OVERVIEW
In the fifth grade, we will build on our math foundation by deepening our understanding of place value, extending it to decimals up to the thousandths place. We will learn to fluently add, subtract, multiply, and divide whole numbers and decimals, using a variety of strategies like area models and the standard algorithm. The world of fractions will open up as we learn to add, subtract, multiply, and divide them, including mixed numbers. We'll explore volume in three-dimensional shapes and use line plots to analyze data. Finally, we'll begin our journey into algebraic thinking by learning the order of operations and exploring patterns, which will prepare us for future math studies.
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 person 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 students 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 us see math as a part of our everyday lives.
Unit 2: Volume
Learning Targets
Students will find the volume of a rectangular prism by counting unit cubes.
Students will apply volume formulas (V=l×w×h and V=B×h) to find the volume of rectangular prisms.
Students will find the volume of a composite solid figure by breaking it into smaller rectangular prisms and adding their volumes.
Students will solve real-world problems involving volume, including finding a missing dimension.
Essential Questions
What is volume and how is it measured?
How can we find the volume of a rectangular prism?
How can a shape's base help us calculate its volume?
How can we find the volume of a complex shape?
Questions to Ask at Home
How can we figure out the volume of a shoebox? What unit of measurement would we use?
Can you show me the base of this rectangular container?
If a toy box is 2 feet long, 1 foot wide, and 3 feet tall, what is its volume?
How are volume and area different?
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.
Sir Cumference and the Off-the-Charts Dessert by Cindy Neuschwander: This book focuses on interpreting data on graphs, but it can be used as a springboard to discuss volume by talking about how much dessert can fit into a container.
A House for Hermit Crab by Eric Carle: In this story, a hermit crab outgrows its shell and must find a new one. You can use this story to talk about how much space (volume) the hermit crab needs.
Unit 3: Place Value and Number Relationships
Learning Targets
Students will generalize the concept of place value, understanding that a digit in one place is 10 times the value of the same digit in the place to its right.
Students will read and write decimals to the thousandths place in standard form, expanded form, and word form.
Students will compare decimals to the thousandths place.
Students will round decimals to any given place value.
Essential Questions
How are the places in a number, including decimals, related to each other?
How can we read and write decimals in different ways?
How can we compare two decimal numbers?
Questions to Ask at Home
Can you read the number 2.345? What is the value of each digit?
How would you write the price of an item that is "three dollars and twenty-five cents" as a decimal?
Which is a larger number, 0.45 or 0.425? How do you know?
If you round 8.76 to the nearest tenth, what number do you get? Why?
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.
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.
The Phantom Tollbooth by Norton Juster: This classic story includes characters like the Mathemagician, who can bring up interesting conversations about numbers and their properties in a fun, non-traditional way.
Unit 4: Add and Subtract Decimals
Learning Targets
Students will estimate the sum and difference of decimals by rounding.
Students will add decimals using different methods, including decomposing numbers and using place value.
Students will subtract decimals using different methods, such as decomposing the number being subtracted.
Students will understand that the strategies for adding and subtracting whole numbers can be applied to decimals.
Essential Questions
How are adding and subtracting decimals similar to adding and subtracting whole numbers?
How can estimation help us check our work with decimals?
What are different strategies for adding and subtracting decimals?
Questions to Ask at Home
If we buy an item that costs $2.50 and another that costs $1.75, about how much will we spend?
Can you show me how to solve 1.25+0.50 using place value?
If we have $10.00 and we spend $4.25, how much money do we have left?
Why is it important to line up the decimal points when adding or subtracting?
The Hershey's Milk Chocolate Bar Fractions Book by Jerry Pallotta: This book uses a chocolate bar to show different fractions, which can be extended to decimals by talking about how a tenth of the bar is also 0.1.
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 decimals.
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.
Unit 5: Multiply Multi-Digit Whole Numbers
Learning Targets
Students will multiply by powers of 10 using the relationship between the base and the exponent.
Students will estimate products to check for reasonable answers.
Students will multiply multi-digit numbers using area models and partial products.
Students will learn to multiply whole numbers using a standard algorithm.
Essential Questions
What are some strategies for multiplying multi-digit numbers?
How can area models help us understand multiplication?
How are partial products used in multiplication?
Questions to Ask at Home
What is a quick way to solve 1,000×16?
Can you show me how to solve 15×24 using an area model?
What is a good estimate for 58×32?
How are partial products used in the multiplication algorithm?
The Best of Times: Math Strategies That Multiply by Greg Tang: This book presents clever rhymes and visual tricks to help students master multiplication facts and see how they are connected to each other.
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.
