Standard 1: Demonstrate an understanding of data collection, analysis, and probability.
Enduring Understanding: Data can be collected, represented, and analyzed to solve problems and make predictions. Probability helps describe the likelihood of events.
Indicators:
5.DPSR.1.1 – Describe data by determining the range and mode, including whole numbers, fractions, and decimals (to the hundredths).
5.DPSR.1.2 – Solve two-step, real-world problems using data shown in tables, line graphs, bar graphs, or dot plots.
5.DPSR.1.3 – Analyze data in graphs to make predictions and draw conclusions.
5.DPSR.2.1 – Represent the probability of simple events as 0, a fraction, or 1.
Standard 2: Demonstrate an understanding of measurement, geometry, and spatial reasoning.
Enduring Understanding:
Measurement and geometric reasoning help us describe, compare, and solve real-world problems involving space, shape, and size.
Indicators:
5.MGSR.1.1 – Solve problems involving area and perimeter of composite figures by breaking them into rectangles.
5.MGSR.1.2 – Measure and estimate the volume of rectangular prisms using unit cubes.
5.MGSR.2.1 – Convert measurements within the same system (length, weight, liquid volume, and time) and apply them to real-world problems.
5.MGSR.2.2 – Measure lengths to the nearest eighth of an inch or millimeter.
5.MGSR.3.1 – Identify and use the coordinate plane to write and plot ordered pairs in the first quadrant.
5.MGSR.3.2 – Graph and interpret real-world situations using points on the coordinate plane.
Standard 1: Demonstrate an understanding of the economic, political, and social effects of expansion and industrialization on the United States and South Carolina between 1860–1910.
Enduring Understanding: The Second Industrial Revolution, urbanization, and access to resources contributed to U.S. expansion. Migration within and into the U.S. created tensions and enriched national culture.
Indicators:
5.1.CO – Compare the physical landscape and demographics of the U.S. before and after the Transcontinental Railroad. (Focus on how building the railroad changed the land and settlement patterns.)
5.1.CE – Examine push- and pull-factors related to immigration and expansion on urban and rural populations. (Focus on why people immigrated and how immigrant cultures influenced society.)
5.1.P – Summarize how U.S. involvement in the Spanish American War led to increased economic expansion and imperialism. (Focus on U.S. overseas markets and industrial growth.)
5.1.CX – Contextualize how the Second Industrial Revolution led to a desire for raw materials and U.S. involvement in imperialistic efforts and economic expansion. (Focus on industrialization in the U.S. and South Carolina.)
5.1.CC – Summarize how imperialism and economic expansion impacted different groups and shaped American cultural identities. (Topics may include labor, working conditions, and population growth.)
5.1.E – Analyze multiple perspectives on economic, political, and social effects of western expansion, the Industrial Revolution, and immigration using primary and secondary sources.
Standard 1: Demonstrate an understanding of data collection, analysis, and probability.
Enduring Understanding:
Data can be collected, represented, and analyzed to solve problems and make predictions. Probability helps describe the likelihood of events.
Indicators:
5.DPSR.1.1 – Describe data by determining the range and mode, including whole numbers, fractions, and decimals (to the hundredths).
5.DPSR.1.2 – Solve two-step, real-world problems using data shown in tables, line graphs, bar graphs, or dot plots.
5.DPSR.1.3 – Analyze data in graphs to make predictions and draw conclusions.
5.DPSR.2.1 – Represent the probability of simple events as 0, a fraction, or 1.
Standard 3: Demonstrate an understanding of numbers and relationships within the base-ten system and fractions.
Enduring Understanding:
Numbers can be represented in multiple ways, and understanding their relationships helps solve problems involving whole numbers, decimals, and fractions.
Indicators:
5.NR.1.1 – Read, write, and represent numbers up to 999 with decimals to the thousandths place.
5.NR.1.2 – Explain how the value of a digit changes based on its place in a number.
5.NR.1.3 – Round decimal numbers to the nearest whole number, tenth, or hundredth.
5.NR.1.4 – Use patterns to explain multiplying and dividing by powers of 10.
5.NR.2.1 – Compare fractions and mixed numbers using common denominators and symbols (<, >, =).
Standard 4: Demonstrate an understanding of operations with whole numbers and decimals.
Enduring Understanding:
Efficient strategies and mathematical properties can be used to solve problems involving all four operations with whole numbers and decimals.
Indicators:
5.PAFR.1.1 – Multiply multi-digit numbers using strategies and real-world contexts.
5.PAFR.1.2 – Divide multi-digit numbers using strategies, including interpreting remainders.
5.PAFR.1.3 – Add and subtract decimals to the hundredths.
5.PAFR.1.4 – Multiply and divide decimals by one-digit whole numbers and explain the reasoning.
Standard 5: Demonstrate an understanding of operations with fractions.
Enduring Understanding:
Fractions can be combined, compared, and applied to real-world situations using multiple strategies and representations.
Indicators:
5.PAFR.2.1 – Add and subtract fractions and mixed numbers with unlike denominators.
5.PAFR.2.2 – Multiply fractions and whole numbers in real-world situations.
5.PAFR.2.3 – Interpret and solve division problems involving whole numbers and unit fractions.
Standard 6: Demonstrate an understanding of numerical and algebraic reasoning.
Enduring Understanding:
Patterns, relationships, and expressions help represent and solve real-world mathematical situations.
Indicators:
5.PAFR.3.1 – Determine the least common multiple (LCM) to find common denominators.
5.PAFR.3.2 – Determine the greatest common factor (GCF) to simplify fractions.
5.PAFR.3.3 – Identify patterns in function tables and write rules as expressions.
