Grade 4 - Richland Parish School Board
Grade 4
Mathematics
Unit 5: Measurement
Time Frame: Approximately five weeks
Unit Description
This unit focuses on the ability to measure and to apply knowledge of measurement to finding perimeters, areas, and volumes. Use of appropriate units and correct abbreviations and selection of appropriate tools to measure are central to this study. Conversion of units of measure within the same system to solve real-life measurement problems using all four operations and graphing to create graphs based on measurement data are also included.
Student Understandings
Students will understand how and when to use the units, tools, and abbreviations for the different measurement systems. They will identify units as customary or metric. Students will estimate and calculate the area and perimeter of shapes. Students will convert measures including length, weight, capacity, and volume within the same systems. Students will determine which graph should be used based on measurement data.
Guiding Questions
1. Can students recognize, select, and apply appropriate measurement units, abbreviations, and tools to measurement settings?
2. Can students find the perimeters and areas of rectangular objects?
3. Can students convert measures within the same system?
4. Can students use the four operations to solve real-life measurement word problems?
5. Can students determine which graph best fits a set of data?
6. Can students graph data?
Unit 5 Grade-Level Expectations (GLEs) and Common Core State Standards (CCSS)
|Grade-Level Expectations |
|GLE # |GLE Text and Benchmarks |
|Algebra |
|15. |Write number sentences or formulas containing a variable to represent real-life problems (A-1-E) |
|19. |Solve one-step equations with whole number solutions (A-2-E) (N-4-E) |
|Measurement |
|22. |Select and use the appropriate standard units of measure, abbreviations, and tools to measure length and |
| |perimeter (i.e., in., cm, ft., yd., mile, m, km), area (i.e., square inch, square foot, square centimeter), |
| |capacity (i.e., fl. oz., cup, pt., qt., gal., l, ml), weight/mass (i.e., oz., lb., g, kg, ton), and volume |
| |(i.e., cubic cm, cubic in.) (M-2-E), (M-1-E) |
|25. |Use estimates and measurements to calculate perimeter and area of rectangular objects (including squares) in|
| |U.S. (including square feet) and metric units (M-3-E) |
|27. |Use unit conversions within the same system to solve real-life problems (e.g., 60 sec. = 1 min., 12 objects |
| |= 1 dozen, 12 in. = 1 ft., 100 cm = 1 m, 1 pt. = 2 cups) (M-4-E) (N-2-E) (M-5-E) |
|Data Analysis, Probability, and Discrete Math |
|36. |Analyze, describe, interpret, and construct various types of charts and graphs using appropriate titles, |
| |axis labels, scales, and legends (D-2-E) (D-1-E) |
|CCSS for Mathematical Content |
|CCSS # |CCSS Text |
|Measurement and Data |
|4.MD.2 |Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, |
| |masses of objects, and money, including problems involving simple fractions or decimals, and problems that |
| |require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement |
| |quantities using diagrams such as number line diagrams that feature a measurement scale |
|4.MD.4 |Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). Solve problems |
| |involving addition and subtraction of fractions by using information presented in line plots. |
|ELA CCSS |
|CCSS # |CCSS Text |
|Writing Standards |
|W.4.2d |Write informative/explanatory texts to examine a topic and convey ideas and information clearly. Use precise|
| |language and domain-specific vocabulary to inform about or explain the topic. |
|Speaking and Listening Standards |
|SL.4.1 |Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with |
| |diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. |
| |Follow agreed-upon rules for discussions and carry out assigned roles. |
| |Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on|
| |the remarks of others. |
| |Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the |
| |discussions. |
Sample Activities
Activity 1: Customary and Metric Measurements (GLEs: 22; CCSS: W.4.2.d)
Materials List: The Internet or encyclopedias, Customary and Metric Vocabulary Self-Awareness BLM (2 pages), Measurement Chart BLM, scissors, glue, paper, crayons, pencil, chart paper, learning logs
This activity asks students to compose questions about measurement and then research their answers. It provides them with information about measuring length, weight/mass, and capacity/volume that they will use later in the unit. A more in-depth study of each attribute will occur in subsequent activities.
Have students create a modified vocabulary self-awareness (view literacy strategy descriptions) chart in their math learning logs (view literacy strategy descriptions) using the Customary and Metric Vocabulary Self-Awareness BLM. Over the course of this unit, students will return to this chart and add new information to it. Since they will be returning often to this chart, they will have multiple opportunities to practice and extend their knowledge.