Anno's Mysterious Multiplying Jar by Mitsumasa Anno: This beautifully illustrated book takes students on a journey through a multiplying jar, subtly introducing the concept of repeated multiplication in a creative way.
Unit 6: Multiply Decimals
Learning Targets
Students will use patterns to multiply decimals by powers of 10.
Students will estimate the product of two decimals to check if their answer is reasonable.
Students will make a generalization about the relationship between the decimal factors and their product.
Students will learn to multiply decimals using the partial products method.
Essential Questions
How can a pattern help us multiply decimals by powers of 10?
How can estimation help us place the decimal point in our answer?
How does the number of digits after the decimal point in the factors relate to the number of digits in the product?
Questions to Ask at Home
What is a good estimate for 5.2×3.8?
Can you solve 0.7×100? How did you know the answer so fast?
If we're buying 5 items that each cost $2.50, about how much will the total be?
What is the relationship between the products of 12×4 and 1.2×0.4?
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, which is key to understanding why decimal multiplication works.
The Go-Around Dollar by Barbara Johnston Adams: This book follows a dollar bill as it is used and reused, showing how money circulates. This provides a great context for multiplying decimals by whole numbers, for example, "If 4 people each have $2.50, how much money do they have in all?"
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, a key skill for making generalizations in this unit.
Unit 7: Divide Whole Numbers
Learning Targets
Students will use compatible numbers to estimate a quotient.
Students will divide multi-digit whole numbers by a two-digit whole number using the partial quotients algorithm.
Students will relate multiplication and division.
Students will learn to interpret the meaning of a remainder in a division problem.
Essential Questions
How can we divide large numbers?
How can estimation help us check if an answer is reasonable?
What does a remainder tell us about a problem?
Questions to Ask at Home
What is a good estimate for 1,250÷25?
Can you show me how to solve 185÷15 using the partial quotients method?
We have 500 cookies to put into bags, with 24 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?
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.
The Doorbell Rang by Pat Hutchins: A classic for a reason! It's a great book for introducing the concepts of dividing items into equal shares, which is a key concept in division.
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: Divide Decimals
Learning Targets
Students will use equivalent representations to divide a decimal by a whole number.
Students will learn to divide a whole number by a decimal using powers of 10.
Students will divide a decimal by a decimal using powers of 10.
Students will use compatible numbers to estimate a quotient with decimals.
Essential Questions
What are some strategies for dividing with decimals?
How can a power of 10 help us make a division problem easier to solve?
How are dividing whole numbers and dividing decimals related?
Questions to Ask at Home
If a bag of oranges costs $2.50, and each orange costs $0.50, how many oranges can we buy?
Can you show me how to solve 1.2÷0.2 with a drawing?
What is a good estimate for 15÷0.3?
How can you tell if an answer is reasonable before you even do the math?
The Doorbell Rang by Pat Hutchins: A classic for a reason! It's a great book for introducing the concepts of dividing items into equal shares, which is a key concept in division. You can extend the problems to decimals by asking, "If you have a pie that weighs 1.5 pounds and you want to divide it equally, how much does each person get?"
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. This can be a great way to talk about the relationship between fractions and decimals and why dividing by a decimal can result in a larger number.
The Great Graph Gimmick by Lynne W. Taggart: A fun story that shows how to use a simple graph to organize information. You can use it to create division problems with decimals, for example, "If each student drinks 0.5 liters of water, how many students are needed to drink 4 liters of water?"
Unit 9: Add and Subtract Fractions
Learning Targets
Students will estimate sums and differences of fractions using benchmarks like 0, 1/2, and 1.
Students will add fractions and mixed numbers with unlike denominators by finding a common denominator.
Students will learn to regroup a mixed number when subtracting, such as 4 1/4= 3 5/4.
Students will subtract fractions and mixed numbers with unlike denominators by finding a common denominator and regrouping when necessary.
Essential Questions
How can we add and subtract fractions that have different denominators?
How can a benchmark help us check our work?
How can we regroup with fractions and mixed numbers?
Questions to Ask at Home
Is the sum of 3/4 and 1/3 greater or less than 1? How do you know?
Can you show me how to solve 1/2+31/3?
If a recipe calls for 2 1/2 cups of flour, and you have 1 3/4 cups, how much more do you need?
What does it mean to regroup when subtracting mixed numbers?
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 that shows how to combine and separate fractional parts of a whole, which is a great way to talk about adding and subtracting fractions.
The Wishing Club: A Story About Fractions by Donna Jo Napoli: Four kids make wishes on a star, but only a fraction of each wish comes true. This book uses a relatable scenario to explain concepts like one-half, one-third, and one-quarter.
Unit 10: Multiply Fractions
Learning Targets
Students will multiply a fraction by a fraction by multiplying the numerators and denominators.