5.PAFR.3.4 – Write and evaluate numerical expressions using parentheses to represent real-world situations.
Table of Contents
Unit 1: Math is . . .
Unit 2: Place Value and Number Relationships
Unit 3: Add and Subtract Decimals
Unit 4: Multiplying Multi-Digit Whole Numbers & Multiplying Numbers with Decimals
Unit 5: Dividing Whole Numbers & Dividing Numbers with Decimals
Unit 6: Add & Subtract Fractions and Mixed Numbers
Unit 7: Multiplying Fractions
Unit 8: Dividing Fractions
Unit 9: Measurement & Data
Unit 10: Geometry, Algebraic Thinking, & Volume
Unit 11: Proficiency with Power Standards
Divisibility Rules
Manipulatives
August
Standard 3: Demonstrate an understanding of numbers and relationships within the base-ten system and fractions.
Enduring Understanding:
Numbers can be represented in multiple ways, and understanding their relationships helps solve problems involving whole numbers, decimals, and fractions.
Indicators:
5.NR.1.1 – Read, write, and represent numbers up to 999 with decimals to the thousandths place.
5.NR.1.2 – Explain how the value of a digit changes based on its place in a number.
5.NR.1.3 – Round decimal numbers to the nearest whole number, tenth, or hundredth.
I can . . .
Understanding Numbers
☐ I can tell the difference between whole numbers and decimals. (Example: 5 is a whole number, 5.3 is a decimal.)
Reading and Writing Numbers
☐ I can read and write numbers up to 999 with decimals to the thousandths. (Example: 3.125 = three and one hundred twenty-five thousandths.)
☐ I can show numbers using base-ten blocks or pictures. (Example: 2.4 = 2 wholes and 4 tenths.)
☐ I can write numbers in standard form. (Example: three and five tenths = 3.5)
☐ I can write numbers in word form (Example: 2.51 = two and fifty-one hundredths)
☐ I can write numbers in expanded form. (Example: 4.26 = 4 + 0.2 + 0.06)
☐ I can represent numbers using decimals and fractions. (Example: 0.5 = 1/2)
Breaking Apart Numbers
☐ I can break apart (decompose) decimals in different ways. (Example: 1.75 = 1 + 0.7 + 0.05)
☐ I can show how decimals can make wholes (Example: 15 tenths = 1 whole and 5 tenths)
Understanding Place Value
☐ I can use a place value chart to understand numbers. (Example: In 3.45, 4 is in the tenths place.)
☐ I can explain that a digit is 10 times greater than the digit to its right. (Example: In 50, the 5 is 10 times greater than the 5 in 5.)
☐ I can explain that a digit is 1/10 of the value of the digit to its left. (Example: In 0.5, the 5 is 1/10 of the value of the 5 in 5.)
☐ I can apply place value understanding to whole numbers and decimals. (Example: In 2.3, the 2 is in the ones place and the 3 is in the tenths place.)
Comparing Digits
☐ I can compare the value of the same digit in different places. (Example: In 4.4, the 4 in the ones place is greater than the 4 in the tenths place.)
Rounding Decimals
☐ I can round decimals to the nearest whole number, tenth, or hundredth. (Example: 3.67 rounds to 3.7 to the nearest tenth.)
☐ I can use a number line to help me round. (Example: 2.3 is closer to 2 than 3 on a number line.)
☐ I can use benchmark numbers and midpoints to decide how to round. (Example: 4.5 is halfway between 4 and 5, so it rounds up to 5.)
Place Value of Whole Numbers and Decimals with Problem Solving
distinguish and recognize the difference between whole numbers and decimals.
read and write decimals to thousandths using concrete models (base-ten blocks), base-ten numerals, number names (ex. 2.51 = two and fifty-one hundredths, not 2 point five one), and expanded form
decompose decimals in a variety of ways. (ex. 15 tenths = 1 whole and 5 tenths and 261 hundredths = 2 wholes and 61 hundredths)
explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. (whole numbers & decimals)
explain what an exponent means (the number of times you multiply by 10).
103 = 10 x 10 x 10
3 x 103 = 3 x (10 x 10 x 10)
write and evaluate repeated factors in exponent form with factors of 10. (Exponents are only used with 10 as the base number.)
whole numbers (ex. 5 x 103 and 546 ÷ 103)
decimals (ex. 1.5 x 102 and 1.5 ÷ 102)
Compare Decimals
compare two decimals to thousandths based on meanings of the digits in each place using <, >, and = to record the comparisons.
Round Decimals
round decimals to any place within thousandths using place value understanding number lines and the standard method
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
W.4 Place values in decimal numbers X8U
W.5 Relationship between decimal place values DVM
W.6 Convert decimals between standard and expanded form WTU
W.7 Convert decimals between standard and expanded form using fractions BLQ
W.8 Compose and decompose decimals in multiple ways 7U9
X.4 Compare decimal numbers NSG
BB.1 Multiply a decimal by a power of ten DN2
BB.2 Multiply a decimal by a power of ten: with exponents 5KC
Writing Decimals in Standard, Word, and Expanded Form (16:50)
Decimal Place Values (11:50)
Comparing Decimals (8:50)
Comparing Decimals (4:32)
Rounding Decimals Using a Number Line (4:58)
Rounding Decimals (6:52)
10 Times Greater Than the Value Vs 1/10 the Value of (17:20)
Comparing Decimal Place Values (4:41)
September
Standard 4: Demonstrate an understanding of operations with whole numbers and decimals.
Enduring Understanding:
Efficient strategies and mathematical properties can be used to solve problems involving all four operations with whole numbers and decimals.
Indicators:
5.PAFR.1.3 – Add and subtract decimals to the hundredths.
