Fifth Grade Overview
Overview
In fifth grade your children will focus in 3 critical areas:
Critical Area 1
Your child will develop computational fluency with fractions. Students will apply their understanding of fractions and fraction models in order to represent addition and subtraction of fractions with unlike denominators as equivalent calculations. Your child will use the meaning of fractions and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense.
Critical Area 2
Your child with further develop operations with decimals to hundredths and integrating decimal fractions to the place value system. Students will develop understanding of division procedures and properties of operations. They will finalize fluency with multidigit addition, subtraction, multiplication, and division. Your child will apply understandings of decimals, decimal notation, and properties of operations to add and subtract decimals to the hundredths. They will also use the relationships between decimals and fractions, as well as the relationship between finite (nonrepeating) decimals and whole numbers to explain why the procedures for multiplying and dividing decimals make sense. They will also accurately and efficiently compute decimals to the hundredths.

Critical Area 3
Your child will develop an understanding of volume. Students will recognize that volume is an attribute of a 3dimensional space. They will understand that volume can be measure by finding the total number of samesized units required to fill the space without gaps or overlaps. They understand that a 1x1x1 cube is a standard for measuring volume. Your child will select appropriate units, strategies, and tools for solving problems that involve measuring volume. They will decompose 3dimensional shapes and find volumes of rectangular prisms as layers of arrays of cubes. They will measure necessary attributes of shapes in order to determine the volumes of real world and mathematical problems.
Unit 1
Fifth Grade Mathematics
Unit 1
Geometry
Printable Parent Letter
During Unit 1, students learn to analyze and relate categories of twodimensional shapes explicitly based on their properties. Based on analysis of properties, they classify twodimensional figures in hierarchies. For example, they conclude that all rectangles are parallelograms, because they are all quadrilaterals with two pairs of opposite, parallel, equallength sides. In this way, they relate certain categories of shapes as subclasses of other categories. 
Students Need To
 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).
 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
 Understand that attributes belonging to a category of twodimensional 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.
 Classify twodimensional figures in a hierarchy based on properties.
Ways Parents Can Help
 Help your child solve realworld problems by creating and analyzing a graph. For example, Sara has saved $20. She earns $8 for each hour she works. If Sara saves all of her money, how much will she have after working 3 hours? 5 hours? 10 hours?
 Create a graph that shows the relationship between the hours Sara worked and the amount of money she has saved. What other information do you know from analyzing the graph?
Key Vocabulary
Support Sites
Math Open Reference  coordinate planes
Unit 2
Fifth Grade Mathematics
Unit 2
Place Value and Decimal Computation
Printable Parent Letter
During Unit 2, your child will extend their understanding of the baseten system to the relationship between adjacent places, how numbers compare, and how numbers round for decimals to thousandths. 
Students Need To
 Recognize that in a multidigit number, 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.
 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10.
 Read, write, and compare decimals to thousandths.
 Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
 Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
 Use place value understanding to round decimals to any place.
 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
 Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep real world problems.
 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Ways Parents Can Help


Key Vocabulary
Unit 3
Fifth Grade Mathematics
Unit 3
Whole Number Multiplication and Volume
Printable Parent Letter
During Unit 3, your children will recognize volume as an attribute of threedimensional space. They will understand that volume can be measured by finding the total number of samesize units of volume required to fill the space without gaps or overlaps. They will understand that a 1unit by 1unit by 1unit cube is the standard unit for measuring volume. Your children will select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They will decompose threedimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. Your children will measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems. 
Students Need To
 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
 A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
 A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
 Multiply multidigit whole numbers using the standard algorithm.
 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
 Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication.
 Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems.
 Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.
Ways Parents Can Help

Explore volume by finding the volume of boxes you have in your home. Measure the box to find the length, height and width. Use multiplication to find the volume.

If you have cubes at your home, use them to build a variety of rectangular prisms with the same volume. For example with 12 cubes you could make a 2 x 3 x 2 rectangular prism or a 1 x 6 x 2 rectangular prism.

Connect the area model of multiplication to the standard algorithm
Key Vocabulary
Unit 4
Fifth Grade Mathematics
Unit 4
Whole Number Division
Printable Parent Letter
During Unit 4, your child will develop the following understandings for division:

