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School City of Hobart |
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School City of Hobart Mathematics |
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Mathematics - Mathematics - Grade 5 |
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Number Sense
The learner will be able to
compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions, and percents. They understand the relative magnitudes of numbers. They understand prime* and composite* numbers. *whole numbers: 0, 1, 2, 3, etc.
*prime number: number that can be evenly divided only by 1 and itself (e.g., 2, 3, 5, 7, 11)
*composite number: not a prime number (e.g., 4, 6, 8, 9, 10)
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| Strand |
Source |
| Number Sense |
IDOE |
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5.1.1
The learner will be able to
convert between numbers in words and numbers in figures, for numbers up to millions and decimals to thousandths.
Example: Write the number 198.536 in words.
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| Strand |
Source |
| Number Sense |
IDOE |
| |
Assessment Resources |
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| · |
Convert Numbers Words to Figures, McGraw-Hill, Form A, skill test [CTB]. |
| · |
Convert Numbers Words to Figures, McGraw-Hill, Form B, skill test [CTB]. |
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5.1.2
The learner will be able to
round whole numbers and decimals to any place value.
Example: Is 7,683,559 closer to 7,600,000 or 7,700,000? Explain your answer.
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| Strand |
Source |
| Number Sense |
IDOE |
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Assessment Resources |
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| · |
Round Whole Numbers & Decimals, McGraw-Hill, Form A, skill test [CTB]. |
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Round Whole Numbers & Decimals, McGraw-Hill, Form B, skill test [CTB]. |
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5.1.3
The learner will be able to
arrange in numerical order and compare whole numbers or decimals to two decimal places by using the symbols for less than (<), equals (=), and greater than (>).
Example: Write from smallest to largest: 0.5, 0.26, 0.08.
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| Strand |
Source |
| Number Sense |
IDOE |
| |
Assessment Resources |
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| · |
Order Compare Whole Numbers Decimal Fractions, McGraw-Hill, Form A, skill test [CTB]. |
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Order Compare Whole Numbers Decimal Fractions, McGraw-Hill, Form B, skill test [CTB]. |
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5.1.4
The learner will be able to
interpret percents as a part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value.
Example: Shade a 100-square grid to show 30%. What fraction is this?
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| Strand |
Source |
| Number Sense |
IDOE |
| |
Assessment Resources |
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| · |
Convert Decimals Percent Fractions, McGraw-Hill, Form A, skill test [Textbook]. |
| · |
Convert Decimals Percent Fractions, McGraw-Hill, Form B, skill test [CTB]. |
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5.1.5
The learner will be able to
explain different interpretations of fractions: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.
Example: What fraction of a pizza will each person get when 3 pizzas are divided equally among 5 people?
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| Strand |
Source |
| Number Sense |
IDOE |
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Assessment Resources |
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| · |
Interpretations of Fractions, McGraw-Hill, Form A, skill test [CTB]. |
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Interpretations of Fractions, McGraw-Hill, Form B, skill test [CTB]. |
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5.1.6
The learner will be able to
describe and identify prime and composite numbers.
Example: Which of the following numbers are prime: 3, 7, 12, 17, 18? Justify your choices.
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| Strand |
Source |
| Prime/Composite Numbers |
IDOE |
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Assessment Resources |
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| · |
Prime and Composite Numbers, McGraw-Hill, Form A, skill test [CTB]. |
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Prime and Composite Numbers, McGraw-Hill, Form B, skill test [CTB]. |
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5.1.7
The learner will be able to
identify on a number line the relative position of simple positive fractions, positive mixed numbers, and positive decimals.
| Strand |
Source |
| Number Sense |
IDOE |
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Assessment Resources |
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| · |
Number Line Interpretations, McGraw-Hill, Form A, skill test [CTB]. |
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Number Line Interpretations, McGraw-Hill, Form B, skill test [CTB]. |
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Computation
The learner will be able to
solve problems involving multiplication and division of whole numbers and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals.
| Strand |
Source |
| Problem Solving |
IDOE |
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5.2.1
The learner will be able to
solve problems involving multiplication and division of any whole numbers.
