Unit 1 Number Theory 1 a B Find the prime factorization of numbers (Lesson 1.9) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 1b BD Rename numbers written in exponential notation (Lessons 1.7-1.9) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 1 c DS Use a divisibility test to determine if a number is divisible by another 5.2.1 Solve problems involving multiplication and division of any ISTEP+ T1 Pt 2 #1-4 number (Lesson 1.5) whole numbers. 1 d DS Identify prime and composite numbers (Lessons 1.6, 1.9) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 1 e DS Understand how square numbers and their square roots are related (Lesson 1.8) 1 f S Draw arrays to model multiplication (Lesson 1.2, 1.7) 1 g S Know basic multiplication facts (Lessons 1.2-1.9) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 4.2.4 Demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts. 4.2.5 Use a standard algorithm to multiply numbers up to 100 by numbers up to 10, using relevant properties of the number system. 1 h S Identify even and odd numbers (Lessons 1.4, 1.5) 3.1.7 Identify odd and even numbers up to 1,000 and describe their characteristics. 1 i S List the factors of a number (Lessons 1.3, 1.4, 1.6, 1.9) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 Unit 2 Estimation and Computation 2 a B Write and solve open sentences for number stories (Lesson 2.4) 5.1.3 Arrange in numerical order and compare whole numbers or ISTEP+ T1 Pt 1 #7-10 decimals to two decimal places by using the symbols for less than (<), equals (=), and greater than (>). 5.5.7 Add and subtract with money in decimal notation. ISTEP+ T1 #2 5.2.5 Add and subtract decimals and verify the reasonableness of the ISTEP+ T1 Pt 2 #8-11 results. 5.3.1 Use a variable to represent an unknown number. ISTEP+ T1 #1 2 b D Round numbers to designated places (Lessons 2.7) 5.1.2 Round whole numbers and decimals to any place value. ISTEP+ T1 Pt 1 #3-6 2 c DS Make magnitude estimates (Lessons 2.7) 2 d DS Find the product of multi-digit whole numbers and decimals (Lesson 5.2.1 Solve problems involving multiplication and division of any ISTEP+ T1 Pt 2 #1-4 2.8, 2.9) whole numbers. 2 e DS Know place value to billions (Lesson 2.10) 5.1.1 Convert between numbers in words and numbers in figures, for numbers up to millions and decimals to thousandths. ISTEP+ T1 Pt 1 #1-2 Grade 5 1 of 7
2 f S Find the sum and difference of multi-digit whole numbers and 5.2.5 Add and subtract decimals and verify the reasonableness of the ISTEP+ T1 Pt 2 #8-11 decimals (Lessons 2.2, 2.3) results. 5.2.7 Use mental arithmetic to add or subtract simple decimals. 2 g S Identify the maximum, minimum, median, mode, and mean for a data 5.2.5 Add and subtract decimals and verify the reasonableness of the ISTEP+ T1 Pt 2 #8-11 set (Lessons 2.5) results. 5.6.2 Find the mean, median, mode, and range of a set of data and ISTEP+ T1 #3-6 describe what each does and does not tell about the data set. No learning goal mapped to this lesson Unit 3 Geometry Explorations and the American Tour 3 a D Determine angle measures based on relationships between angles (Lesson 3.3-3.5, 3.9) 5.6.4 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4, 3/4). 5.4.1 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). 3b DS Estimate the measure of an angle (Lessons 3.6, 3.8) 3c DS Measure an angle to within 2 degrees (Lesson 3.4, 3.9) 5.4.1 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). 