Example:
Customary and Metric Vocabulary Self Awareness Chart
|Word |+ |√ |– |Example |Descriptions |
|capacity | |√ | | |How much something can hold. |
|fluid ounce | | |– | | |
|cup |+ | | |Cup of hot chocolate |8 ounces |
Have students devise measurement questions like the following:
• How tall is the Eiffel Tower?
• How long does an anaconda grow?
• How much does a baby rhinoceros weigh?
• How much water can a pail hold?
Have students research the answers and provide customary and metric measurements for their answers (linear, weight/mass, capacity or volume measurements). Display the results of the activity with pictures and measurements on a classroom measurement chart. Arrange the pictures and measurements by attribute and put them in order from shortest to longest, lightest to heaviest, etc.
Provide students with the Measurement Chart BLM, scissors, and glue. Have students cut out each section and glue the sections into their math learning logs. This table will be used often throughout the unit as a quick reference and study guide. It should include:
• benchmarks for a better understanding of measurement sizes,
• abbreviations of each unit,
• a list of linear, weight, and capacity units by size from smallest to largest, and
• a list of conversions.
Activity 2: Customary and Metric Length Drawings (GLEs: 15, 22, 25)
Materials List: Selecting Appropriate Units of Length BLM, customary and metric rulers, pencil
Provide students with the Selecting Appropriate Units of Length BLM. Tell students that the dimensions of the rectangle in the example are 4 by 2. Have students make predictions about whether the units of the dimensions are in millimeters, centimeters, or inches. Have students measure the rectangle using both customary and metric rulers.
On the BLM, have students draw 3 rectangles for the 2 sets of dimensions --- one rectangle using inches, one using centimeters, and one using millimeters. Have students label the dimensions of each rectangle. Discuss the difference in the size of the units among inches, centimeters, and millimeters. Refer to this activity to help students see the relationship among the three as the unit progresses and to guide struggling students to select appropriate units when they are measuring the length of objects.
Have the students determine the perimeter of each of the rectangles on the BLM. Explain to students that the perimeter is the length around the outside of a figure. Have the students measure the length around the outside of each figure making sure the students measure the lengths of all four sides, not just the two sides that they used as dimensions for drawing the figures. Have students write the number sentences they used to determine the perimeter of the rectangles. Have students look at each figure to determine if there is any pattern in the number sentences (length + width + length + width = perimeter or length + length + width + width = perimeter). Ask students to write the formula for finding the perimeter (2 ( length + 2 ( width = perimeter). Discuss how the number of units for each figure is the same. They should see that the number for the perimeter is the same in each figure, but the difference is the units. Discuss the importance of properly labeling the units when calculating perimeter so that they avoid misconceptions.
Activity 3: Area vs. Perimeter (GLEs: 19, 25; CCSS: SL.4.1c)
Materials List: Area vs. Perimeter Anticipation-Guide BLM, square tiles, Grid Paper BLM, pencil
Provide students with the Area vs. Perimeter Anticipation-Guide BLM. An anticipation-guide (view literacy strategy descriptions) is a list of statements about a topic to be studied. Students are asked to respond to these statements before and after learning about the content. The anticipation-guide activates students’ prior knowledge and helps students set the purpose for their learning. Have the students respond to the Area vs. Perimeter Anticipation-Guide BLM statements.
Provide square tiles and the Grid Paper BLM for students to use. Give them an area measurement and have them create all the possible rectangles with that area using the square tiles. Have students draw models of the rectangles on the grid paper. After they have found all the possible rectangles with that area, have them record the dimensions and the perimeter of each shape. The purpose of this part of activity is for students to discover that rectangles with the same areas can have different perimeters. Have them repeat this activity, but this time all the rectangles must have the same perimeter. The purpose of this part of the activity is for students to discover that rectangles with the same perimeters can have different areas.
Example: If the area given is 12 square units, the possible dimensions for a rectangle with that area are 12 ( 1, 1 ( 12, 2 ( 6, 6 ( 2, 3 ( 4, 4 ( 3.
| | | | | | |
| | | | | | |
2 by 6
For 2 ( 6 or 6 ( 2 rectangles, the area is 12 sq. units. The perimeter is 16 units.
| | | | |
| | | | |
| | | | |
3 by 4
For 3 ( 4 or 4 ( 3 rectangles, the area is 12 sq. units. The perimeter is 14 units.