Students Need To
 Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep real world problems.
Key Vocabulary
Unit 5
Fifth Grade Mathematics
Unit 5
Addition and Subtraction of Fractions
Printable Parent Letter
During Unit 5, your children will apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They will develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. 
Students Need To
 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
 Make a line plot to display a data set of measurements in fractions of a unit (12, 14, 18). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Ways Parents Can Help
 The website listed to the right is the national library of virtual manipulatives. This site will provide your child with practice adding fractions with like and unlike denominators by taking them through steps that include using fraction manipulatves while they solve the problem.
 When cooking includes using fractional measurements have your child figure out total amounts added into the recipe. For example, ½ cup sugar and ¾ cup flour would total 5/4 or 1 ¼ cups.
 Create real world problems involving food that is already partitioned into equal pieces (e.g. pizza, a cake, Hershey’s chocolate bar). An example of a problem might be: I ate ¼ of the pizza and you ate 3/8 of the pizza. How much did we eat together and how much of the pizza is left? ¼ = 2/8 2/8 + 3/8 = 5/8 8/8 – 5/8 = 3/8
Key Vocabulary
Support Videos and Sites
Adding Fractions with Unlike Denominators
Some Support Sites
National Library of Virtual Manipulatives
Unit 6
Fifth Grade Mathematics
Unit 6
Multiplying and Dividing Fractions
Printable Parent Letter
During Unit 6, your child will use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.) 
Students Need To
 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
 Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
 Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
 Interpret multiplication as scaling (resizing), by:
 Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
 Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
 Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
 Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5)= 4.
 Make a line plot to display a data set of measurements in fractions of a unit (12, 14, 18). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Ways Parents Can Help
Help your child to make real world problem connections with multiplication and division of fractions when they come up in your home.
For example:
 cutting a recipe in half would be the same as multiplying each ingredient amount by ½ ( ½ of ¼ cup would be ½ X ¼ = 1/8 cup) or by dividing it by 2 ( ¼ cup divided by 2 would be ¼ ÷ 2 = 1/8 cup)
 doubling a recipe would be the same as multiplying each ingredient by 2 ( ¼ cup doubled is ¼ X 2 = 2/4 cup).
Key Vocabulary
Key Vocabulary to Know  
Unit Fraction Numerator Denominator Mixed number Multiple Factor Product Expression Equation Benchmark fractions 
The reflexive property of equality a=a The identity property (multiplicative identity) 1 x a = a If the product of two numbers is one, the numbers are multiplicative inverses. Since 6 x 1/6 = 1 (the multiplicative identity), the multiplicative inverse of 6 is 1/6. (Zero does not have a multiplicative inverse, since no matter what you multiply it by, the answer is always 0, not 1.) 
Video Support
Unit 7
Fifth Grade Mathematics
Unit 7
Multiplying and Dividing Decimals
Printable Parent Letter
During Unit 7, your child will use the same place value understanding for adding and subtracting decimals that they used for adding and subtracting whole numbers. Similarly, they will learn that the general methods used for computing products and quotients of whole numbers extend to computing the products and quotients of decimals, with the additional issue of placing the decimal point. 
Students Need To
 Multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between repeated addition and subtraction; relate the strategy to a written method and explain the reasoning used.
 Multiply tenths by tenths or tenths by hundredths
 Divide in problems involving tenths and hundredths
Ways Parents Can Help
This is a skill that will be used heavily in secondary mathematics. It is important for students to have an understanding of the concept and have the ability to visualize the algorithm of “shifting decimals.” Look for opportunities for students to visually represent problems to prove computational accuracy.
Key Vocabulary
Unit 8
Fifth Grade Mathematics
Unit 8
Algebraic Thinking and Coordinate Planes
Printable Parent Letter
During Unit 8, students will learn to write expressions to express a calculation, e.g., writing 2 x (8+7) to express the calculation “add 8 and 7, then multiply by 2.” They will also evaluate and interpret expressions, e.g., using their conceptual understanding of multiplication to interpret 3 x (18932 + 921) as being three times as large as 18932+ 921, without having to calculate the indicated sum or product. Students will extend their Grade 4 pattern work by working briefly with two numerical patterns that can be related and examining these relationships within sequences of ordered pairs and in the graphs in the first quadrant of the coordinate plane. Students will also extend their knowledge of the coordinate plane. They will connect ordered pairs of (whole number) coordinates to points on the grid, so that these coordinate pairs constitute numerical objects and ultimately can be operated upon as single mathematical entities. Students will solve mathematical and realworld problems using coordinates. 
Students Need To
 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).
 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
Ways Parents Can Help
Help your child solve realworld problems by creating and analyzing a graph. For example, Sara has saved $20. She earns $8 for each hour she works. If Sara saves all of her money, how much will she have after working 3 hours? 5 hours? 10 hours? Create a graph that shows the relationship between the hours Sara worked and the amount of money she has saved. What other information do you know from analyzing the graph?
Key Vocabulary
Unit 9
Fifth Grade Mathematics
Unit 9
Fluently Divide Whole Numbers and Apply Knowledge of Concepts
Students Need To
Students Need To:
 Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 Fluently divide multidigit numbers using the standard algorithm
 Apply all fifth grade concepts in order to complete math tasks