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School City of Hobart
School City of Hobart Mathematics
Mathematics - Mathematics - Grade 4

Number Theory
Number Sense
The learner will be able to understand the place value of whole numbers* and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. *whole numbers: 0, 1, 2, 3, etc.
Strand Source
Number Sense IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.1
The learner will be able to read and write whole numbers up to 1,000,000. Example: Read aloud the number 394,734. .
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Read Write Whole Numbers to 1,000,000, McGraw-Hill, Form A, skill test [CTB].  
· Read Write Whole Numbers to 1,000,000, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.2
The learner will be able to identify and write whole numbers up to 1,000,000, given a place-value model. Example: Write the number that has 2 hundred thousands, 7 ten thousands, 4 thousands, 8 hundreds, 6 tens, and 2 ones. .
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Place Value and Expanded Notation, McGraw-Hill, Form A, skill test [CTB].  
· Place Value and Expanded Notation, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.3
The learner will be able to round whole numbers up to 10,000 to the nearest ten, hundred, and thousand. Example: Is 7,683 closer to 7,600 or 7,700? Explain your answer. .
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Round Whole Numbers, McGraw-Hill, Form A, skill test [CTB].  
· Round Whole Numbers, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.4
The learner will be able to order and compare whole numbers using symbols for "less than" (<), "equal to" (=), and "greater than" (>). Example: Put the correct symbol in 328 __ 142. .
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Order and Compare Whole Numbers, McGraw-Hill, Form A, skill test [CTB].  
· Order and Compare Whole Numbers, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.5
The learner will be able to rename and rewrite whole numbers as fractions. Example: 3 = 6/2 = 9/3 = ?/4 = ?/5. .
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Rename and Rewrite Whole Numbers as Fractions, McGraw-Hill, Form A, skill test [CTB].  
· Rename and Rewrite Whole Numbers as Fractions, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.6
The learner will be able to name and write mixed numbers, using objects or pictures. Example: You have 5 whole straws and half a straw. Write the number that represents these objects. .
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Name and Write Mixed Numbers, McGraw-Hill, Form A, skill test [CTB].  
· Name and Write Mixed Numbers, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.7
The learner will be able to name and write mixed numbers as improper fractions, using objects or pictures. Example: Use a picture of 3 rectangles, each divided into 5 equal pieces, to write 2 3/5 as an improper fraction. .
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Name and Write Mixed Numbers Improper Fractions, McGraw-Hill, Form A, skill test [CTB].  
· Name and Write Mixed Numbers Improper Fractions, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.8
The learner will be able to write tenths and hundredths in decimal and fraction notations. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75).
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Write Tenth & Hundredth Decimal Fraction Notation, McGraw-Hill, Form A, skill test [CTB].  
· Write Tenth & Hundredth Decimal Fraction Notation, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.1.9
The learner will be able to round two-place decimals to tenths or to the nearest whole number. Example: You ran the 50-yard dash in 6.73 seconds. Round your time to the nearest tenth. .
Strand Source
Number Sense IDOE
  Assessment Resources
 
· Round 2-Place Decimals to 10ths Whole Numbers, McGraw-Hill, Form A, skill test [CTB].  
· Round 2-Place Decimals to Tenths Whole Numbers, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Whole Numbers
Computation
The learner will be able to solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among these operations. They extend their use and understanding of whole numbers to the addition and subtraction of simple fractions and decimals.
Strand Source
Problem Solving IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.1
The learner will be able to understand and use standard algorithms* for addition and subtraction. Example: 45,329 + 6,984 = ?, 36,296 - 12,075 = ? *algorithm: a step-by-step procedure for solving a problem. .
Strand Source
Add/Subtract Whole Numbers IDOE
  Assessment Resources
 
· Addition and Subtraction Whole Numbers, McGraw-Hill, Form A, skill test [CTB].  
· Addition and Subtraction Whole Numbers, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.2
The learner will be able to represent as multiplication any situation involving repeated addition. Example: Each of the 20 students in your physical education class has 3 tennis balls. Find the total number of tennis balls in the class. .
Strand Source
Multiplication Story Problems IDOE
  Assessment Resources
 