Have students revisit their Area vs. Perimeter Anticipation-Guide BLM throughout the activity. Discuss with students how their anticipation guide responses were different after the learning than before the learning. Discuss what conclusions they made after the activity. Use this time to clarify any lingering misconceptions about the content.
Activity 4: What’s My Capacity? (GLEs: 22, 27)
Materials List: Capacity Units BLM, scissors, variety of containers, capacity measurement tools, paper, pencil, water
Provide students with a copy of the Capacity Units BLM. Have the students cut and shuffle the cards. Have students sort them into metric and customary units and match the abbreviations to the corresponding units. Provide students with empty containers that hold a specific number of fluid ounces or milliliters (e.g., eye dropper for milliliter; cream cheese container for cup; whipping cream bottle for pint; tall, skinny milk or juice carton for quart; large water bottle for liter; and large milk jug for gallon). Make sure all labels have been removed or are covered using a permanent marker. Have the students predict which capacity card matches each container.
Provide students with standard tools to measure capacity. Have students work in pairs to find the capacity of each of the containers. Begin by having students fill the smaller tools with water and pour the water into the empty container. For example, if a student is trying to determine the capacity of the cream cheese container (cup), have the student use a liquid medicine cup marked off in ounces. Make sure the students keep track of how many times they pour water into the empty container (8 oz = 1 cup). Discuss with students if there are other tools that would be more efficient in finding the capacity of the container (the cup). Have students repeat the process with larger containers using smaller tools at first and then allowing them to use the other tools to determine the capacity. Have students compare their measurement with their conversion tables using their Measurement Chart BLM that is in their learning logs. Ask students also to check their predictions from the beginning of the activity.
Activity 5: What’s My Weight? (GLEs: 22, 27)
Materials List: Weight/Mass Units BLM, scissors, variety of objects, platform scale, paper, pencil
Provide students with a copy of the Weight/Mass Units BLM. Have the students cut and shuffle the cards. Have students sort them into metric and customary units and match the abbreviation to the corresponding unit. Provide students with a variety of objects (e.g., book, stapler, can of beans, bag of rice) that are heavy enough to be read on a platform scale. Have students work in groups to estimate the weight of the objects and then measure the objects in ounces, pounds, grams and kilograms. Working in pairs, have students find the weight of each of the objects and record the weight and unit for each object in their notebooks. Have students weigh the can of beans last. Discuss with students why the weight of the can is different from what the label says. (The can itself weighs something.) Have students brainstorm other items to which this problem would also apply.
Activity 6: Selecting the Appropriate Unit of Measurement (GLEs: 22; CCSS: SL.4.1b, SL.4.1c, SL.4.1d)
Materials List: Measurement Situation Cards BLM, scissors
Provide each student with a copy of the Measurement Situation Cards BLM. Have the students cut the cards and shuffle them.
Using a modification of Inside-Outside Circles discussion strategy (view literacy strategy descriptions), have students stand and face each other in two concentric circles. The purpose of this activity is for students to participate in a dialog about class topics. It promotes a deeper processing of the content. The inside circle faces out and the outside circle faces in. Have students take turns reading a situation card to their partners. Have students rotate and discuss how they can answer different questions about measurement situations. After students have seen several measurement situations, engage them in a discussion about how they came to their answers. Ask them why they chose the units they did and what considerations led them to their conclusions. Refer to this activity throughout the unit as students encounter various measurement activities.
Activity 7: Converting Units of Measurement – Part I (GLEs: 22, 27)
Materials List: paper clips, erasers, paper, pencils
Display a paper clip and an eraser. Ask students if they measured the length of the room with a paper clip or an eraser, which item would they use more of? (paper clips) Why? (They are smaller.) Develop the idea that the smaller the unit, the more of that unit is needed. Ask, If you measure the room in inches or feet, which unit would there be more of? (inches) Why? (They are smaller.) Discuss how when going from a big unit like a foot to a smaller unit like an inch, there will be more inches.
Have students continue to explore the relationship between larger and smaller units of measurement by using a two-column chart to record equivalent measurements. Students should make statements such as, if one foot is 12 inches, then 3 feet has to be 36 inches because there are 3 groups of 12. Have students make number line diagrams to express the same information.
Example: 12 in. or 1 ft 12 in. or 1 ft 12 in. or 1 ft
|ft |in. |
|1 |12 |
|2 |24 |
|3 |36 |
36 in. or 3 ft
Ask students by what number they need to multiply the number of feet to get the number of inches (12). Have students repeat this process for other linear, weight, capacity, and volume measurements.