3d DS Identify types of angles (Lessons 3.4, 3.5) 5.4.1 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). ISTEP+ T1 #8-11 ISTEP+ T3 #1-2 ISTEP+ T3 #1-2 ISTEP+ T3 #1-2 3e DS Identify types of triangles (Lessons 3.6) 5.4.2 Identify, describe, draw, and classify triangles as equilateral, ISTEP+ T3 #3-6 isosceles, scalene, right, acute, obtuse, and equiangular. 5.4.3 Identify congruent triangles and justify your decisions by referring to sides and angles. ISTEP+ T3 #7 3f S Identify place value in numbers to billions (Lesson 3.2) 5.1.1 ISTEP+ T1 Pt 2 #8-11 3g S Know properties of polygons (Lesson 3.7) 5.4.4 Identify, describe, draw, and classify polygons, such as ISTEP+ T3 #8-11 pentagons and hexagons. 3h S Define and create tessellations (Lesson 3.8) Lesson 3.5 No learning goal mapped to this lesson ISTEP+ T3 #12-14 Unit 4 Division 4 a B Divide decimal numbers by whole numbers with no remainders (Lessons 4.4, 4.5) 5.4.5 Identify and draw the radius and diameter of a circle and understand the relationship between the radius and diameter. Grade 5 2 of 7
4 b B Write and solve number sentences with variables for division number stories (Lessons 4.5, 4.6) 4 c D Find the quotient and remainder of a whole number divided by a 1- digit whole number (Lessons 4.1, 4.2, 4.4, 4.5) 4 d D Find the quotient and remainder of a whole number divided by a 2- digit whole number (Lessons 4.2, 4.4, 4.5) 4 e D Make magnitude estimates for quotients of whole and decimal numbers divided by whole numbers (Lessons 4.4, 4.5) 4 f D Interpret the remainder in division number stories (Lesson 4.5) 4 g D Determine the value of a variable; use this value to complete a number sentence (Lesson 4.6) 4 h S Know place value to hundredths (Lesson 4.1) 5.2.1 Solve problems involving multiplication and division of any ISTEP+ T1 Pt 2 #1-4 whole numbers. 5.2.6 Use estimation to decide whether answers are reasonable in addition, subtraction, multiplication, and division problems. ISTEP+ T1 Pt 2 #5-6 Unit 5 Fractions, Decimals, and Percents 5a BD Add fractions with like denominators (Lesson 5.3) 5 b D Order and compare fractions (Lesson 5.3) 5 c D Convert between fractions and percents (Lessons 5.8) 5.1.4 Interpret percents as a part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value. ISTEP+ T4 #1-2 5 d D Draw a circle graph for a set of data (Lesson 5.11) 5 e D Measure pieces of a circle graph; interpret a circle graph (Lesson 5.10) 5.5.6 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 110 C and 212 F. ISTEP+ T4 #9-10 5 f DS Convert between fractions and mixed numbers (Lessons 5.2) 5.1.5 ISTEP+ T4 #3-4 Explain different interpretations of fractions: as parts of a whole, parts of a set, and division of whole numbers by whole numbers. 5 g DS Find equivalent fractions (Lesson 5.4) 5.1.4 Interpret percents as a part of a hundred. Find decimal and ISTEP+ T4 #1-2 percent equivalents for common fractions and explain why they represent the same value. Lesson 5.1 No learning goal mapped to this lesson 5.1.5 ISTEP+ T4 #3-4 Explain different interpretations of fractions: as parts of a whole, parts of a set, and division of whole numbers by whole numbers. Lesson 5.6 No learning goal mapped to this lesson 5.1.7 Identify on a number line the relative position of simple positive fractions, positive mixed numbers, and positive decimals. ISTEP+ T4 #5-8 Unit 6 Using Data; Addition and Subtraction of Fractions 6a BD Construct stem-and-leaf plots (Lessons 6.3) Grade 5 3 of 7
