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Acquisition of Vocabulary

for Grade 5

5th Number Sense 5th Measurement5th Geometry5th Patterns, Functions, Algebra5th Data and Probability

 
Number, Number Sense, and Operations
Number and Number Systems
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

  1.  Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.

 

Ratios show the relationship of one group to another.

 

Part to part:  Of the shapes above, you could say there are 3 red squares to every 7 blue circles.

 

Part to whole:  Of the shapes above, you could also say that 3 out of 10 shapes are red squares.

    Example:

Part to whole as percent:  Since 3 out of 10 shapes are red squares, you could state that 30% of the shapes are red squares.

    Example:

Number, Number Sense, and Operations
Number and Number Systems
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

  2.  Use various forms of “one” to demonstrate the equivalence of fractions.

 

One can be shown as fractions:
    Example:

        

Remember, any number multiplied by 1 is still that number.

    Example:

 

The same is true for numbers that are fractions.   

    Example:

Remember, any number divided by 1 is still that number.

    Example:

The same is true for numbers that are fractions.

    Example:

  

Why is it important?

Understanding this helps us find common denominators when we add or subtract fractions.

    Example:

 

Understanding this also helps us reduce fractions to lowest terms.

 

Number, Number Sense, and Operations
Number and Number Systems
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

3.  Identify and generate equivalent forms of fractions, decimals and percents.

 

Percent means "out of 100." We use the percent symbol (%) to express percent. Percents are used everywhere in real life, so you'll need to understand them well. Here are some examples of ways to write the same thing:
 

Fraction Decimal Percent
1/4 = 25/100 .25 25%
3/5= 60/100 .60 60%
4/10=40/100 .40 40%
1/3 (1 divided by 3) .33.. 33.3..%
2/3 (2 divided by 3) .66.. 66.6..%
3/8 (3 divided by 8) .375 37.5%

 

 

Number, Number Sense, and Operations
Number and Number Systems
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

  4.  Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half.

 

Decimal Place Value
First, pay attention to the place value of digits in decimal numbers.
Here's some practice:

To round decimals

  1. Underline the place value you are rounding to (the "rounding digit") and look at the digit just to the right of it.
  2. If that digit is less than 5, do not change the rounding digit. Write all the digits to the right of it as zeros. For example:

    Round 41.263 to the nearest hundredth.

        41.263  (3 is less than 5)
        41.260    
     

  3. If that digit is greater than or equal to five, add one to the rounding digit. Write all digits to the right of it as zeros. For example:

Round 41.267 to the nearest hundredth.

    41.267  (7 is more than 5)
    41.270

 

To round fractions

  1. When rounding fractions to the nearest half, it helps to picture the number on a number line or ruler.

 

Number, Number Sense, and Operations
Number and Number Systems
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

  5.  Recognize and identify perfect squares and their roots.

 

Squaring a number means taking a number times itself, such as 5 x 5:

52 = 5 x 5 = 25

Finding the square root of a number is the opposite (inverse operation) of squaring a number.

25 = 5

The array representing a number squared would be square, for example:

5 x 5

x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
Number, Number Sense, and Operations
Number and Number Systems
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

  6.  Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money.

Negative numbers are numbers that are less than 0.

We use negative numbers to show when the temperature goes below 0 on a thermometer.

We use negative numbers to show that we owe money, like when you don't have any money in your wallet and you have to borrow lunch money for $2.00, you might say you have -$2.00 (you owe more than you have!).

We even use negative numbers on game shows like Jeopardy, such as when a contestant has 0 points and misses a question, they then have -200 points.

Number, Number Sense, and Operations
Number and Number Systems
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

  7.  Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations.

 

Commutative Property - An operation is commutative if you can change the order of the numbers involved without changing the result. Addition and multiplication are both commutative. Examples:

Addition: 2 + 1 = 1 + 2

Multiplication: 5 × 9 = 9 × 5

NOTE: Subtraction and division are not commutative. Examples:
4 - 3 is not equal to 3 - 4
6 ÷ 2 is not equal to 2 ÷ 6



Associative property - An operation is associative if you can group numbers in any way without changing the answer. It doesn't matter how you combine them, the answer will always be the same. Addition and multiplication are both associative.

Addition: (3 + 2) + 1 = 3 + (2 + 1)

Multiplication: (4 × 5) × 9 = 4 × (5 × 9)

NOTE: Subtraction and division are not associative:
(4 - 3) - 2 is not equal to 4 - (3 - 2)
(12 ÷ 2) ÷ 3 is not equal to 12 ÷ (2 ÷ 3)



Distributive Property - When you distribute something, you give pieces of it to many different people. The most common distributive property is the distribution of multiplication over addition. It says that when a number is multiplied by the sum of two other numbers, the first number can be handed out or distributed to the other two numbers and multiplied by each of them separately.

3 × (2 + 1) = (3 × 2) + (3 × 1)

 
Number, Number Sense, and Operations
Meaning of Operations
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

  8.  Identify and use relationships between operations to solve problems.

 

There is an inverse (opposite) relationship between addition and subtraction.

Example:

3 + 7 = 10.

  • 10 - 3 = 7

  • 10 - 7 = 3

The same relationship exists for subtraction.

Example:

10 - 3 = 7

  • 3 + 7 = 10
  • 7 + 3 = 10

Why is it important?
It's important because we can use this to solve problems.

Example:
? + 7 = 15 

(Work backwards and use the inverse operation!)

15 - 7 = 8
       ? = 8

The same thing is true for multiplication and division.

Number, Number Sense, and Operations
Meaning of Operations
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

  9.  Use order of operations, including use of parentheses, to simplify numerical expressions.

 

Using Order of Operations

Incorrect

Correct


 2 + 5 x 3 - 22 =
 7 x 3 - 22 =
 21 - 22 =
 21 - 4 = 17

This student solved the problem incorrectly by going left to right.