Example: 2,867 x 34 = ? Explain your method.
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| Strand |
Source |
| Multiply/Divide Whole Numbers |
IDOE |
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Assessment Resources |
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| · |
Multiply & Divide Whole Numbers, McGraw-Hill, Form A, skill test [CTB]. |
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Multiply & Divide Whole Numbers, McGraw-Hill, Form B, skill test [CTB]. |
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5.2.2
The learner will be able to
add and subtract fractions (including mixed numbers) with different denominators.
Example: 3 4/5 - 2 2/3 = ?
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| Strand |
Source |
| Add/Subtract Fractions |
IDOE |
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Assessment Resources |
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| · |
Add and Subtract Fractions, McGraw-Hill, Form A, skill test [CTB]. |
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Add and Subtract Fractions, McGraw-Hill, Form B, skill test [CTB]. |
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5.2.3
The learner will be able to
use models to show an understanding of multiplication and division of fractions.
Example: Draw a rectangle 5 squares long and 3 squares wide. Shade 4/5 of the rectangle, starting from the left. Shade 2/3 of the rectangle, starting from the top. Look at the fraction of the squares that you have double-shaded and use that to show how to multiply 4/5 by 2/3.
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| Strand |
Source |
| Multiply Fractions |
IDOE |
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5.2.4
The learner will be able to
multiply and divide fractions to solve problems.
Example: You have 3 1/2 pizzas left over from a party. How many people can have 1/4 of a pizza each?
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| Strand |
Source |
| Multiply/Divide Fractions |
IDOE |
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Assessment Resources |
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| · |
Multiply and Divide Fractions, McGraw-Hill, Form A, skill test [CTB]. |
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Multiply & Divide Fractions, McGraw-Hill, Form B, skill test [CTB]. |
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5.2.5
The learner will be able to
add and subtract decimals and verify the reasonableness of the results.
Example: Compute 39.46 - 20.89 and check the answer by estimating.
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| Strand |
Source |
| Add/Subtract Decimals |
IDOE |
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Assessment Resources |
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| · |
Add and Subtract Decimals, McGraw-Hill, Form A, skill test [CTB]. |
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Add and Subtract Decimals, McGraw-Hill, Form B, skill test [CTB]. |
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5.2.6
The learner will be able to
use estimation to decide whether answers are reasonable in addition, subtraction, multiplication, and division problems.
Example: Your friend says that 2,867 x 34 = 20,069. Without solving, explain why you think the answer is wrong.
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| Strand |
Source |
| Reasoning/Estimation |
IDOE |
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Assessment Resources |
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| · |
Use Estimation to Determine Reasonableness, McGraw-Hill, Form A, skill test [CTB]. |
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Use Estimation to Determine Reasonableness, McGraw-Hill, Form B, skill test [CTB]. |
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5.2.7
The learner will be able to
use mental arithmetic to add or subtract simple decimals.
Example: Add 0.006 to 0.027 without using pencil and paper.
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| Strand |
Source |
| Add Decimals |
IDOE |
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Algebra and Functions
The learner will be able to
use variables in simple expressions, compute the value of an expression for specific values of the variable, and plot and interpret the results. They use two-dimensional coordinate grids to represent points and graph lines.
| Strand |
Source |
| Expressions |
IDOE |
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5.3.1
The learner will be able to
use a variable to represent an unknown number.
Example: When a certain number is multiplied by 3 and then 5 is added, the result is 29. Let x stand for the unknown number and write an equation for the relationship.
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| Strand |
Source |
| Variable |
IDOE |
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Assessment Resources |
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| · |
Variable to Represent Unknown Number, McGraw-Hill, Form A, skill test [CTB]. |
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Number Sentences, McGraw-Hill, Form A, skill test [CTB]. |
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Variable to Represent Unknown Number, McGraw-Hill, Form B, skill test [CTB]. |
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Number Sentences, McGraw-Hill, Form B, skill test [CTB]. |
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5.3.2
The learner will be able to
write simple algebraic expressions in one or two variables and evaluate them by substitution.