Standard 6: Demonstrate an understanding of numerical and algebraic reasoning.
Enduring Understanding:
Patterns, relationships, and expressions help represent and solve real-world mathematical situations.
Indicators:
5.PAFR.3.4 – Write and evaluate numerical expressions using parentheses to represent real-world situations.
I can . . .
☐ I can explain what addition means (put together, add to). (Example: 2 + 3 means putting 2 and 3 together to make 5.)
☐ I can explain what subtraction means (take from, take apart, compare). (Example: 5 − 2 means taking 2 away from 5 to get 3.)
☐ I can estimate sums and differences to check if my answer makes sense. (Example: 3.4 + 2.1 is about 5.5, so my answer should be close to 5.5.)
☐ I can add decimals to the hundredths. (Example: 2.35 + 1.40 = 3.75)
☐ I can subtract decimals to the hundredths. (Example: 5.60 − 2.25 = 3.35)
☐ I can use models or drawings to add and subtract decimals. (Example: Using a grid to show 0.5 + 0.25 = 0.75)
☐ I can use the standard algorithm to add and subtract decimals. (Example: Line up decimal points when solving 3.2 + 1.45.)
☐ I can explain how addition and subtraction are related. (Example: If 4 + 3 = 7, then 7 − 3 = 4.)
☐ I can solve one-step addition and subtraction word problems. (Example: You have $5.50 and spend $2.25. You have $3.25 left.)
☐ I can solve two-step word problems using addition and subtraction. (Example: $5.00 − $1.50 + $2.00 = $5.50)
☐ I can solve real-life problems using decimals. (Example: Adding prices while shopping.)
☐ I can write an expression to match a real-life problem. (Example: “You buy 2 items for $1.50 each” → 1.50 + 1.50)
☐ I can use parentheses in expressions. (Example: (2 + 3) + 4 = 9)
☐ I can use a variable to represent an unknown number. (Example: x + 2 = 5)
☐ I can write equations with variables to match word problems. (Example: “A number plus 3 equals 7” → x + 3 = 7)
☐ I can check if my answer is correct. (Example: I estimate first to see if my answer is reasonable.)
☐ I can explain if an answer is correct or incorrect. (Example: If 3.2 + 1.8 = 4, I know it is incorrect because the sum should be 5.)
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
October
Standard 3: Demonstrate an understanding of numbers and relationships within the base-ten system and fractions.
Enduring Understanding:
Numbers can be represented in multiple ways, and understanding their relationships helps solve problems involving whole numbers, decimals, and fractions.
Indicators:
5.NR.1.4 – Use patterns to explain multiplying and dividing by powers of 10.
Standard 4: Demonstrate an understanding of operations with whole numbers and decimals.
Enduring Understanding:
Efficient strategies and mathematical properties can be used to solve problems involving all four operations with whole numbers and decimals.
Indicators:
5.PAFR.1.1 – Multiply multi-digit numbers using strategies and real-world contexts.
5.PAFR.1.4 – Multiply and divide decimals by one-digit whole numbers and explain the reasoning.
Standard 6: Demonstrate an understanding of numerical and algebraic reasoning.
Enduring Understanding:
Patterns, relationships, and expressions help represent and solve real-world mathematical situations.
Indicators:
5.PAFR.3.4 – Write and evaluate numerical expressions using parentheses to represent real-world situations.
I can . . .
☐ I can explain what an exponent means. (Example: 10³ means 10 × 10 × 10.)
☐ I can write repeated multiplication using exponents. (Example: 10 × 10 × 10 = 10³)
☐ I can evaluate expressions with powers of 10. (Example: 3 × 10³ = 3 × 1,000 = 3,000)
☐ I can write numbers using powers of 10 with whole numbers and decimals. (Example: 1.5 × 10² = 150)
☐ I can explain that multiplication means combining equal groups. (Example: 3 × 4 means 3 groups of 4.)
☐ I can estimate products to check if my answer makes sense. (Example: 23 × 41 is about 20 × 40 = 800.)
☐ I can multiply a two- or three-digit number by a two-digit number. (Example: 34 × 12)
☐ I can use the area model to solve multiplication problems. (Example: 23 × 15 = (20 × 10) + (20 × 5) + (3 × 10) + (3 × 5))
☐ I can use partial products to solve multiplication problems. (Example: 23 × 15 = 200 + 100 + 30 + 15)
☐ I can use the distributive property to multiply. (Example: 7 × 23 = (7 × 20) + (7 × 3))
☐ I can use the standard algorithm to multiply. (Example: solving 34 × 12 using regrouping)
☐ I can explain how the area model and partial products connect to the standard algorithm.
☐ I can use the commutative property. (Example: 4 × 6 = 6 × 4)
☐ I can use the associative property. (Example: (2 × 3) × 4 = 2 × (3 × 4))
☐ I can solve one-step multiplication word problems. (Example: 4 bags with 6 apples each = 24 apples.)
☐ I can solve two-step word problems using addition, subtraction, and multiplication. (Example: 3 × 5 + 2 = 17)
☐ I can solve real-life problems using multiplication. (Example: Finding total cost of multiple items.)
☐ I can write an expression to match a real-life problem. (Example: “3 groups of 8” → 3 × 8)
☐ I can use parentheses in expressions. (Example: (3 × 4) + 2 = 14)
☐ I can use a variable to represent an unknown number. (Example: 4 × x = 20)
☐ I can write equations with variables to match word problems. (Example: “A number times 5 equals 25” → 5x = 25)
☐ I can check if my answer is reasonable using estimation. (Example: 39 × 21 ≈ 40 × 20 = 800)
☐ I can explain if a multiplication answer is correct or incorrect. (Example: 12 × 12 = 124 is incorrect because it should be 144.)