· Multiplication of Whole Numbers, McGraw-Hill, Form A, skill test [CTB].  
· Multiplication of Whole Numbers, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.3
The learner will be able to represent as division any situation involving the sharing of objects or the number of groups of shared objects. Example: Divide 12 cookies equally among 4 students. Divide 12 cookies equally so that each person gets 4 cookies. Compare your answers and methods. .
Strand Source
Division Story Problems IDOE
  Assessment Resources
 
· Division of Whole Numbers, McGraw-Hill, Form A, skill test [CTB].  
· Division of Whole Numbers, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.4
The learner will be able to demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts. Example: Know the answers to 9 x 4 and 35 / 7. .
Strand Source
Multiply Whole Numbers IDOE
  Assessment Resources
 
· Multiplication Tables Between 1 and 10, McGraw-Hill, Form A, skill test [CTB].  
· Multiplication Tables Between 1 and 10, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.5
The learner will be able to use a standard algorithm to multiply numbers up to 100 by numbers up to 10, using relevant properties of the number system. Example: 67 x 3 = ? .
Strand Source
Multiply Whole Numbers IDOE
  Assessment Resources
 
· Use Algorithm Multiplication Numbers to 100 by Nos 10, McGraw-Hill, Form A, skill test [CTB].  
· Use Algorithm Multiplication Numbers to 100 by Nos 10, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.6
The learner will be able to use a standard algorithm to divide numbers up to 100 by numbers up to 10 without remainders, using relevant properties of the number system. Example: 69 / 3 = ? .
Strand Source
Divide Whole Numbers IDOE
  Assessment Resources
 
· Use Algorithm Multiplication Numbers to 100 by Nos 10, McGraw-Hill, Form A, skill test [CTB].  
· Use Algorithm Multiplication Numbers to 100 by Nos 10, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.7
The learner will be able to understand the special properties of 0 and 1 in multiplication and division. Example: Know that 73 x 0 = 0 and that 42 / 1 = 42. .
Strand Source
Multiply/Divide Whole Numbers IDOE
  Assessment Resources
 
· Properties of 0 and 1 in Multiplication and Division, McGraw-Hill, Form A, skill test [CTB].  
· Properties of 0 and 1 in Multiplication and Division, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Fractions
4.2.8
The learner will be able to add and subtract simple fractions with different denominators, using objects or pictures. Example: Use a picture of a circle divided into 6 equal pieces to find 5/6 - 1/3 . .
Strand Source
Add Fractions IDOE
  Assessment Resources
 
· Add Subtract Simple Fractions, McGraw-Hill, Form A, skill test [CTB].  
· Add Subtract Simple Fractions, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Decimals
4.2.9
The learner will be able to add and subtract decimals (to hundredths), using objects or pictures. Example: Use coins to help you find $0.43 - $0.29. .
Strand Source
Add/Subtract Decimals IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.10
The learner will be able to use a standard algorithm to add and subtract decimals (to hundredths). Example: 0.74 + 0.80 = ? .
Strand Source
Add/Subtract Decimals IDOE
  Assessment Resources
 
· Use Algorithm to Add Subtract Decimals to 100th, McGraw-Hill, Form A, skill test [CTB].  
· Use Algorithm to Add Subtract Decimals to 100th, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Whole Numbers
4.2.11
The learner will be able to know and use strategies for estimating results of any whole-number computations. Example: Your friend says that 45,329 + 6,984 = 5,213. Without solving, explain why you think the answer is wrong. .
Strand Source
Reasoning/Estimation IDOE
  Assessment Resources
 
· Estimating Results Whole-No Computation, McGraw-Hill, Form A, skill test [CTB].  
· Estimating Results Whole-No Computation, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.2.12
The learner will be able to use mental arithmetic to add or subtract numbers rounded to hundreds or thousands. Example: Add 3,000 to 8,000 without using pencil and paper. .
Strand Source
Reasoning/Estimation IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Algebraic Concepts
Algebra and Functions
The learner will be able to use and interpret variables, mathematical symbols, and properties to write and simplify numerical expressions and sentences. They understand relationships among the operations of addition, subtraction, multiplication, and division.
Strand Source
Number Sentence IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.3.1
The learner will be able to use letters, boxes, or other symbols to represent any number in simple expressions, equations, or inequalities (i.e., demonstrate an understanding of and the use of the concept of a variable). Example: In the expression 3x + 5, what does x represent? .
Strand Source
Expressions IDOE
  Assessment Resources
 