Example: Find the value of 5x + 2 when x = 3.
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| Strand |
Source |
| Expressions |
IDOE |
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Assessment Resources |
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| · |
Simple Algebraic Expressions, McGraw-Hill, Form A, skill test [CTB]. |
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Simple Algebraic Expressions, McGraw-Hill, Form B, skill test [CTB]. |
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5.3.3
The learner will be able to
use the distributive property* in numerical equations and expressions.
Example: Rewrite 3(16 - 11) by removing the parentheses. *distributive property: e.g., 3 x (5 + 2) = 3 x 5 + 3 x 2
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| Strand |
Source |
| Equations |
IDOE |
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Assessment Resources |
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| · |
Distributive Property, McGraw-Hill, Form A, skill test [CTB]. |
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Distributive Property, McGraw-Hill, Form B, skill test [CTB]. |
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5.3.4
The learner will be able to
identify and graph ordered pairs of positive numbers.
Example: Plot the points (3, 1), (6, 2), and (9, 3). What do you notice?
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| Strand |
Source |
| Graphing Functions |
IDOE |
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Assessment Resources |
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| · |
Ordered Pairs Coordinate Plane, McGraw-Hill, Form A, skill test [CTB]. |
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Ordered Pairs Coordinate Plane, McGraw-Hill, Form B, skill test [CTB]. |
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5.3.5
The learner will be able to
find ordered pairs (positive numbers only) that fit a linear equation, graph the ordered pairs, and draw the line they determine.
Example: For x = 1, 2, 3, and 4, find points that fit the equation y = 2x + 1. Plot those points on graph paper and join them with a straight line.
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| Strand |
Source |
| Graphing Functions |
IDOE |
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5.3.6
The learner will be able to
understand that the length of a horizontal line segment on a coordinate plane equals the difference between the x-coordinates and that the length of a vertical line segment on a coordinate plane equals the difference between the y-coordinates.
Example: Find the distance between the points (2, 5) and (7, 5) and the distance between the points (2, 1) and (2, 5).
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| Strand |
Source |
| Graphing Functions |
IDOE |
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5.3.7
The learner will be able to
use information taken from a graph or equation to answer questions about a problem situation.
Example: The speed (v feet per second) of a car t seconds after it starts is given by the formula v = 12t. Find the car's speed after 5 seconds.
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| Strand |
Source |
| Problem Solving |
IDOE |
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Assessment Resources |
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| · |
Data Interpretation, McGraw-Hill, Form A, skill test [CTB]. |
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Data Interpretation, McGraw-Hill, Form B, skill test [CTB]. |
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Geometry
The learner will be able to
identify, describe, and classify the properties of plane and solid geometric shapes and the relationships between them.
| Strand |
Source |
| Figures: Identify |
IDOE |
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5.4.1
The learner will be able to
measure, identify, and draw angles, perpendicular and parallel lines, rectangles, triangles, and circles by using appropriate tools (e.g., ruler, compass, protractor, appropriate technology, media tools).
Example: Draw a rectangle with sides 5 in and 3 in.
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| Strand |
Source |
| Figures: Construct |
IDOE |
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Assessment Resources |
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| · |
Geometric Figures, McGraw-Hill, Form A, skill test [CTB]. |
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Geometric Figures, McGraw-Hill, Form B, skill test [CTB]. |
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5.4.2
The learner will be able to
identify, describe, draw, and classify triangles as equilateral*, isosceles*, scalene*, right*, acute*, obtuse*, and equiangular*.
Example: Draw an isosceles right triangle. *equilateral triangle: all sides are congruent
*sosceles triangle: at least two sides are congruent
*scalene triangle: no sides are equal
*right triangle: one angle measures 90 degrees
*acute triangle: all angles are less than 90 degrees
*obtuse triangle: one angle is more than 90 degrees
*equiangular triangle: all angles are of equal measure
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| Strand |
Source |
| Triangles |
IDOE |
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5.4.3
The learner will be able to
identify congruent* triangles and justify your decisions by referring to sides and angles.