Students will multiply a mixed number by a whole number or another mixed number by converting it into a fraction greater than 1.
Students will predict whether a product will be greater than or less than one of its factors.
Essential Questions
How can we multiply fractions?
How can a mixed number be converted to a fraction?
How does the value of the factors affect the size of the product?
Questions to Ask at Home
We have a recipe that calls for 1/2 cup of sugar, but we want to make 1/2 of the recipe. How much sugar do we need?
Can you show me how to multiply 2/3 by 1/4?
If a piece of wood is 2 1/2 feet long, and we need 3 pieces that long, how much wood do we need in all?
Why is the product of 10× 1/2 less than 10?
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.
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.
Unit 11: Divide Fractions
Learning Targets
Students will learn to interpret a quotient with a remainder as a mixed number.
Students will learn to divide a whole number by a unit fraction and a unit fraction by a whole number.
Students will solve word problems involving the division of fractions.
Essential Questions
How are multiplication and division related with fractions?
What does a fractional quotient represent?
What does it mean to divide by a fraction?
Questions to Ask at Home
If we have 3 pounds of flour, and we need to use 1/2 pound for each cake, how many cakes can we make?
Can you show me with a drawing how to solve 1/4÷2?
If a pizza is cut into 8 equal slices, and we eat 3 of them, what fraction of the pizza is left?
If we have a ribbon that is 5 feet long, and we need to cut it into pieces that are 1/3 of a foot long, how many pieces can we get?
The Doorbell Rang by Pat Hutchins: A classic for a reason! It's a great book for introducing the concepts of dividing items into equal shares, which is a key concept in division. You can extend the problems to fractions by asking, "If you have a pie that weighs 1.5 pounds and you want to divide it equally, how much does each person get?"
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.
The Great Graph Gimmick by Lynne W. Taggart: A fun story that shows how to use a simple graph to organize information. You can use it to create division problems with decimals, for example, "If each student drinks 0.5 liters of water, how many students are needed to drink 4 liters of water?"
Unit 12: Measurement and Data
Learning Targets
Students will convert between larger and smaller units within the customary and metric systems.
Students will learn when to multiply and when to divide when converting units.
Students will create and interpret a line plot to display measurement data.
Students will solve problems using the data presented on a line plot.
Essential Questions
How are the customary units of measurement related to each other?
How are the metric units of measurement related to each other?
How can a line plot help us organize and solve problems with data?
Questions to Ask at Home
If a recipe calls for 1 cup of milk, and we need to double it, how many quarts of milk do we need?
How many millimeters are in a centimeter?
If a person is 5 feet tall, how many inches is that?
Can you show me how a line plot works using the different lengths of pencils we have in the house?
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 13: Geometry
Learning Targets
Students will learn about the x-axis and y-axis and the origin of a coordinate plane.
Students will plot ordered pairs on a coordinate plane and interpret the location of points.
Students will classify triangles as equilateral, isosceles, or scalene based on their side lengths.
Students will classify quadrilaterals, including parallelograms, rectangles, rhombuses, and squares, based on their properties.
Essential Questions
How can the coordinate plane help us describe locations?
How can we use the properties of a shape to classify it?
What are the relationships between different types of quadrilaterals?
Questions to Ask at Home
Can you find an isosceles triangle in our house? What about a scalene triangle?
How can we use the coordinate plane to give someone directions from one place to another?
Why is a square always a rectangle, but a rectangle is not always a square?
What are the differences between a parallelogram and a rhombus?
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.
Unit 14: Algebraic Thinking
Learning Targets
Students will write, interpret, and evaluate numerical expressions using the order of operations.
Students will learn to generate a numerical pattern using a rule.
Students will identify corresponding terms in two numerical patterns.
Students will create ordered pairs from two numerical patterns and plot them on a coordinate plane.
Essential Questions
Why is the order of operations important?
How can a rule help us generate a pattern?
What is the relationship between two numerical patterns?
Questions to Ask at Home
Can you solve 2+3×4? Why did you multiply first?
What is the rule for this pattern: 10, 15, 20, 25...?
Let's say one pattern starts at 0 and adds 2, and another starts at 0 and adds 6. What is the relationship between the corresponding terms?
How can a graph help us see a pattern?
One Grain of Rice: A Mathematical Folktale by Demi: This beautiful book tells a classic story of doubling, which is a powerful way to introduce the concept of patterns and exponential growth.
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, which is a key skill for algebraic thinking.
The Phantom Tollbooth by Norton Juster: This classic story includes characters like the Mathemagician, who can bring up interesting conversations about numbers, rules, and logic in a fun, non-traditional way.