☐ I can estimate products with decimals to check if my answer makes sense. (Example: 3 × 0.6 ≈ 3 × 1 = 3)
☐ I can determine where the decimal belongs in a product. (Example: 3 × 0.6 = 1.8, not 18 or 0.18)
☐ I can multiply a whole number by a decimal to the hundredths. (Example: 2 × 0.4 = 0.8)
☐ I can multiply a whole number by a decimal in the hundredths place. (Example: 3 × 0.28 = 0.84)
☐ I can use place value to help multiply decimals. (Example: 0.3 × 2 = 0.6)
☐ I can use models like decimal grids to show multiplication. (Example: shading 2 groups of 0.34)
☐ I can use the commutative property with decimals. (Example: 2 × 0.5 = 0.5 × 2)
☐ I can use the distributive property to multiply decimals. (Example: 2 × 0.34 = (2 × 0.3) + (2 × 0.04))
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
Multiplication
IXL Lessons
Multiplying 2-Digit Numbers
Multiplying 2-Digit Numbers
Multiplying 2-Digit Numbers
Estimating by Rounding when Multiplying
Estimating by Rounding when Multiplying
Multiplying 3-Digit Numbers
Multiplying 3-Digit Numbers
Games & Activities:
November & December
Standard 3: Demonstrate an understanding of numbers and relationships within the base-ten system and fractions.
Enduring Understanding:
Numbers can be represented in multiple ways, and understanding their relationships helps solve problems involving whole numbers, decimals, and fractions.
Indicators:
5.NR.1.4 – Use patterns to explain multiplying and dividing by powers of 10.
Standard 4: Demonstrate an understanding of operations with whole numbers and decimals.
Enduring Understanding:
Efficient strategies and mathematical properties can be used to solve problems involving all four operations with whole numbers and decimals.
Indicators:
5.PAFR.1.2 – Divide multi-digit numbers using strategies, including interpreting remainders.
5.PAFR.1.4 – Multiply and divide decimals by one-digit whole numbers and explain the reasoning.
Standard 6: Demonstrate an understanding of numerical and algebraic reasoning.
Enduring Understanding:
Patterns, relationships, and expressions help represent and solve real-world mathematical situations.
Indicators:
5.PAFR.3.4 – Write and evaluate numerical expressions using parentheses to represent real-world situations.
I can . . .
☐ I can explain what an exponent means (how many times a number is multiplied by itself). (Example: 10³ = 10 × 10 × 10)
☐ I can write repeated multiplication using exponents. (Example: 10 × 10 × 10 = 10³)
☐ I can divide numbers using powers of 10. (Example: 1,000 ÷ 10³ = 1)
☐ I can write and evaluate expressions with powers of 10 when dividing. (Example: 546 ÷ 10³ = 0.546)
☐ I can use powers of 10 with decimals when dividing. (Example: 1.5 ÷ 10² = 0.015)
☐ I can explain that division means breaking into equal groups. (Example: 12 ÷ 3 means 12 split into 3 equal groups = 4 in each group.)
☐ I can estimate quotients to check if my answer makes sense. (Example: 420 ÷ 7 is about 420 ÷ 7 = 60)
☐ I can divide a 4-digit number by a 2-digit number. (Example: 1,248 ÷ 12)
☐ I can use the area model to divide. (Example: Breaking apart 1,248 into easier parts to divide by 12)
☐ I can use partial quotients to divide. (Example: Subtracting groups of 12 step by step)
☐ I can use the distributive property to divide. (Example: 1,200 ÷ 12 + 48 ÷ 12)
☐ I can use the standard algorithm to divide. (Example: long division)
☐ I can connect models and partial quotients to the standard algorithm. (Example: All methods give the same quotient)
☐ I can explain how multiplication and division are related. (Example: 4 × 3 = 12, so 12 ÷ 3 = 4)
☐ I can check division using multiplication. (Example: 15 × 4 = 60, so 60 ÷ 4 = 15)
☐ I can solve one-step division word problems. (Example: 20 cookies shared by 5 people = 4 each)
☐ I can solve two-step problems using different operations. (Example: (24 ÷ 6) + 3 = 7)
☐ I can solve real-life problems using division. (Example: Sharing items equally)
☐ I can decide when to ignore the remainder. (Example: 8 flowers ÷ 3 vases = 2 in each vase, 2 left over)
☐ I can decide when to round up the quotient. (Example: 6 people need cars that hold 4 → 2 cars needed)
☐ I can write the remainder as a fraction. (Example: 3 liters ÷ 2 = 1 1/2 liters each)
☐ I can write an expression to match a real-life problem. (Example: “24 shared by 6” → 24 ÷ 6)
☐ I can use parentheses in expressions. (Example: (12 ÷ 3) + 2 = 6)
☐ I can use a variable to represent an unknown number. (Example: x ÷ 4 = 5)
☐ I can write equations with variables to match word problems. (Example: “A number divided by 3 equals 7” → x ÷ 3 = 7)
☐ I can check if my answer is reasonable. (Example: Estimate before solving)
☐ I can explain if an answer is correct or incorrect. (Example: 100 ÷ 10 should be 10, not 1)
☐ I can estimate decimal division problems to check my answer. (Example: 0.6 ÷ 2 is about 0.3)
☐ I can predict where the decimal goes in my answer. (Example: 0.62 ÷ 2 = 0.31, not 31 or 3.1)
☐ I can divide decimals (to the hundredths) by a whole number. (Example: 0.36 ÷ 3 = 0.12)
☐ I can divide decimals in the tenths by a whole number. (Example: 0.4 ÷ 2 = 0.2)
☐ I can use place value to help divide decimals. (Example: 0.3 ÷ 3 = 0.1)
☐ I can use models or decimal grids. (Example: splitting a shaded grid into equal parts)
☐ I can use the distributive property. (Example: 0.36 ÷ 3 = (0.3 ÷ 3) + (0.06 ÷ 3))
☐ I can use the relationship between multiplication and division. (Example: If 0.12 × 3 = 0.36, then 0.36 ÷ 3 = 0.12)
☐ I can check my answer using multiplication. (Example: Multiply the quotient by the divisor to check)
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
Dividing Whole Numbers
D.4 Divide multi-digit numbers by 1-digit numbers: word problems 5DE
D.14 Divide 2-digit and 3-digit numbers by 2-digit numbers HMA
D.15 Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems AJW
