Teddy Slater: While a counting book, it provides a great way to talk about groups of 10 and 100, which is the foundation for understanding tenths and hundredths.
Unit 13: Units of Measurement and Data
Learning Targets
Students will convert larger units of measure to smaller units in both the customary and metric systems.
Students will learn to convert units of time, such as hours to minutes and minutes to seconds.
Students will create and interpret line plots to display measurement data.
Students will solve word problems involving measurement conversions and data from line plots.
Essential Questions
How can we change a measurement from one unit to another?
What are the different systems we use for measurement?
How can a line plot help us organize and understand data?
Questions to Ask at Home
How many inches are in a foot? How many feet are in a yard?
If a recipe calls for 2 liters of milk, and we only have 500 milliliters, how many more milliliters do we need?
How many minutes are in 2 hours?
Let's look at the line plot. What does each 'X' represent?
How Big Is a Foot? by Rolf Myller: A fun story that highlights the importance of using a standard unit of measurement.
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.
Unit 14: Geometric Figures
Learning Targets
Students will identify and draw points, lines, line segments, rays, parallel lines, and perpendicular lines.
Students will learn to classify angles as right, acute, or obtuse.
Students will estimate and measure angles using a protractor.
Students will find a missing angle measure when given the measures of the other parts.
Students will classify polygons and triangles based on their sides and angles.
Students will recognize and draw a line of line symmetry for a two-dimensional figure.
Essential Questions
How can we describe and classify shapes based on their attributes?
How can a right angle help us measure other angles?
What makes a shape symmetrical?
Questions to Ask at Home
Can you find a right angle in the room? What about an acute or obtuse angle?
What are some shapes in our home that have line symmetry?
How are parallel lines different from perpendicular lines?
If a pizza is cut into 8 equal slices, what is the angle of each slice? (Hint: A full circle is 360°.)
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 the First Round Table by Cindy Neuschwander: In this story, King Arthur and his knights must solve a problem with the king's round table, which introduces concepts of shapes, angles, and geometry.
Mummy Math: An Adventure in Geometry by Cindy Neuschwander: In this adventure story, three kids use their knowledge of shapes and geometry to solve a mystery, which is a fun way to apply concepts in a new context.