Fifth Grade - MATH
5: Math
Unit 1: Place Value
Lesson 3
Digits to the Left and Right
Students practice multiplying and dividing whole numbers and decimals by 10 (e.g., 6 × 10 = 60, 54 ÷ 10 = 5.4, 1.2 ÷ 10 = 0.12) on the "Values Left and Right" and "Digit Values" activity pages. Activities and the parent notes explicitly tell students that multiplying by 10 moves the decimal point to the right and dividing by 10 moves it to the left, and include practice problems with numbers like 500 × 10, 0.5 × 10, and 200,000 ÷ 10. Real-world contexts such as groups of dimes, jellybeans, and steps are used to practice finding one-tenth and understanding numeric change when values move left or right on the place-value chart.
Lesson 5
Comparing Decimals
Students are asked to convert 27 feet to yards on the Basic Skills Review #1 and to label units for measurement problems. Students also solve a volume problem that requires converting 2 liters to 2,000 milliliters and adding it to 3,600 ml to get 5,600 ml. The review explicitly includes a "Measurement Conversion" item and an answer key that shows the conversion steps for those items.
Lesson 7
Powers of 10
Students convert units in several applied problems: they change 60 inches to 5 feet, sum pounds then convert to ounces for the cats (32 lb -> 512 oz), and convert ounces to cups to find total smoothie volume (8 oz = 1 cup, etc.). The Basic Skills Review instructs students to label units and shows step-by-step conversions (division by 12 for inches-to-feet, multiplication by 16 for pounds-to-ounces). Activity 3 has students multiply and divide decimals by powers of 10, supporting decimal-shift conversions between units (e.g., moving a decimal when converting metric units).
Lesson 8
Working With Powers of 10
The lesson has students multiply and divide numbers by powers of ten and practice moving the decimal point (e.g., 4.5 × 10,000 → 45,000; 653,000 ÷ 10^n examples). Students convert between scientific notation and standard form using large and small numbers (Try It Yourself and problems converting 3.5 × 10^6 to 3,500,000 and 2.4 × 10^5 to 240,000). Several real-world word problems present quantities with units (grams, miles, inches, light years) written in powers of ten notation, requiring students to rewrite or compute standard decimal values.
Lesson 9
Roman Numerals
Students are asked to perform direct unit conversions such as "6 pints = _______ cups" (Basic Skills Review #3) and to convert ounces to cups when solving the trail-mix problem that combines ingredients given in ounces and cups. The review answer key explicitly shows conversions used (e.g., 4 ounces = 1/2 cup, 8 ounces = 1 cup) and students are instructed to label units (e.g., include minutes or seconds). These items require students to convert among differently sized units within the same measurement system and to apply those conversions when finding a total quantity.
Unit 2: Four Operations
Lesson 4
Adding Decimals
Students complete a conversion problem in the Basic Skills Review asking "39 feet = ___ yards" and record the answer 13 yards. Students work with measurement contexts that use decimals, such as adding trail lengths in miles on the "Hiking Green Park" tasks and totaling rock weights in pounds. Students are reminded to label units when answering measurement problems.
Lesson 8
Dividing Decimals
Students are asked to perform an explicit unit conversion in Basic Skills Review #5 where they complete "39 yards = ______ feet." Students solve many measurement word problems involving units (yards of fabric, miles, ounces, pounds) such as dividing 2.8 yards among 4 pillows and finding miles per day for a multi-day drive. The lesson also instructs students to label units on answers, reinforcing attention to measurement units.
Lesson 12
Working With PEMDAS
Students are asked to convert quarts and gallons on the Basic Skills Review #6: the answer key shows "How many quarts make 7 gallons? (28 quarts)" and explains "There are 4 quarts in a gallon, so 7 x 4 = 28 quarts." The review also tells students to label units (for example, time answers should include "seconds" or "minutes"). These items require students to use a standard-unit conversion and record units with their answers.
Unit 3: Measurement
Lesson 2
Converting Units of Measurement
Students are taught rules for converting within a system (multiply when going from a larger to a smaller unit; divide when going from a smaller to a larger unit) and practice applying those rules on the "Which Operation?" and "Unit Conversions" activities. The lesson explicitly teaches metric conversions using powers of ten and decimal shifts (How the Metric System Works, King Henry mnemonic) and provides examples converting meters to millimeters and kilometers. Students complete applied, real-world problems such as choosing a 3-foot mailing tube for a 36-inch poster and computing how many ounces are in 2 tons by converting tons → pounds → ounces. Multiple practice pages, a crossword, online quizzes, and conversion tables require students to convert between customary and metric units and to use those conversions in problem solving.