D.17 Divide 4-digit numbers by 2-digit numbers: word problems J8L
IXL Lessons
Estimating Quotients Using Compatible Numbers
Estimating Quotients Using Compatible Numbers
You may start the video at 1:10.Dividing by Two-Digit Numbers
Dividing by Two-Digit Numbers
Dividing by Two-Digit Numbers
Dividing by Two-Digit Numbers (Start at 5:12)
Long Division
Long Division
Interpreting Remainders
Dividing using Base 10 Blocks
Dividing using the Rectangular Array Box Method
Dividing using the Partial Quotients Method
Dividing using the Partial Quotients Method
Dividing using the Partial Quotients Method
Dividing using the Partial Quotients Method
Dividing using the Partial Quotients Method
Games & Activities:
December & January
Standard 3: Demonstrate an understanding of numbers and relationships within the base-ten system and fractions.
Enduring Understanding:
Numbers can be represented in multiple ways, and understanding their relationships helps solve problems involving whole numbers, decimals, and fractions.
Indicators:
5.NR.2.1 – Compare fractions and mixed numbers using common denominators and symbols (<, >, =).
Standard 5: Demonstrate an understanding of operations with fractions.
Enduring Understanding:
Fractions can be combined, compared, and applied to real-world situations using multiple strategies and representations.
Indicators:
5.PAFR.2.1 – Add and subtract fractions and mixed numbers with unlike denominators.
Standard 6: Demonstrate an understanding of numerical and algebraic reasoning.
Enduring Understanding:
Patterns, relationships, and expressions help represent and solve real-world mathematical situations.
Indicators:
5.PAFR.3.1 – Determine the least common multiple (LCM) to find common denominators.
5.PAFR.3.2 – Determine the greatest common factor (GCF) to simplify fractions.
I can . . .
☐ I can explain what addition means (put together, add to). (Example: 1/4 + 1/4 means combining parts to make 2/4.)
☐ I can explain what subtraction means (take from, take apart, compare). (Example: 3/4 − 1/4 means taking away 1 part to get 2/4.)
☐ I can estimate sums and differences of fractions to check if my answer makes sense. (Example: 1/2 + 1/3 is about 1)
☐ I can add fractions with unlike denominators. (Example: 1/2 + 1/4 = 3/4)
☐ I can subtract fractions with unlike denominators. (Example: 3/4 − 1/2 = 1/4)
☐ I can add and subtract mixed numbers. (Example: 1 1/2 + 2 1/4 = 3 3/4)
☐ I can regroup when adding or subtracting fractions. (Example: 2 1/4 − 1 3/4 = 1/2)
☐ I can use models or drawings to solve fraction problems. (Example: using fraction bars or circles)
☐ I can use a number line to add and subtract fractions. (Example: jumping forward or backward on a number line)
☐ I can use the standard algorithm to add and subtract fractions. (Example: finding a common denominator first)
☐ I can find a common denominator to add or subtract fractions. (Example: 1/3 + 1/6 = 2/6 + 1/6 = 3/6)
☐ I can find the least common multiple (LCM) to help find a common denominator. (Example: LCM of 3 and 6 is 6)
☐ I can simplify fractions using the greatest common factor (GCF). (Example: 4/8 = 1/2)
☐ I can identify prime numbers (only 2 factors: 1 and itself). (Example: 3 = 1 × 3)
☐ I can identify composite numbers (more than 2 factors). (Example: 8 = 1 × 8 and 2 × 4)
☐ I can explain how addition and subtraction are related. (Example: If 1/2 + 1/4 = 3/4, then 3/4 − 1/4 = 1/2)
☐ I can solve one-step fraction word problems. (Example: You eat 1/4 of a pizza and then 1/4 more = 1/2 total)
☐ I can solve two-step problems using addition and subtraction. (Example: 1/2 + 1/4 − 1/4 = 1/2)
☐ I can solve real-life problems using fractions. (Example: measuring ingredients in a recipe)
☐ I can write an expression to match a real-life problem. (Example: “1/2 plus 1/4” → 1/2 + 1/4)
☐ I can use parentheses in expressions. (Example: (1/2 + 1/4) − 1/4 = 1/2)
☐ I can use a variable to represent an unknown number. (Example: x + 1/4 = 3/4)
☐ I can write equations with variables to match word problems. (Example: “A number plus 1/2 equals 1” → x + 1/2 = 1)
☐ I can check if my answer is reasonable. (Example: estimating before solving)
☐ I can explain if an answer is correct or incorrect. (Example: 1/2 + 1/2 = 1, not 2/2 + 2/2)
☐ I can explain that fractions must refer to the same whole to be compared. (Example: 1/2 of a small pizza is not the same as 1/2 of a large pizza)
☐ I can compare fractions using <, >, or =. (Example: 1/2 > 1/3)
☐ I can compare improper fractions and mixed numbers. (Example: 5/4 > 1)
☐ I can compare fractions with different denominators by finding a common denominator. (Example: 1/2 = 2/4, so 2/4 > 1/4)
☐ I can read fraction comparisons correctly. (Example: 3/5 < 4/3 is read “three-fifths is less than four-thirds”)
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
L.1 Estimate sums and differences of fractions using benchmarks 9JR
L.4 Add and subtract fractions with like denominators: word problems 7YQ
L.8 Add fractions with unlike denominators D9N (IXL Video)
L.10 Estimate sums and differences of fractions using benchmarks 9JR
L.12 Add and subtract fractions with unlike denominators: word problems TCD
Adding Fractions with Common Denominators (4:34)
Subtracting Fractions with Common Denominators (4:34)
Adding Fractions with Unlike Denominators (7:39)
Adding Fractions with Unlike Denominators (7:23)
Subtracting Fractions with Unlike Denominators (8:37)
Adding Three Fractions with Unlike Denominators (4:34)
Adding Mixed Numbers with Common Denominators (2:52)
Adding Mixed Numbers (9:03)
Adding Mixed Numbers with Unlike Denominators (5:07)
Subtracting a Mixed Number from a Mixed Number (3:26)
Simplifying Fractions (song) (3:26) NumberRock
January & February
Standard 5: Demonstrate an understanding of operations with fractions.
