Math

This page contains a description of each unit we will be studying throughout the year, as well as supplemental resources. The time spent on each unit varies.

The videos provided for each unit are for students and parents to support what is being taught in class!

Data & Graphing

How to plot coordinate pairs:

Analyzing line graphs:

Data and tables:

Focus of the Unit

In this unit, students will determine whether a survey question will yield categorical data, numerical data, or data over time. They will formulate a question that yields data over time (i.e. rainfall, plant growth, temperature, etc.) and collect the data. Students will also create and interpret a line graph of the data.

Strategies that Students Will Learn

In this unit, students will: (1) ask questions that will yield data that changes over time, (2) collect the data, (3) represent it using a line graph, and (4) answer questions about the data.

For example, when investigating the growth of a class plant, students may ask the question, “How tall will our class plant grow during the first 18 weeks?” They would then collect the data over time to create a graph, similar to the line graph shown on the left.

Ideas for Home Support

Identify opportunities to track data over time. Some opportunities might include recording the money in a savings account or changes in gas prices. Use a line graph to track the data and discuss changes that occur over time. Talk about patterns you notice and what can be learned from those patterns.

Standards:

Properties of Multiplication (whole numbers, with models)

Focus of the Unit

This unit on whole number multiplication and division builds on students’ work from fourth grade. Students are introduced to the traditional U.S. standard algorithm for multiplication. Students also extend their understanding of division to 2-digit numbers.

Strategies that Students Will Learn

In fifth grade, students use their previous understanding of multiplication and division strategies, and apply them to larger numbers. Below are some specific strategies that students use as they solve multiplication situations:

Multiplying using area model:

Multiplication (standard algorithm):

Volume

Focus of the Unit

This unit is based on the understanding that volume is a form of measurement. Students will learn that the unit of volume, such as a cube with side lengths of 1 inch, is called a unit cube. They will explore by building objects, such as rectangular prisms (like shoe boxes, tissue boxes, juice boxes, etc.), with layers of unit cubes to see how the volume is comprised. Students will use this experience to help them visualize and compare the volumes of rectangular prisms with different dimensions. Students will begin to reason about volume and understand that they can find the number of unit cubes in each layer by multiplying the length times the width of the rectangular prism. They also come to understand that the height of the prism is important, as it identifies how many layers of unit cubes will fit in the prism. After many opportunities to explore this idea, students can begin to utilize the formula, V=l x w x h (The volume of a rectangular prism is the same as the length times the width times the height).

Strategies that Students Will Learn

Students use their prior experiences with area to help them determine the area of the bottom layer of a rectangular prism then add the layers of unit cubes on top of that bottom layer. For example, students can find the volume of a 3 x 3 bottom layer and 4 additional layers on top of the bottom layer, by finding the area of the bottom layer (3 x 3) and then multiplying that by the 4 additional layers to find the total volume: (3 x 3) x 4. Students also learn that they can break apart a rectangular array into smaller sections to find the volume of the whole object (example one). Students will apply this same strategy with solids that are comprised of more than one rectangular prism (example two). See examples below:

Ideas for Home Support

Volume can be found in many places in our world. As you shop at the grocery store, notice items that are packaged and sold in boxes (non-standard units). Predict with your child how many objects might fit in a box. Another opportunity for discussing volume is to compare the space in different rooms in your home or at school. Ask questions such as, “Which room do you predict has the largest volume? Smallest volume?”

Volume provides a third dimension to measurement, and students can become confused about how it relates to objects and area. Consider providing opportunities for your child to build rectangular prisms with unit cubes (standard units), and describe how they know how many unit objects there are (the volume). Emphasize that the unit objects are arranged in rows and columns, not randomly.

Measuring volume with unit cubes:

Division of whole numbers (with models)

Focus of the Unit

This unit on whole number multiplication and division builds on students’ work from fourth grade.Students also extend their understanding of division to 2-digit numbers.

Strategies that Students Will Learn

Students use their understanding of multiplication and division to solve story problems about real-life situations. These story problems involve situations where the number of groups, number of objects in a group, or total amount are missing. It is important that students “act out” story problem situations, so they can clearly see what information is given and still needed.