· Number Sentences, McGraw-Hill, Form A, skill test [CTB].  
· Number Sentences, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.3.2
The learner will be able to use and interpret formulas to answer questions about quantities and their relationships. Example: Write the formula for the area of a rectangle in words. Now let l stand for the length, w for the width, and A for the area. Write the formula using these symbols. .
Strand Source
Formulas IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.3.3
The learner will be able to understand that multiplication and division are performed before addition and subtraction in expressions without parentheses. Example: You go to a store with 90¢ and buy 3 pencils that cost 20¢ each. Write an expression for the amount of money you have left and find its value. .
Strand Source
Expressions IDOE
  Assessment Resources
 
· Order of Operations, McGraw-Hill, Form A, skill test [CTB].  
· Order of Operations, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.3.4
The learner will be able to understand that an equation such as y = 3x + 5 is a rule for finding a second number when a first number is given. Example: Use the formula y = 3x + 5 to find the value of y when x = 6. .
Strand Source
Formulas IDOE
  Assessment Resources
 
· Replacing Number in Equations, McGraw-Hill, Form A, skill test [CTB].  
· Replacing Number in Equations, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.3.5
The learner will be able to continue number patterns using multiplication and division. Example: What is the next number: 160, 80, 40, 20, ...? Explain your answer. .
Strand Source
Operations: Multiply/Divide IDOE
  Assessment Resources
 
· Number Patterns, McGraw-Hill, Form A, skill test [CTB].  
· Number Patterns, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.3.6
The learner will be able to recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve problems. Example: Find another way of writing 13 + 13 + 13 + 13 + 13. .
Strand Source
Problem Solving IDOE
  Assessment Resources
 
· Relationships Among Operations, McGraw-Hill, Form A, skill test [CTB].  
· Relationships Among Operations, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.3.7
The learner will be able to relate problem situations to number sentences involving multiplication and division. Example: You have 150 jelly beans to share among the 30 members of your class. Write a number sentence for this problem and use it to find the number of jelly beans each person will get. .
Strand Source
Number Sentence IDOE
  Assessment Resources
 
· Write Number Sentences, McGraw-Hill, Form A, skill test [CTB].  
· Write Number Sentences, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Functions
4.3.8
The learner will be able to plot and label whole numbers on a number line up to 100. Estimate positions on the number line. Example: Draw a number line and label it with 0, 10, 20, 30, ..., 90, 100. Estimate the position of 77 on this number line. .
Strand Source
Functional Relationships IDOE
  Assessment Resources
 
· Numbers and Number Lines, McGraw-Hill, Form A, skill test [CTB].  
· Numbers and Number Lines, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Geometry
Geometry
The learner will be able to show an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems.
Strand Source
Geometric Concepts IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.4.1
The learner will be able to identify, describe, and draw rays, right angles, acute angles, obtuse angles and straight angles using appropriate mathematical tools and technology. Example: Draw two rays that meet in an obtuse angle. .
Strand Source
Angles IDOE
  Assessment Resources
 
· Describe Draw Angles, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.4.2
The learner will be able to identify, describe and draw parallel, perpendicular, and oblique lines using appropriate mathematical tools and technology. Example: Use the markings on the gymnasium floor to identify two lines that are parallel. Place a jump rope across the parallel lines and identify any obtuse angles created by the jump rope and the lines. .
Strand Source
Lines: Parallel/Perpendicular IDOE
  Assessment Resources
 
· Describe Draw Lines, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.4.3
The learner will be able to identify, describe, and draw parallelograms*, rhombuses*, and trapezoids*, using appropriate mathematical tools and technology. Example: Use a geoboard to make a parallelogram. How do you know it is a parallelogram? *parallelogram: a four-sided figure with both pairs of opposite sides parallel *rhombus: a parallelogram with all sides equal *trapezoid: a four-sided figure with one pair of opposite sides parallel .
Strand Source
Figures: Identify IDOE
  Assessment Resources
 