Enduring Understanding:
Fractions can be combined, compared, and applied to real-world situations using multiple strategies and representations.
Indicators:
5.PAFR.2.2 – Multiply fractions and whole numbers in real-world situations.
Standard 6: Demonstrate an understanding of numerical and algebraic reasoning.
Enduring Understanding:
Patterns, relationships, and expressions help represent and solve real-world mathematical situations.
Indicators:
5.PAFR.3.4 – Write and evaluate numerical expressions using parentheses to represent real-world situations.
I can . . .
☐ I can explain what multiplication means (combining equal groups). (Example: 3 × 1/2 means 3 groups of 1/2 = 3/2 or 1 1/2)
☐ I can explain multiplication as repeated addition. (Example: 1/4 + 1/4 + 1/4 = 3/4)
☐ I can estimate products of fractions to check if my answer makes sense. (Example: 1/2 × 8 is about half of 8, which is 4)
☐ I can multiply a fraction by a whole number. (Example: 3 × 1/4 = 3/4)
☐ I can multiply a mixed number by a whole number. (Example: 1 1/2 × 2 = 3)
☐ I can multiply a fraction greater than 1 by a whole number. (Example: 5/4 × 2 = 10/4 = 2 1/2)
☐ I can multiply a fraction by a fraction. (Example: 1/2 × 1/3 = 1/6)
☐ I can multiply a fraction by a mixed number. (Example: 1/2 × 1 1/2 = 3/4)
☐ I can multiply a fraction by a fraction greater than 1. (Example: 1/2 × 5/4 = 5/8)
☐ I can multiply a whole number by a fraction. (Example: 4 × 1/3 = 4/3 = 1 1/3)
☐ I can use models or drawings to multiply fractions. (Example: shading parts of a shape to show 1/2 × 1/3)
☐ I can use the area model to multiply fractions. (Example: overlapping shaded regions to find 1/6)
☐ I can use partial products to multiply fractions. (Example: breaking apart mixed numbers before multiplying)
☐ I can use the distributive property. (Example: 3 × (1/2 + 1/4))
☐ I can use the commutative property. (Example: 1/2 × 3 = 3 × 1/2)
☐ I can use the standard algorithm to multiply fractions. (Example: multiply numerators and denominators)
☐ I can simplify fractions using the greatest common factor (GCF). (Example: 6/8 = 3/4)
☐ I can identify prime numbers (only 2 factors: 1 and itself). (Example: 5 = 1 × 5)
☐ I can identify composite numbers (more than 2 factors). (Example: 9 = 1 × 9 and 3 × 3)
☐ I can solve one-step multiplication word problems with fractions. (Example: 3 groups of 1/2 = 1 1/2)
☐ I can solve two-step problems using addition, subtraction, and multiplication. (Example: (1/2 × 4) + 1 = 3)
☐ I can solve real-life problems using fractions. (Example: finding part of a recipe)
☐ I can write an expression to match a real-life problem. (Example: “3 groups of 1/4” → 3 × 1/4)
☐ I can use parentheses in expressions. (Example: (2 × 1/2) + 1 = 2)
☐ I can use a variable to represent an unknown number. (Example: x × 1/2 = 3)
☐ I can write equations with variables to match word problems. (Example: “Half of a number is 4” → 1/2x = 4)
☐ I can check if my answer is reasonable. (Example: estimating before solving)
☐ I can explain if an answer is correct or incorrect. (Example: 1/2 × 4 should be 2, not 8)
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
Multiplying a Fraction by a Fraction (5:41)
Multiplying a Fraction by a Fraction (3:26)
Multiplying a Fraction by a Fraction (song) (3:26) NumberRock
Multiplying a Fraction by a Whole Number (5:15)
Multiplying Fractions Using Cancellation (8:04)
February & March
Standard 5: Demonstrate an understanding of operations with fractions.
Enduring Understanding:
Fractions can be combined, compared, and applied to real-world situations using multiple strategies and representations.
Indicators:
5.PAFR.2.3 – Interpret and solve division problems involving whole numbers and unit fractions.
Standard 6: Demonstrate an understanding of numerical and algebraic reasoning.
Enduring Understanding:
Patterns, relationships, and expressions help represent and solve real-world mathematical situations.
