Fifth Grade Overview

• 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., x-axis and x-coordinate, y-axis and y-coordinate).
   
• 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 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.
   
• Classify two-dimensional figures in a hierarchy based on properties.

• Help your child solve real-world 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?

Math Open Reference - coordinate planes

Geometry Terms

• Recognize that in a multi-digit 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 whole-number exponents to denote powers of 10.
• Read, write, and compare decimals to thousandths.
  • Read and write decimals to thousandths using base-ten 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 different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real world problems.
• Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

• 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 multi-digit 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 whole-number 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 whole-number 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 whole-number edge lengths in the context of solving real world and mathematical problems.
  • Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

• 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

• Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit 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 different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real world problems.

• 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.

• 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

Adding Fractions with Unlike Denominators

Some Support Sites

National Library of Virtual Manipulatives

• 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 non-zero 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.

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).

Carroll County Public Schools Video Support

Dividing a Fraction by a Whole Number

Multiplying Fractions Using an Area Model

Using Number Lines to Multiply Fractions

• 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

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.

• 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., x-axis and x-coordinate, y-axis and y-coordinate).
• 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.

Help your child solve real-world 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?

Students Need To:

• Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit 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 multi-digit numbers using the standard algorithm
   
• Apply all fifth grade concepts in order to complete math tasks