· Describe Draw Polygons, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.4.4
The learner will be able to identify congruent* quadrilaterals* and give reasons for congruence using sides, angles, parallels and perpendiculars. Example: In a collection of parallelograms, rhombuses, and trapezoids, pick out those that are the same shape and size and explain your decisions. *congruent: two figures that are the same shape and size *quadrilateral: a two-dimensional figure with four sides .
Strand Source
Congruence IDOE
  Assessment Resources
 
· Congruent Polygons, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.4.5
The learner will be able to identify and draw lines of symmetry in polygons. Example: Draw a rectangle and then draw all its lines of symmetry. .
Strand Source
Symmetry IDOE
  Assessment Resources
 
· Lines of Symmetry in Polygons, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.4.6
The learner will be able to construct cubes and prisms* and describe their attributes. Example: Make a 6-sided prism from construction paper. *prism: solid shape with fixed cross-section (right prism is a solid shape with two parallel faces that are congruent polygons and other faces that are rectangles) .
Strand Source
Constructions IDOE
  Assessment Resources
 
· Describe Construct Solid Objects, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Measurement
Measurement
The learner will be able to understand perimeter and area, as well as measuring volume, capacity, time, and money.
Strand Source
Measurement Concepts IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.1
The learner will be able to measure length to the nearest quarter-inch, eighth-inch, and millimeter. Example: Measure the width of a sheet of paper to the nearest millimeter. .
Strand Source
Length IDOE
  Assessment Resources
 
· Length, McGraw-Hill, Form A, skill test [CTB].  
· Length, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.2
The learner will be able to subtract units of length that may require renaming of feet to inches or meters to centimeters. Example: The shelf was 2 feet long. Jane shortened it by 8 inches. How long is the shelf now? .
Strand Source
Length IDOE
  Assessment Resources
 
· Subtract Units of Length, McGraw-Hill, Form A, skill test [CTB].  
· Subtract Units of Length, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.3
The learner will be able to know and use formulas for finding the perimeters of rectangles and squares. Example: The length of a rectangle is 4 cm and its perimeter is 20 cm. What is the width of the rectangle? .
Strand Source
Perimeter IDOE
  Assessment Resources
 
· Perimeter of Rectangle and Square, McGraw-Hill, Form A, skill test [CTB].  
· Perimeter of Rectangle and Square, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.4
The learner will be able to know and use formulas for finding the areas of rectangles and squares. Example: Draw a rectangle 5 inches by 3 inches. Divide it into one-inch squares and count the squares to find its area. Can you see another way to find the area? Do this with other rectangles. .
Strand Source
Area IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.5
The learner will be able to estimate and calculate the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square inch (in2), or square yard (yd2). Example: Measure the length and width of a basketball court and find its area in suitable units. .
Strand Source
Area IDOE
  Assessment Resources
 
· Calculate Area of Rectangle, McGraw-Hill, Form A, skill test [CTB].  
· Calculate Area of Rectangle, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.6
The learner will be able to understand that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas. Example: Make a rectangle of area 12 units on a geoboard and find its perimeter. Can you make other rectangles with the same area? What are their perimeters? .
Strand Source
Area IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.7
The learner will be able to find areas of shapes by dividing them into basic shapes such as rectangles. Example: Find the area of your school building. .
Strand Source
Area IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.8
The learner will be able to use volume and capacity as different ways of measuring the space inside a shape. Example: Use cubes to find the volume of a fish tank and a pint jug to find its capacity. .
Strand Source
Volume IDOE
  Assessment Resources
 
· Volume and Capacity, McGraw-Hill, Form A, skill test [CTB].  
· Volume and Capacity, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.9
The learner will be able to add time intervals involving hours and minutes. Example: During the school week, you have 5 recess periods of 15 minutes. Find how long that is in hours and minutes. .
Strand Source
Time IDOE
  Assessment Resources
 
· Add Line Intervals, McGraw-Hill, Form A, skill test [CTB].  
· Add Line Intervals, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.5.10
The learner will be able to determine the amount of change from a purchase. Example: You buy a chocolate bar priced at $1.75. How much change do you get if you pay for it with a five-dollar bill? .
Strand Source
Money IDOE
  Assessment Resources
 