Example: In a collection of triangles, pick out those that are the same shape and size and explain your decisions. *congruent: two figures that are the same shape and size
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| Strand |
Source |
| Congruence |
IDOE |
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Assessment Resources |
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| · |
Congruent Triangles, McGraw-Hill, Form A, skill test [CTB]. |
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Congruent Triangles, McGraw-Hill, Form B, skill test [CTB]. |
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5.4.4
The learner will be able to
identify, describe, draw, and classify polygons*, such as pentagons and hexagons.
Example: In a collection of polygons, pick out those with the same number of sides. *polygon: two-dimensional shape with straight sides (e.g., triangle, rectangle, pentagon)
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| Strand |
Source |
| Polygons |
IDOE |
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Assessment Resources |
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| · |
Polygons, McGraw-Hill, Form A, skill test [CTB]. |
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Polygons, McGraw-Hill, Form B, skill test [CTB]. |
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5.4.5
The learner will be able to
identify and draw the radius and diameter of a circle and understand the relationship between the radius and diameter.
Example: On a circle, draw a radius and a diameter and describe the differences and similarities between the two.
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| Strand |
Source |
| Circles |
IDOE |
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5.4.6
The learner will be able to
identify shapes that have reflectional and rotational symmetry*.
Example: What kinds of symmetries have the letters M, N, and O? *reflectional and rotational symmetry: letter M has reflectional symmetry in a line down the middle; letter N has rotational symmetry around its center
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| Strand |
Source |
| Symmetry |
IDOE |
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Assessment Resources |
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| · |
Reflectional & Rotational Summetry, McGraw-Hill, Form A, skill test [CTB]. |
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Reflectional & Rotational Symmetry, McGraw-Hill, Form B, skill test [CTB]. |
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5.4.7
The learner will be able to
understand that 90°, 180°, 270°, and 360° are associated with quarter, half, three-quarters, and full turns, respectively.
Example: Face the front of the room. Turn through four right angles. Which way are you now facing?
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| Strand |
Source |
| Angles |
IDOE |
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5.4.8
The learner will be able to
construct prisms* and pyramids using appropriate materials.
Example: Make a square-based pyramid from construction paper. *prism: solid shape with fixed cross-section (right prism is a solid shape with
two parallel faces that are polygons and other faces that are rectangles)
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| Strand |
Source |
| Constructions |
IDOE |
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5.4.9
The learner will be able to
given a picture of a three-dimensional object, build the object with blocks.
Example: Given a picture of a house made of cubes and rectangular prisms, build the house.
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| Strand |
Source |
| Constructions |
IDOE |
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Measurement
The learner will be able to
understand and compute the areas and volumes of simple objects, as well as measuring weight, temperature, time, and money.
| Strand |
Source |
| Measurement Concepts |
IDOE |
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5.5.1
The learner will be able to
understand and apply the formulas for the area of a triangle, parallelogram, and trapezoid.
Example: Find the area of a triangle with base 4 m and height 5 m.
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Assessment Resources |
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| · |
Formulas for Areas of Geometric Shape, McGraw-Hill, Form A, skill test [CTB]. |
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Formulas for Areas of Geometric Shape, McGraw-Hill, Form B, skill test [CTB]. |
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5.5.2
The learner will be able to
solve problems involving perimeters and areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
Example: A trapezoidal garden bed has parallel sides of lengths 14 m and 11 m and its width is 6 m. Find its area and the length of fencing needed to enclose it. Be sure to use correct units.
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| Strand |
Source |
| Perimeter |
IDOE |
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Assessment Resources |
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| · |
Problems with Perimeter & Area, McGraw-Hill, Form A, skill test [CTB]. |
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Problems with Perimeter & Area, McGraw-Hill, Form B, skill test [CTB]. |
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5.5.3
The learner will be able to
use formulas for the areas of rectangles and triangles to find the area of complex shapes by dividing them into basic shapes.