6b BD Read and interpret stem-and-leaf plots (Lessons 6.4) 6 c D Add and subtract fractions with common denominators (Lessons 6.8 6.10) 6 d D Add and subtract fractions with unlike denominators (Lessons 6.8-6.10) 6 e D Understand how sample size affects results (Lessons 6.5) 6 f D Find a common denominator (Lessons 6.9, 6.10) 6 g DS Convert among fractions, decimals, and percents (Lessons 6.5, 6.8, 6.10) 5.2.2 Add and subtract fractions (including mixed numbers) with different denominators. 5.1.4 Interpret percents as a part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value. 6 h S Find and use data landmarks (Lessons 6.1, 6.5, 6.6) 5.6.2 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. ISTEP+ T5 #2-5 ISTEP+ T4 #1-4 ISTEP+ T2 #3-6 Unit 7 Exponents and Negative Numbers 7a BD Understand and apply scientific notation (Lesson 7.3) 7 b D Understand and apply powers of 10 (Lesson 7.2) 7 c D Understand and apply order of operations to evaluate expressions and solve number sentences (Lesson 7.5) 7 d D Add and subtract positive and negative numbers (Lesson 7.7-7.10) 7 e DS Understand and apply exponential notation (Lesson 7.1, 7.2) 7 f DS Identify number sentences; tell whether a number sentence is true or false (Lesson 7.4) 7 g DS Understand and apply the use of parentheses in number sentences (Lesson 7.4) 7 h DS Order and compare positive and negative numbers (Lesson 7.6) 5.6.1 Explain which types of displays are appropriate for various sets of data. 5.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. ISTEP+ T5 #1 Unit 8 Fractions and Ratios 8 a B Use an algorithm to multiply mixed numbers (Lessons 8.8) 5.2.4 Multiply and divide fractions to solve problems. ISTEP+ T5 #6 8 b D Use an algorithm to multiply fractions (Lessons 8.5-8.7, 8.9) 5.2.3 Use models to show an understanding of multiplication and ISTEP+ T5 #7-8 division of fractions. 8 c D Use an algorithm to subtract mixed numbers with like denominators (Lessons 8.3) 8 d D Find a percent of a number (Lessons 8.9-8.11) 8 e DS Use an algorithm to add mixed numbers (Lesson 8.2, 8.4) 5.2.2 Add and subtract fractions (including mixed numbers) with different denominators. ISTEP+ T5 #2-5 Grade 5 4 of 7
8 f DS Order and compare fractions (Lessons 8.1, 8.2, 8.12) 5.2.4 Multiply and divide fractions to solve problems. ISTEP+ T5 #6 8 g S Convert among fractions, decimals, and percents (Lessons 8.8, 8.9) 5.2.4 Multiply and divide fractions to solve problems. ISTEP+ T5 #6 8 h S Convert between fractions and mixed or whole numbers (Lessons 5.2.2 Add and subtract fractions (including mixed numbers) with ISTEP+ T5 #2-5 8.2, 8.3, 8.8) different denominators. 8 i S Find common denominators (Lessons 8.1, 8.2, 8.4, 8.12) Unit 9 Coordinates, Area, Volume, and Capacity 9 a D Plot ordered pairs on a four-quadrant coordinate grid (Lessons 9.3) 5.3.4 Identify and graph ordered pairs of positive numbers. ISTEP+ T6 #1 9 b D Understand the concept of volume of a figure (Lesson 9.8-9.10) 9 c D Use a formula to find the volume of prisms (Lesson 9.8, 9.9) 9 d DS Plot ordered pairs on a one-quadrant coordinate grid (Lessons 9.1-9.3) 5.3.4 Identify and graph ordered pairs of positive numbers. ISTEP+ T6 #1 9 e DS Identify the base and height of triangles and parallelograms (Lessons 5.5.1 Understand and apply the formulas for the area of a triangle, ISTEP+ T6 #5-6 9.4-9.6) 9 f DS Use a formula to find the area of triangles and parallelograms (Lessons 9.6) 5.5.1 Understand and apply the formulas for the area of a triangle, ISTEP+ T6 #5-6 9 g S Understand the concept of area of a figure (Lessons 9.4-9.6) 5.5.1 Understand and apply the formulas for the area of a triangle, ISTEP+ T6 #5-6 9 h S Use a formula to find the area of rectangles (Lessons 9.4) 5.5.2 Solve problems involving perimeters and areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units. ISTEP+ T6 #4, 7-8 5.5.3 Use formulas for the areas of rectangles and triangles to find the ISTEP+ T6 #9 area of complex shapes by dividing them into basic shapes. Lesson 9.3 5.4.6 Identify shapes that have reflectional and rotational symmetry. ISTEP+ T6 #3-4 Unit 10 Algebra Concepts and Skills 10 a B Solve two-step pan-balance problems (Lesson 10.2, 10.5) 10 b D Write algebraic expressions to describe situations (Lessons 10.3-10.5, 10.7) 5.3.2 Write simple algebraic expressions in one or two variables and evaluate them by substitution. 