Indicators:
5.PAFR.3.4 – Write and evaluate numerical expressions using parentheses to represent real-world situations.
I can . . .
☐ I can explain what division means (breaking into equal groups). (Example: 4 ÷ 2 means 4 split into 2 equal groups = 2 in each group.)
☐ I can estimate quotients with fractions to check if my answer makes sense. (Example: 4 ÷ 1/2 is about 8 because halves fit into 4 many times.)
☐ I can divide a whole number by a unit fraction. (Example: 4 ÷ 1/2 = 8)
☐ I can divide a unit fraction by a whole number. (Example: 1/2 ÷ 2 = 1/4)
☐ I can use models or drawings to divide fractions. (Example: showing how many 1/2 pieces fit into 4)
☐ I can use a number line to divide fractions. (Example: counting jumps of 1/2 to reach 4)
☐ I can use an area model to divide fractions. (Example: splitting a shape into equal parts)
☐ I can connect division to multiplication. (Example: 4 ÷ 1/2 = 4 × 2 = 8)
☐ I can simplify fractions using the greatest common factor (GCF). (Example: 4/8 = 1/2)
☐ I can identify prime numbers (only 2 factors: 1 and itself). (Example: 7 = 1 × 7)
☐ I can identify composite numbers (more than 2 factors). (Example: 6 = 1 × 6 and 2 × 3)
☐ I can solve one-step division word problems with fractions. (Example: How many 1/2 cups are in 4 cups? → 8)
☐ I can solve two-step problems using different operations. (Example: (4 ÷ 1/2) − 2 = 6)
☐ I can solve real-life problems using fraction division. (Example: sharing or measuring amounts)
☐ I can write an expression to match a real-life problem. (Example: “4 divided by 1/2” → 4 ÷ 1/2)
☐ I can use parentheses in expressions. (Example: (6 ÷ 1/2) + 2 = 14)
☐ I can use a variable to represent an unknown number. (Example: x ÷ 1/2 = 6)
☐ I can write equations with variables to match word problems. (Example: “A number divided by 1/2 equals 10” → x ÷ 1/2 = 10)
☐ I can check if my answer is reasonable. (Example: estimating before solving)
☐ I can explain if an answer is correct or incorrect. (Example: 4 ÷ 1/2 should be greater than 4, not smaller)
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
N.2 Divide unit fractions by whole numbers GXY
N.3 Divide whole numbers by unit fractions using models VDU
N.4 Divide whole numbers by unit fractions 3L9
N.5 Divide unit fractions and whole numbers using area models A7W
N.6 Divide unit fractions and whole numbers SPB
N.7 Divide unit fractions and whole numbers: word problems G2N
N.8 Divide fractions by whole numbers FKT
N.9 Divide whole numbers by fractions RHL
Dividing a Fraction by a Fraction (5:12)
Dividing a Fraction by a Fraction (4:27)
Dividing a Fraction by a Fraction (song) (4:27) NumberRock
Dividing a Fraction by a Fraction (5:41)
Dividing a Whole Number by a Fraction (4:32)
Dividing a Mixed Number by a Fraction (7:10)
Dividing Mixed Numbers and Fractions (7:33)
Dividing a Mixed Number by a Mixed Number (7:16)
March & April
Standard 1: Demonstrate an understanding of data collection, analysis, and probability.
Enduring Understanding:
Data can be collected, represented, and analyzed to solve problems and make predictions. Probability helps describe the likelihood of events.
Indicators:
5.DPSR.1.1 – Describe data by determining the range and mode, including whole numbers, fractions, and decimals (to the hundredths).
5.DPSR.1.2 – Solve two-step, real-world problems using data shown in tables, line graphs, bar graphs, or dot plots.
5.DPSR.1.3 – Analyze data in graphs to make predictions and draw conclusions.
5.DPSR.2.1 – Represent the probability of simple events as 0, a fraction, or 1.
Standard 2: Demonstrate an understanding of measurement, geometry, and spatial reasoning.
Enduring Understanding:
Measurement and geometric reasoning help us describe, compare, and solve real-world problems involving space, shape, and size.
Indicators:
5.MGSR.2.1 – Convert measurements within the same system (length, weight, liquid volume, and time) and apply them to real-world problems.
I can . . .
☐ I can tell the difference between categorical and numerical data. (Example: Favorite color = categorical; number of pets = numerical)
☐ I can read and analyze data from tables and graphs. (Example: using a bar graph to compare amounts)
☐ I can use data to make predictions and draw conclusions. (Example: If sales are increasing, I can predict they may continue to rise)
☐ I can read graphs with scales using whole numbers, halves, fourths, and eighths. (Example: each line increases by 1/2)
☐ I can read and interpret tables. (Example: finding information in rows and columns)
☐ I can read and interpret bar graphs. (Example: comparing heights of bars)
☐ I can read and interpret dot plots. (Example: dots show how many times a value appears)
☐ I can read and interpret line plots. (Example: Xs show how many times a value appears)
☐ I can read and interpret circle graphs (without percentages). (Example: showing parts of a whole)
☐ I can match a graph to the correct data in a table. (Example: choosing the graph that correctly represents the data given)
☐ I can solve one-step and two-step problems using data. (Example: adding or comparing values from a graph)
☐ I can solve real-life problems using tables and graphs. (Example: finding total votes in a survey)
☐ I can find the range of a data set. (Example: highest value − lowest value)
☐ I can find the mode of a data set. (Example: the number that appears most often)
☐ I can identify the maximum and minimum values. (Example: greatest and least numbers in a data set)
☐ I can convert between customary units of length. (Example: 1 yard = 3 feet)
☐ I can convert between customary units of weight. (Example: 1 pound = 16 ounces)
☐ I can convert between customary units of liquid volume. (Example: 1 gallon = 4 quarts)
☐ I can convert units of time. (Example: 60 seconds = 1 minute)
☐ I can convert between metric units. (Example: 1 meter = 100 centimeters)
☐ I can use place value to understand metric conversions. (Example: moving the decimal when multiplying or dividing by 10)
☐ I can understand metric prefixes (milli-, centi-, kilo-). (Example: 1 kilometer = 1,000 meters)
☐ I can solve real-life problems using unit conversions. (Example: converting inches to feet)
☐ I can complete multi-step conversions. (Example: 3 yards = 9 feet = 108 inches)
☐ I can check if my answer is reasonable using estimation. (Example: estimating before converting)
☐ I can explain what probability means. (Example: how likely something is to happen)
☐ I can represent the probability of an event as 0, a fraction, or 1. (Example: impossible = 0, certain = 1, likely = 3/4)
☐ I can describe simple events using fractions. (Example: 1 out of 4 chances = 1/4)
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
April
Standard 1: Demonstrate an understanding of data collection, analysis, and probability.