 2 + 5 x 3 - 22 =
 2 + 5 x 3 - 4  =
 2 + 15 - 4 =
 17 - 4 = 13

This student solved correctly by applying order of operations:

Parentheses
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)

A popular method for remembering Order of Operations is by thinking about this mnemonic:

Please
Excuse
My Dear
Aunt Sally

Number, Number Sense, and Operations
Meaning of Operations
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

 10. Justify why fractions need common denominators to be added or subtracted.

If you have two apples and four oranges, your total is six pieces of fruit -- not six apples, and not six oranges. You had to use the term fruit, that they both have in common.

Before adding or subtracting fractions, you have to have denominators that are the same. You can't add 1/4 and 1/2 because the sections are not the same size.


 

Number, Number Sense, and Operations
Meaning of Operations
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

11.  Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths.

 

 

Adding Decimals

Line them up!

        

Subtracting Decimals

Line them up!

       

Multiplying Decimals

In your answer, put your decimal to the left by however many decimal places there were in your multipliers.

Dividing Decimals

Always divide by a whole number. However many places you move the decimal to the right in your divisor, you must move that many places to the right in the dividend!

 

 

 

Number, Number Sense, and Operations
Computation and Estimation
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

12.  Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals.

 

 
Number, Number Sense, and Operations
Meaning of Operations
5th Grade
Ohio Indicator
Explanation ....  Websites for Students

13.  Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.

 

 
 
Measurement
Measurement Units
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Identify and select appropriate units to measure angles; i.e., degrees.

 
Measurement
Measurement Units
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length.

 
 

1. Coordinates
2.
Grid with four quadrants

Measurement
Measurement Units
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects.

 
 
Measurement
Measurement Units
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Demonstrate understanding of the differences among linear units, square units and cubic units.

 

 
Measurement
Use Measurement Techniques and Tools
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Make conversions within the same measurement system while performing computations.

First, practice what you know about measuring.

 

Measurement
Use Measurement Techniques and Tools
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms.

 

Measurement
Use Measurement Techniques and Tools
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Use benchmark angles (e.g.; 45º, 90º, 120º) to estimate the measure of angles, and use a tool to measure and draw angles.

 

 

1. Angles are a measure of turn
2.
Types of angles
3.
Adding up angles
4.
Using a protractor
5.
Perpendicular and parallel lines

 
Geometry and Spatial Sense
Characteristics and Properties          [Study Guide]
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of Pi.

Geometry and Spatial Sense
Characteristics and Properties
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular.

 
Geometry and Spatial Sense
Characteristics and Properties
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Label vertex, rays, interior and exterior for an angle.

 
Geometry and Spatial Sense
Characteristics and Properties
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Describe and use properties of congruent figures to solve problems.

 
Geometry and Spatial Sense
Characteristics and Properties
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Use physical models to determine the sum of the interior angles of triangles and quadrilaterals.

The sum of the interior angles of a triangle are always 180°, regardless of what type of triangle it is!

The sum of the interior angles of a quadrangle (quadrilateral) are always 360°, regardless of what type of quadrangle it is.
 

Geometry and Spatial Sense
Spatial Relationships
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Extend understanding of coordinate system to include points whose x or y values may be negative numbers.

 
 
Geometry and Spatial Sense
Visualization and Geometric Models
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side.

 
Geometry and Spatial Sense
Visualization and Geometric Models
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net.
     

First, practice by looking at shapes!

 

 
Patterns, Functions, and Algebra
Use Patterns, Relations, and Functions
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs.

 
 First, practice identifying patterns!

 

Patterns, Functions, and Algebra
Use Patterns, Relations, and Functions
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Use calculators or computers to develop patterns, and generalize them using tables and graphs.

 
 
Patterns, Functions, and Algebra
Use Algebraic Representation
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Use variables as unknown quantities in general rules when describing patterns and other relationships.

 
 
Patterns, Functions, and Algebra
Use Patterns, Relations, and Functions
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Create and interpret the meaning of equations and inequalities representing problem situations.

 
 
Patterns, Functions, and Algebra
Use Patterns, Relations, and Functions
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions.

 
 
Patterns, Functions, and Algebra
Analyze Change
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph.

 
 
 
Data Analysis and Probability
Data Collection
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Read, construct and interpret frequency tables, circle graphs and line graphs.

Data Analysis and Probability
Data Collection
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data.

Data Analysis and Probability
Data Collection
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Read and interpret increasingly complex displays of data, such as double bar graphs.

 
Data Analysis and Probability
Data Collection
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings.

 
Data Analysis and Probability
Data Collection
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected.

 
Data Analysis and Probability
Statistical Methods
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data.

 
Data Analysis and Probability
Probability
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. List and explain all possible outcomes in a given situation.

 
Data Analysis and Probability
Probability
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Identify the probability of events within a simple experiment, such as three chances out of eight.

 
Data Analysis and Probability
Probability
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome.

 
Data Analysis and Probability
Probability
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Compare what should happen (theoretical /expected results) with what did happen (experimental/actual results) in a simple experiment.

 
Data Analysis and Probability
Probability
5th Grade
Ohio Indicator
Explanation ....  Websites for Students
  1. Make predictions based on experimental and theoretical probabilities.

 
 

Online Practice Ohio Achievement Tests

Students,

You can see or even take a practice test online all on your own! Just click on the link below, then choose Grade 5 Math test!

I want to do the Ohio Achievement online practice test!

 I want to review and take fun quizzes on BBC Bitesize!

 I want to have fun on the Math Study Table!

Other online practice tests:

More skills practice on Internet4Classrooms

 

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