In fifth grade, students use their previous understanding of division strategies, and apply them to larger numbers. Below are some specific strategies that students use as they solve division situations:

Dividing with area model:

Operations and Algebraic Thinking with Expressions

Focus of the Unit

This unit on operations and algebraic thinking builds on students’ work with addition, subtraction, multiplication, and division. This unit focuses on the use of expressions, which are series of numbers and symbols (+, -, x, ÷) without an equal sign. Students are expected to interpret numerical expressions without actually calculating them. See a sample example below:

Strategies that Students Will Learn

In fifth grade, students use their previous understanding of the properties listed above to help them explain the use of parentheses. There are different scenarios that students will see in regards to expressions:

Ideas for Home Support

An important component to this work in fifth grade is that students are reasoning about the expressions, without actually calculating them. Encourage your child to think about what they know about addition, subtraction, multiplication, and division and how that can help them determine the reasonableness of an answer. Can they interpret 3 x (18932 + 921) as being three times as large as 18932 + 921? Talk with your child about how that can help them with real life situations such as measuring and estimation.

Talk with your student about real-life situations where the order of operations is used. Here is an example from The Math Forum:

Suppose two classes are going on a field trip to the zoo. There are 28 people in one class and 22 people in the other class. The teachers want to order lunch for all of the students, and in each lunch, they want there to be 2 packages of crackers. How many packages of crackers should the teachers order? Well, here is where order of operations comes in: The teachers want to order 2 x (28+22) packages of graham crackers. If the teachers didn't use order of operations, then instead of ending up with 100 packages of graham crackers, the teachers would end up with 78 packages of graham crackers, and some of the kids would be very unhappy.

Numerical Expressions:

Order of Operations (PEMDAS) --- no exponents in 5th grade!:

Connecting Fractions & Division

Fractions AS DIVISION:

Multiplying & Dividing Fractions (with models)

Multiplying Fractions by Fractions:

Multiply a fraction by a mixed number:

Multiply a fraction by a whole number:

Divide a fraction by a whole number:

Divide a whole number by a fraction:

Dividing Fractions - all :

Multiplying Mixed numbers (model):

Focus of the Unit

This unit builds on the understanding that fractions are equal parts of a whole. Students will continue to develop fluency with adding and subtracting fractions while also learning to multiply and divide fractions. They will learn how to multiply a fraction or whole number by a fraction. They will also learn how to model and interpret a fraction as the division of the numerator by the denominator and interpret a fraction as an equal sharing context.

Strategies that Students Will Learn

In this unit, students will extend their work with multiplying fractions to solve situations involving fractions times fractions and fractions times mixed numbers. When multiplying fractions, students often expect the product (the answer) to be larger, like multiplication with whole numbers. It is very important for students to show these situations with drawings and other models to visualize what is actually happening in the problem. This visualization helps students make sense of the process to build understanding of the math in the problem.

In this unit, students also extend their understanding of division of whole numbers by unit fractions and division of unit fractions by whole numbers. Unit fractions are fractions with 1 as a numerator (½, ⅓, ¼, etc.). It is important that students continue to use models and drawings to justify their thinking and make sense of what the problem is asking. These models and drawings are especially important because there are different types of situations for dividing fractions, as shown below:

Ideas for Home Support

As students are making sense of fractions it is important that they have opportunities to talk about their reasoning. Encourage your child to talk about their thinking, explain the mathematics that supports their reasoning, and show their thinking with models and drawings. Thinking about fraction problems with real-life scenarios helps children visualize what is happening and understand what makes sense in relation to the problem.

The idea of “leftovers” from meals can be a great real-life example of fractional parts. Discuss how much is left of the whole and how much each person receives. Build on this work of division of fractions by discussing how much of the leftovers each person would have as well. Also, discuss predictions about the result of the problem:

-Will the size of the pieces be larger or smaller than the original pieces?

-If more people joined, will the pieces be larger or smaller?

When you see opportunities to use fractions in everyday life, have conversations about estimating how much is needed, whether or not you have enough, and how much more you might need.

Understanding Place Value in the Context of Metric Measurement

Focus of the Unit

This unit on place value builds on students’ work from previous grades. Students will reason about the magnitude of whole numbers and decimal numbers.

Strategies that Students Will Learn

Students will continue to learn how numbers compare and extend this understanding to decimal numbers. They will understand that the relationships between whole numbers also exist between decimal numbers. Specifically, a digit in one place represents 10 times as much as it represents in the place to its right, and 1/10 of what it represents in the place to its left. For example:

Ideas for Home Support

Be on the look-out for numbers that have the same digit in multiple places. You might see this in grocery store totals, gas totals, mileage, weight and other forms of measurement. Discuss with your child why the values of those digits are different, based on where they are placed in the number. Encourage your child to reason about how much larger or smaller the value of the digit is, based on its place.