Example: A square room of length 17 feet has a tiled fireplace area that is 6 feet long and 4 feet wide. You want to carpet the floor of the room, except the fireplace area. Find the area to be carpeted.
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Assessment Resources |
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| · |
Area of Complex Shapes Using Basic Shapes, McGraw-Hill, Form A, skill test [CTB]. |
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Area of Complex Shapes Using Basic Shapes, McGraw-Hill, Form B, skill test [CTB]. |
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5.5.4
The learner will be able to
find the surface area and volume of rectangular solids using appropriate units.
Example: Find the volume of a shoe box with length 30 cm, width 15 cm, and height 10 cm.
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| Strand |
Source |
| Volume |
IDOE |
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Assessment Resources |
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| · |
Surface Area & Volume, McGraw-Hill, Form A, skill test [CTB]. |
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Surface Area & Volume, McGraw-Hill, Form B, skill test [CTB]. |
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5.5.5
The learner will be able to
understand and use the smaller and larger units for measuring weight (ounce, gram, and ton) and their relationship to pounds and kilograms.
Example: How many ounces are in a pound?
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| Strand |
Source |
| Weight |
IDOE |
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Assessment Resources |
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| · |
Measuring Weight, McGraw-Hill, Form A, skill test [CTB]. |
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Measuring Weight, McGraw-Hill, Form B, skill test [CTB]. |
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5.5.6
The learner will be able to
compare temperatures in Celsius and Fahrenheit, knowing that the freezing point of water is 0°C and 32°F and that the boiling point is 100°C and 212°F.
Example: What is the Fahrenheit equivalent of 50°C? Explain your answer.
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| Strand |
Source |
| Temperature |
IDOE |
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Assessment Resources |
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| · |
Converting Temperatures, McGraw-Hill, Form A, skill test [CTB]. |
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Converting Temperatures, McGraw-Hill, Form B, skill test [CTB]. |
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5.5.7
The learner will be able to
add and subtract with money in decimal notation.
Example: You buy articles that cost $3.45, $6.99, and $7.95. How much change will you receive from $20?
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Assessment Resources |
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| · |
Add Subtract Money Decimal Notation, McGraw-Hill, Form A, skill test [CTB]. |
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Add Subtract Money Decimal Notation, McGraw-Hill, Form B, skill test [CTB]. |
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Data Analysis and Probability
The learner will be able to
collect, display, analyze, compare, and interpret data sets. They use the results of probability experiments to predict future events.
| Strand |
Source |
| Data Collection and Classification |
IDOE |
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5.6.1
The learner will be able to
explain which types of displays are appropriate for various sets of data.
Example: Conduct a survey to find the favorite movies of the students in your class. Decide whether to use a bar, line, or picture graph to display the data. Explain your decision.
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| Strand |
Source |
| Analyzing/Evaluating Graphical Forms |
IDOE |
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5.6.2
The learner will be able to
find the mean*, median*, mode*, and range* of a set of data and describe what each does and does not tell about the data set.
Example: Find the mean, median, and mode of a set of test results and describe how well each represents the data. *mean: the average obtained by adding the values and dividing by the number of values
*median: the value that divides a set of data written in order of size into two equal parts
*mode: the most common value in a set of data
*range: the difference between the largest and the smallest values
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| Strand |
Source |
| Average/Median/Mode/Range |
IDOE |
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Assessment Resources |
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| · |
Mean Median Mode of Data Set, McGraw-Hill, Form A, skill test [CTB]. |
| · |
Mean Median Mode of Data Set, McGraw-Hill, Form B, skill test [CTB]. |
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5.6.3
The learner will be able to
understand that probability can take any value between 0 and 1, events that are not going to occur have probability 0, events certain to occur have probability 1, and more likely events have a higher probability than less likely events.
Example: What is the probability of rolling a 7 with a number cube?
.
| Strand |
Source |
| Probability Concepts |
IDOE |
| |
Assessment Resources |
| |
| · |
Meaning of Probability, McGraw-Hill, Form A, skill test [CTB]. |
| · |
Meaning of Probability, McGraw-Hill, Form B, skill test [CTB]. |
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5.6.4
The learner will be able to
express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4, 3/4).