4.3.1 Use letters, boxes, or other symbols to represent any number in simple expressions, equations, or inequalities. ISTEP+ T7 #1-4 ISTEP+ Gr 4 T3 #6 Grade 5 5 of 7
10 c D Represent rate problems as formulas, graphs, and tables (Lessons 5.3.5 Find ordered pairs (positive numbers only) that fit a linear ISTEP+ T7 #7 10.4-10.7) equation, graph the ordered pairs, and draw the line they determine. 4.3.4 Understand that an equation such as y = 3x + 5 is a rule for finding a second number when a first number is given. (L 10.4) ISTEP+ Gr 4 T 8 #8-10 10 d D Use formulas to find circumference and area of a circle (Lessons 10.8, 10.9) 10 e D Distinguish between circumference and area of circle problems (Lessons 10.9) 10 f DS Solve one-step pan-balance problems (Lesson 10.9) 10 g DS Interpret mystery line plots and graphs (Lesson 10.7) 5.3.7 Use information taken from a graph or equation to answer questions about a problem situation. Unit 11 Volume 11 a B Understand the relationship between the volume of pyramids and prisms, and the volume of cones and cylinders (Lesson 11.4) 11 b B Find the surface area of prisms (Lesson 11.7) 11 c B Understand how to find the surface area of cylinders (Lesson 11.7) 5.3.6 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. 11 d B Understand the concept of capacity and how to calculate it (Lessons 11.6) 11 e DS Use formulas to find the volume of prisms and cylinders (Lessons 11.3) 11 f S Use formulas to find the area of polygons and circles (Lessons 11.1, 11.4) 5.5.4 Find the surface area and volume of rectangular solids using appropriate units. 5.5.4 Find the surface area and volume of rectangular solids using appropriate units. 5.5.1 Understand and apply the formulas for the area of a triangle, 5.5.2 Solve problems involving perimeters and areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units. 11 g S Know the properties of geometric solids (Lesson 11.1, 11.2) 5.4.8 Construct prisms and pyramids using appropriate materials. Unit 12 Probability, Ratios, and Rates 12 a B Use tree diagrams to find all possible ways a sequence of choices can be made (Lesson 12.2) ISTEP+ T7 #6, 8 ISTEP+ T8 #1 ISTEP+ T8 #2 ISTEP+ T8 #2 ISTEP+ T6 #5-6 ISTEP+ T6 #7-8 Grade 5 6 of 7
12 b B Compute the probability of outcomes when choices are equally likely 5.2.7 Use mental arithmetic to add or subtract simple decimals. (Lesson 12.2) 12 c BD Use the Multiplication Counting Principle to find the total number of possible outcomes of a sequence of choices (Lesson 12.2) 12 d D Find the greatest common factor of two numbers (Lesson 12.1) 12 e D Find the least common multiple of two numbers.(lesson 12.1) 12 f DS Solve ratio and rate number stories (Lesson 12.1, 12.3-12.8) 12 g S Find the factors of numbers. (Lessons 12.1) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 12 h S Find the prime factorizations of numbers (Lesson 12.1) 5.1.6 Describe and identify prime and composite numbers. ISTEP+ T1 Pt 1 #11-14 Lesson 12.7 No learning goal mapped to this lesson. 5.6.1 Explain which types of displays are appropriate for various sets of data. ISTEP+ T5 #1 Grade 5 7 of 7