Multiplying & Dividing by Powers of Ten

Metric Conversions using King Henry Doesn't Usually Drink Chocolate Milk

Adding & Subtracting Fractions (with models)

Adding Fractions with Unlike Denominators (model):

Adding Mixed Numbers with unlike denominators (model):

Subtracting Fractions with unlike denominators (model):

Subtracting mixed numbers with unlike denominators (model):

Subtracting Mixed Numbers Standard Algorithm:

Practice:

Focus of the Unit

This unit is based on the understanding that fractions are equal parts of a whole. Students will continue to develop fluency with addition and subtraction of fractions and explore making reasonable estimates as well. They will also learn to add and subtract fractions and mixed numbers with unlike denominators

Ideas for Home Support

As students are making sense of fractions, unlike denominators and using equivalence, it is important that they have opportunities to talk about their reasoning. Encourage your child to talk about their thinking and explain the mathematics that supports their reasoning.

A fraction number line (as shown above) is a great tool for visualizing fractional parts and equivalence. A measuring cup is a great example of the use of a fraction number line. While cooking, talk about how the measuring cup shows fractions, whole numbers, and equivalent measurements. Other tools that support this conversation at home are speedometers, rulers, and thermometers. Consider also looking for tools that have marks with no numbers and discuss how to use the information around the marks to determine their value.

When you see opportunities to use fractions in everyday life, have conversations about estimating how much is needed, whether or not you have enough, and how much more you might need. Also discuss how certain fractions are most familiar and become “landmark fractions” that help make estimate easier.

Adding and Subtracting Decimals

Adding Decimals (base ten blocks)

Adding decimals (standard algorithm --- LINE UP DECIMALS):

Adding & Subtracting Decimals (number line):

Subtracting Decimals (base ten blocks):

Subtracting Decimals (Standard algorithm) -- LINE UP THE DECIMALS!:

Focus of the Unit

This unit on addition and subtraction of decimals builds on the knowledge of addition and subtraction that students have used with whole numbers in all previous grades. Students also use their understanding of the place value system to help them add and subtract with decimals.

Strategies that Students Will Learn

Students will learn that adding and subtracting decimals is very much like adding and subtracting whole numbers. When adding and subtracting whole numbers, it is often helpful to represent the number in expanded form and then add similar values together. See example:

Ideas for Home Support

We see decimals on a daily basis and we add and subtract them regularly. As you spend time with your child, notice decimals in your daily interactions and point them out. Decimals are used in reference to things that are less than 1 (0.5 cup) or in reference to something that is in between two whole things (13.1 miles). Counting money is also a great way to reinforce the idea of breaking apart a quantity to create a new quantity, such as Student #1’s response. Consider having a change jar that you and your child can count regularly to reinforce this idea.

Multiplying & Dividing Decimals (with models)

Focus of the Unit

This unit on multiplication and division of decimals builds on students’ learning in previous grade levels. Students will apply their prior knowledge of multiplication of whole numbers to make connections to multiplication and division of decimals.

Strategies that Students Will Learn

In fifth grade, students use their previous understanding of multiplication and division strategies and apply them to decimals. Below are some specific strategies and representations that students use as they solve multiplication and division situations:

Ideas for Home Support

As a family, point out experiences when decimals are involved with your everyday life. These experiences might include totaling the grocery bill, doubling or halving a recipe, calculating the bill at a restaurant, determining mileage for a trip, buying gas for your vehicle, and many others. This helps children see and apply multiplication and division with decimals in a real-life context. Discuss mental strategies and estimations before solving to discover how your child is making sense of the mathematical context. When solving, prompt your child to show their thinking with models, as shown above, to remind him/her of the value of each number in the situation and the relationships between the numbers.

Multiplying a decimal by a decimal (model):

Multiplying a decimal by a whole number (number line):

Multiplying decimals (standard algorithm):

Dividing a whole number by a decimal (base ten blocks):

Dividing decimal by whole number (model):

Dividing a decimal by a decimal (number line):

Decimal divided by decimal (model):

Classifying Quadrilaterals

Focus of the Unit

This unit focuses on using the properties of quadrilaterals to sort them into categories and subcategories. Students also classify quadrilaterals in a hierarchy, based on their properties.

In fifth grade, students use their previous understanding of classifying shapes and continue their work with quadrilaterals. Students describe and compare the attributes of shapes and understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

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