Example: What is the probability of rolling an odd number with a number cube?
.
| Strand |
Source |
| Outcomes |
IDOE |
| |
Assessment Resources |
| |
| · |
Probability and Counting Arrangements, McGraw-Hill, Form A, skill test [CTB]. |
| · |
Probability and Counting Arrangements, McGraw-Hill, Form B, skill test [CTB]. |
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Problem Solving
The learner will be able to
make decisions about how to approach problems and communicate their ideas.
| Strand |
Source |
| Analyzing Problems |
IDOE |
|
5.7.1
The learner will be able to
analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
Example: Solve the problem: "When you flip a coin 3 times, you can get 3 heads, 3 tails, 2 heads and 1 tail, or 1 head and 2 tails. Find the probability of each of these combinations." Notice that the case of 3 heads and the case of 3 tails are similar. Notice that the case of 2 heads and 1 tail and the case of 1 head and 2 tails are similar.
.
| Strand |
Source |
| Analyzing Problems |
IDOE |
| |
Assessment Resources |
| |
| · |
Approach Info Sequencing Patterns, McGraw-Hill, Form A, skill test [CTB]. |
| · |
Approach Info Sequencing Patterns, McGraw-Hill, Form B, skill test [CTB]. |
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5.7.2
The learner will be able to
decide when and how to break a problem into simpler parts.
Example: In the first example, decide to look at the case of 3 heads and the case of 2 heads and 1 tail.
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| Strand |
Source |
| Analyzing Problems |
IDOE |
|
5.7.3
The learner will be able to
apply strategies and results from simpler problems to solve more complex problems.
Example: In the first example, begin with the situation where you flip the coin twice.
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| Strand |
Source |
| Strategies |
IDOE |
|
5.7.4
The learner will be able to
express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
Example: In the first example, make a table or tree diagram to show another student what is happening.
.
| Strand |
Source |
| Solution |
IDOE |
|
5.7.5
The learner will be able to
recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
Example: You are buying a piece of plastic to cover the floor of your bedroom before you paint the room. How accurate should you be: to the nearest inch, foot, or yard? Explain your answer.
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| Strand |
Source |
| Evaluating Solutions |
IDOE |
|
5.7.6
The learner will be able to
know and apply appropriate methods for estimating results of rational-number computations.
Example: Will 7 x 18 be smaller or larger than 100? Explain your answer.
.
| Strand |
Source |
| Reasoning/Estimation |
IDOE |
| |
Assessment Resources |
| |
| · |
Estimating Results, McGraw-Hill, Form A, skill test [CTB]. |
| · |
Estimating Results, McGraw-Hill, Form B, skill test [CTB]. |
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5.7.7
The learner will be able to
make precise calculations and check the validity of the results in the context of the problem.
Example: A recipe calls for 3/8 of a cup of sugar. You plan to double the recipe for a party and you have only one cup of sugar in the house. Decide whether you have enough sugar and explain how you know.
.
| Strand |
Source |
| Analyzing Problems |
IDOE |
| |
Assessment Resources |
| |
| · |
Precise Calculations for Solution, McGraw-Hill, Form A, skill test [CTB]. |
| · |
Precise Calculations for Solutions, McGraw-Hill, Form B, skill test [CTB]. |
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5.7.8
The learner will be able to
decide whether a solution is reasonable in the context of the original situation.
Example: In the first example about flipping a coin, check that your probabilities add to 1.
.
| Strand |
Source |
| Evaluating Solutions |
IDOE |
| |
Assessment Resources |
| |
| · |
Reasonableness of Solutions, McGraw-Hill, Form A, skill test [CTB]. |
| · |
Reasonableness of Solutions, McGraw-Hill, Form B, skill test [CTB]. |
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5.7.9
The learner will be able to
note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.
Example: Find the probability of each of the combinations when you flip a coin 4 times.
.
| Strand |
Source |
| Evaluating Solutions |
IDOE |
|
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