· Change from a Purchase, McGraw-Hill, Form A, skill test [CTB].  
· Change from a Purchase, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Data Interpretation
Data Analysis and Probability
The learner will be able to organize, represent, and interpret numerical and categorical data and clearly communicate their findings. They show outcomes for simple probability situations.
Strand Source
Problem Solving IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.6.1
The learner will be able to represent data on a number line and in tables, including frequency tables. Example: The students in your class are growing plants in various parts of the classroom. Plan a survey to measure the height of each plant in centimeters on a certain day. Record your survey results on a line plot. .
Strand Source
Tables/Charts IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.6.2
The learner will be able to interpret data graphs to answer questions about a situation. Example: The line plot below shows the heights of fast-growing plants reported by third-grade students. Describe any patterns that you can see in the data using the words "most," "few," and "none." X X X X X X X X X X X X X X X 0 5 10 15 20 25 30 35 Plant Heights in Centimeters .
Strand Source
Analyzing/Evaluating Graphical Forms IDOE
  Assessment Resources
 
· Data Interpretation, McGraw-Hill, Form A, skill test [CTB].  
· Data Interpretation, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Probability/Statistics
4.6.3
The learner will be able to summarize and display the results of probability experiments in a clear and organized way. Example: Roll a number cube 36 times and keep a tally of the number of times that 1, 2, 3, 4, 5, and 6 appear. Draw a bar graph to show your results. .
Strand Source
Data Analysis IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Problem Solving
Problem Solving
The learner will be able to make decisions about how to approach problems and communicate their ideas.
Strand Source
Analyzing Problems IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.7.1
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: "Find a relationship between the number of faces, edges, and vertices of a solid shape with flat surfaces." Try two or three shapes and look for patterns. .
Strand Source
Analyzing Problems IDOE
  Assessment Resources
 
· Approach Information Sequencing Patterns, McGraw-Hill, Form A, skill test [CTB].  
· Approach Information Sequencing Patterns, McGraw-Hill, Form B, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.7.2
The learner will be able to decide when and how to break a problem into simpler parts. Example: In the first example, find what happens to cubes and rectangular solids. .
Strand Source
Analyzing Problems IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.7.3
The learner will be able to apply strategies and results from simpler problems to solve more complex problems. Example: In the first example, use your method for cubes and rectangular solids to find what happens to other prisms and to pyramids. .
Strand Source
Strategies IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.7.4
The learner will be able to use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, tools, and models to solve problems, justify arguments, and make conjectures. Example: In the first example, make a table to help you explain your results to another student. .
Strand Source
Strategies IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.7.5
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, explain what happens with all the shapes that you tried. .
Strand Source
Solution IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.7.6
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 telling a friend the time of a TV program. How accurate should you be: to the nearest day, hour, minute, or second? .
Strand Source
Solution IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Whole Numbers
4.7.7
The learner will be able to know and use appropriate methods for estimating results of whole-number computations. Example: You buy 2 CDs for $15.95 each. The cashier tells you that will be $49.90. Does that surprise you? .
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].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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Problem Solving
4.7.8
The learner will be able to make precise calculations and check the validity of the results in the context of the problem. Example: The buses you use for a school trip hold 55 people each. How many buses will you need to seat 180 people? .
Strand Source
Evaluating Solutions IDOE
  Assessment Resources
 
· Precise Calculations for Solutions, McGraw-Hill, Form B, skill test [CTB].  
· Precise Calculations for Solutions, McGraw-Hill, Form A, skill test [CTB].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.7.9
The learner will be able to decide whether a solution is reasonable in the context of the original situation. Example: In the last example, would an answer of 3.27 surprise you? .
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].  
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
4.7.10
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: Change the first example so that you look at shapes with curved surfaces. .
Strand Source
Evaluating Solutions IDOE
  Unit Instructional Resources
 
· Saxon Math, Saxon Publishing [Textbook].  
  Unit Assessment Resources
 
· NWEA, Northwest Evaluation Association, Fall and Spring [Standardized Test].  
· ISTEP+, McGraw Hill/IDOE, Fall [Standardized Test].  
· Saxon Math, Saxon Publishing [Textbook].  
  
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