Lesson 3
Measurement Problem Solving
Students convert within the same measurement system in worked examples and visuals such as 1 pint = 2 cups and 4 pints = 8 cups leading to 4 pt 13 c = 21 c, and the ounces-to-pounds example showing 82 ÷ 16 = 5 R 2 and deciding to buy 6 one-pound bags. Student activity pages ask learners to convert mixed units across customary and metric systems (e.g., 20 ft → yards and feet, 3 m 45 cm → 345 cm, 7,056 g → kg and g, 4 pt 13 c → cups). Multiple word problems require multi-step conversions and calculations (e.g., 15 candles × 140 g → total grams → compare to 2 kg; 15 balloons × 48 in → total inches → convert to yards; servings from a gallon converted to cups and ounces).
Lesson 4
Working With Time
Students practice converting units of time throughout the lesson (seconds↔minutes, minutes↔hours, hours↔days, days↔weeks, weeks↔years) and apply the multiply/divide rule for conversions. Students solve multi-step time conversion problems (e.g., 100 years → days → hours) and add/subtract mixed time units in real-world contexts (travel times, race splits, sleep minutes). Activity 2 has students convert other measurement units (feet/inches to inches, pounds to ounces, centimeters to millimeters, cups to fluid ounces, miles to feet), showing practice with length, weight, capacity, and time conversions.
Lesson 6
Unit Test
Students practice metric conversions with the "Metric Conversion" sheet and conversion chart showing kilo–hecto–deka–base–deci–centi–milli and are instructed to change units by multiplying/dividing by powers of ten and moving the decimal. Students fill conversion tables for customary and metric units (inches to feet, cups to pints, meters to kilometers, grams to milligrams) and complete many conversion exercises (e.g., 450 g = 0.45 kg, 1500 m = 1.5 km). Students solve multi-step, real-world word problems that require conversions (Beth: 2 L divided into ml per person; Mollie: total inches to yards for balloon strings; Carter: pounds to ounces to check servings; Marla: km to meters then divide by track length; muffin recipe doubling and cereal/year conversion).
Final Project
Measurement Book
Students are asked on Page 1 to explain why and how to convert between units and to provide examples. Pages 2–7 require students to list units in order, show equivalent measurements (e.g., 1 meter = 100 centimeters, 1000 grams = 1 kilogram, 2 cups = 1 pint, 3 feet = 1 yard) and include examples of converting between units using words/images or word problems. Option 2 and Page 8 require students to create measurement word problems with solutions, including two questions specifically for converting between units and an answer sheet. The directions ask students to use problem-solving strategies (adding, subtracting, multiplying, dividing) and to show real-life scenarios for conversions.
Unit 4: Adding and Subtracting Fractions
Lesson 2
Comparing and Ordering Fractions
Students are asked to work with standard unit conversions in the Basic Skills Review: problems ask them to relate 3 gallons and 8 quarts, compare 6 pints and 4 cups, and fill in 128 oz = ______ lb. A multi-step real-world problem asks students to compute total weight of 800 bricks (800 × 4.5 lb) and then convert 3 tons to pounds to find how many more pounds are needed; the answer key shows 3 tons × 2000 lb/ton = 6000 lb. The review also reminds students to label units, indicating attention to units in their answers.
Lesson 4
Working With Like Denominators
Students are asked to perform at least one explicit unit conversion in Basic Skills Review (#6): "13 yd = _____ in.", which requires converting yards to inches. Students are also asked to compare quantities with mixed customary units ("2 gallons ___ 1 quart 8 pints 2 cups"), which requires converting among gallons, quarts, pints, and cups. The materials remind students to label units (e.g., seconds or minutes), showing attention to unit-aware answers.
Lesson 8
Mixed Numbers With Unlike Denominators
Students are asked to perform explicit unit conversions in the Basic Skills Review (problem 6: "25 yd = ______ in."). Students must compare amounts given in different liquid units in a word problem (Marcy carried 1 gallon and 3 pints; Darcy carried 8 quarts) which requires converting between gallons, quarts, and pints to determine who carried more. The answer key gives converted values (25 yd = 900 in.; Darcy is the correct answer for the liquid comparison), showing that students are expected to produce converted measures.
Lesson 9
Problem Solving With Fractions
Students are asked to solve measurement conversion problems in the Basic Skills Review (e.g., Q1 asks how many 32‑fluid ounce containers are needed for 8 cups of broth; Q6 asks 8 lb = ____ oz; Q8 asks how many ounces of batter per cupcake given 15 pounds for 48 cupcakes). The directions repeatedly tell students to label units and to write out each problem, indicating attention to unit usage. The cupcake and broth problems require students to convert within the customary system and then perform additional calculations (divide to find containers or ounces per piece).