Enduring Understanding: Data can be collected, represented, and analyzed to solve problems and make predictions. Probability helps describe the likelihood of events.
Indicators:
5.DPSR.1.2 – Solve two-step, real-world problems using data shown in tables, line graphs, bar graphs, or dot plots.
5.DPSR.1.3 – Analyze data in graphs to make predictions and draw conclusions.
Standard 2: Demonstrate an understanding of measurement, geometry, and spatial reasoning.
Enduring Understanding:
Measurement and geometric reasoning help us describe, compare, and solve real-world problems involving space, shape, and size.
Indicators:
5.MGSR.1.1 – Solve problems involving area and perimeter of composite figures by breaking them into rectangles.
5.MGSR.1.2 – Measure and estimate the volume of rectangular prisms using unit cubes.
I can . . .
☐ I can create an ordered pair from a function (input/output) table. (Example: input 2, output 6 → (2, 6))
☐ I can explain that the first number is the x-coordinate (horizontal). (Example: in (3, 5), 3 moves right)
☐ I can explain that the second number is the y-coordinate (vertical). (Example: in (3, 5), 5 moves up)
☐ I can graph ordered pairs in the first quadrant. (Example: plot (4, 2) by moving right 4, up 2)
☐ I can graph points on the axes. (Example: (4, 0) or (0, 4))
☐ I can identify the origin and axes. (Example: (0, 0) is the origin)
☐ I can explain what a graph shows in words. (Example: distance increases over time)
☐ I can solve real-world problems using graphs. (Example: reading distance on a map grid)
☐ I can describe and answer questions about line graphs. (Example: identifying when a value increases or decreases)
☐ I can determine the rule from a graph. (Example: points increase by 2 each time → rule is ×2)
☐ I can find the pattern in a function (input/output) table. (Example: 2 → 6, 3 → 9 → rule is ×3)
☐ I can write the rule as an expression. (Example: x × 3 or 3x)
☐ I can explain what an inch is and use it to measure length. (Example: using a ruler)
☐ I can recognize that an inch is divided into fractional parts. (Example: halves, fourths, eighths)
☐ I can measure to the nearest eighth of an inch. (Example: measuring 2 3/8 inches)
☐ I can recognize equivalent fractions of an inch. (Example: 1/2 = 4/8)
☐ I can recognize equivalent fractions. (Example: 2/8 = 1/4, 6/8 = 3/4)
☐ I can explain what a millimeter is. (Example: small unit on a ruler)
☐ I can explain that 10 millimeters = 1 centimeter.
☐ I can measure to the nearest millimeter. (Example: measuring a pencil)
☐ I can find the length of an object that does not start at 0. (Example: subtracting starting point from ending point)
☐ I can explain that the perimeter is the distance around a shape. (Example: walking around a playground)
☐ I can find the perimeter of composite shapes. (Example: adding all side lengths)
☐ I can use grid paper or models to find the perimeter. (Example: counting units around a shape)
☐ I can break shapes into rectangles or squares to find missing sides.
☐ I can use the formula P = 2L + 2W. (Example: rectangle with L=5, W=3 → P=16)
☐ I can use shape properties to find missing sides. (Example: opposite sides of a rectangle are equal)
☐ I can explain that area is the space inside a shape. (Example: covering a surface with tiles)
☐ I can find the area of composite shapes. (Example: adding areas of smaller rectangles)
☐ I can use grid paper or models to find area. (Example: counting squares inside a shape)
☐ I can break shapes into rectangles or squares.
☐ I can use the formula A = L × W. (Example: 5 × 3 = 15 square units)
☐ I can use shape properties to find missing side lengths.
☐ I can explain that volume is the amount of space inside a 3D shape. (Example: how much a box can hold)
☐ I can explain what a unit cube is. (Example: 1 cube = 1 cubic unit)
☐ I can measure volume by counting unit cubes. (Example: 8 cubes = 8 cubic units)
☐ I can find the volume of a rectangular prism. (Example: counting cubes in layers)
☐ I can build a 3D shape with a given volume. (Example: build a shape with volume of 12 cubic units)
IXL Practice
(Each IXL activity contains an example problem and a video demonstrating how to solve a problem.)
Finding Volume (7:50)
Finding Volume (3:20) Study Jams
Finding Volume (Music) (1:54) NumberRock
Finding Volume with Unit Cubes (5:35)
Finding Volume of Irregular Figures (3:42)
Finding Volume of Composite Rectangular Prisms (9:25)
Finding Volume of Composite Rectangular Prisms (3.47)
May