Unit 5: Multiplying Fractions
Lesson 4
Area Models to Algorithm
The Basic Skills Review explicitly includes a unit-conversion item ("Unit conversion from pounds to ounces") and a word problem about fluid ounces and containers that requires students to work with volume units. The review answer key shows students using a conversion factor (16 ounces per pound) and computing ounces and cups in solutions. The lesson also tells students to label units (for example, noting answers about time should include seconds or minutes), which reinforces attention to measurement units.
Lesson 6
Multiplying Mixed Numbers
Students are asked explicitly to convert units in Basic Skills Review #15, problem 6: "Convert 16.2 pounds to ounces." The worksheet instructions also remind students to "be sure to label units," signaling attention to unit work. The review sheet includes a variety of real-world word problems nearby that require arithmetic with units (money, distance), showing opportunities to practice context problems in the same set of activities.
Lesson 8
Finding Fractional Area
The Basic Skills Review section explicitly includes a conversion problem from quarts to cups and the answer key shows a numeric cup result, indicating students perform at least one unit conversion. The lesson also presents many measurement contexts using standard units (inches, feet, yards, meters) and real-world tasks (paint coverage, rope around a pool) where measurement units are used in problem solving.
Unit 6: Geometry
Lesson 2
Identifying and Classifying Polygons
Students complete the Basic Skills Review #17 which includes a direct unit-conversion problem: 192 ounces = 12 pounds (192 ÷ 16 = 12). Students also solve a recipe-scaling problem that multiplies a quantity in cups (1 1/3 cups × 3 1/2 batches = 4 2/3 cups), showing practice with measurement quantities and labeling units.
Lesson 6
More Work With Ordered Pairs
The Basic Skills Review includes a conversion problem ("36 yards = 1,296 inches") and the provided answer shows students multiply 36 × 3 to get feet and then × 12 to get inches, demonstrating a multi-step unit conversion within the customary system. The lesson also instructs students to "be sure to label units" and gives an example about labeling time units, prompting students to attend to units when solving problems.
Lesson 7
Coordinate Plane Pictures
The Basic Skills Review includes a unit conversion item asking students to convert quarts to cups (Item 6), and the answer key shows the conversion 1 quart = 4 cups and works out 11 quarts = 44 cups. The review instructions also remind students to label units (e.g., include seconds or minutes for time problems). These parts require students to perform at least one explicit conversion within a single measurement system.
Unit 7: Dividing Fractions
Lesson 2
Getting Ready to Divide Fractions
Students are asked to label units and complete a Basic Skills Review that includes a conversion task related to weight; the answer key explicitly shows 15 pounds = 240 ounces. The Parent Plan and Basic Skills Review note the need to include units (e.g., seconds or minutes) and present at least one conversion between pounds and ounces. These items show students encounter and record at least one standard-unit conversion during the review portion of the lesson.
Unit 8: Volume
Lesson 1
Perimeter and Area Review
Students are prompted to convert units when dimensions are given in mixed units (e.g., Problem 3: 2 yards x 3.5 feet — answer key converts 2 yards to 6 feet). Students are asked to compute perimeter and area in a different unit (Problem 5: 1 foot and 6 inches — answer key converts 1 foot to 12 inches and then finds perimeter and area in inches). The materials explicitly remind students to make sure all sides are measured in the same unit and to convert when necessary.
Lesson 3
From Area to Volume
Students complete a Basic Skills Review problem that requires converting pints to gallons when scaling a lemonade recipe; the answer key explicitly states 8 pints = 1 gallon and uses that conversion to compute the total. Students are prompted to label units on answers and complete measurement and scaling problems that require tracking units across operations. The Parent Plan mentions using centimeter cubes as models for measuring rectangular prisms, giving students exposure to a metric unit (centimeter).
Unit 9: Skills Review
Lesson 3
Measurement
Students match pairs of equivalent measures (e.g., 2 kg ↔ 2,000 g; 3.5 L ↔ 3,500 mL; 8 lb ↔ 128 oz) on the Converting Units of Measurement sheet, providing direct practice converting within metric and customary systems. Students solve Brigid's bookcase problem by converting 3 ft to 36 in and comparing to 37 in, and solve Ace's Ice Cream problem by converting 8 gallons to 32 quarts, showing conversions applied to real situations. The Parent Plan also explicitly lists the skill "Convert among different-sized standard measurement units within a given measurement system."