Activity 8: Converting Units of Measurement – Part II (GLEs: 22, 27; CCSS: 4.MD.2)
Materials List: Converting Units Process Guide BLM, pencils
Provide each student with the Converting Units Process Guide) BLM. Process guides (view literacy strategy descriptions) scaffold students’ comprehension for new content with the intention of simulating their thinking while being involved in reading, listening, and learning new content. By prompting thinking from simple recall to connecting ideas to prior experience, students are able to focus on important information and concepts within the content and reach higher levels of comprehension.
Begin by giving students conversion problems in which they are working with conversions that do not have a remainder. For example, how many feet are in 48 inches? (4 feet) Have students complete the Converting Units Process Guide BLM, following the steps on the guide to find their answers. Discuss with the students why they need to ask themselves those questions as they go through the process guide. Provide students with multiple examples of conversions from smaller units to larger units and larger units to smaller units.
Extend the activity by giving students more difficult conversion problems. For example, Mary is 4 feet 8 inches tall. How many inches tall is Mary? Have the students use the process guide to convert the measurements. Discuss how to approach the problem since the original measurements have both feet and inches. Provide students with multiple examples of conversions from smaller units to larger units and larger units to smaller units.
Have students use the process guide to study for quizzes, homework, and other activities.
Activity 9: Measurement Word Problems (GLEs: 22, 27, CCSS: 4.MD.2)
Materials List: paper, pencils
Begin by giving students examples of addition measurement problems. For example, Mason ran for 15 minutes on Monday, 25 minutes on Tuesday, and 40 minutes on Wednesday. For how many minutes did Mason run? (80 min) What is this time in hours? (1 hour and 20 min)
Have students draw a number line to show the number of minutes that Mason ran.
15 min 25 min 40 min
Provide students with other addition problems using linear, weight, capacity, and volume measurements as well as money, time and temperature. Allow students to make diagrams or number lines to represent the measurement quantities. Extend the activity by giving them problems that include multiple units. For example, LaToya drank 2 pints and 1 cup of water before her soccer game, 3 cups of water during her game, and 1 pint of water after the game. How much water did LaToya drink? (7 pints or 14 cups) Refer students to their process guides in the previous activity if they need help converting the units.
Give students examples of measurement word problems for the other operations. Allow students to make diagrams or number lines to represent the measurement quantities. Examples are as follows:
Subtraction: A pound of apples cost $1.20. If Letitia gave the clerk a $5.00 bill, how much change would she get back? ($3.80)
Multiplication: Ahmed drove to his friend’s house for a Fourth of July celebration. He drove for 5 hours at an average speed of 62 miles per hour. How many miles did he drive? (310 miles)
Division: Lien has 27 inches of ribbon. She wants to give her ribbon to her 3 best friends so each friend gets the same amount. How many inches of ribbon does each friend get? (9 inches)
Extend the activity by giving students problems that involve multiple operations and multiple units. For example, Mario and his 2 brothers are selling lemonade. Mario bought one and a half liters, Javier bought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade did the boys sell? Have students use diagrams or number lines to represent the measurement quantities. Discuss with students that they could change the liters to milliliters first, and add all of the milliliters to get their answer. Discuss how an answer would be correct in milliliters (3,950 milliliters) or in liters and milliliters (3 liters, 950 milliliters). Provide students with multiple opportunities to solve a variety of different types of measurement word problems.
Activity 10: Test Those Measurements (GLEs: 22, 25, 27; CCSS: 4.MD.2)
Materials List: chart paper and markers, catalogs, paper, pencil
Distribute catalogs to students and have them look through the catalogs to find items that have measurements. Have students create text chains (view literacy strategy descriptions) using some of the measurements listed in the catalogs. Model a sample text chain and then have students create their own. When text chains are completed, make sure groups check for accuracy. Invite groups to exchange their text chains to solve, discuss, and clarify.
Sample Text Chain:
Student 1 – Angie was planning a party, and she was going to decorate the tables with tablecloths.
Student 2 – When she went to the store she didn’t know what size tablecloth to get.
Student 3 – She went back home and measured her table.
Student 4 – The table is 4 feet by 5 feet, so the tablecloth must be at least 4 ft. ( 5 ft. to fit over the table.
Students together – The tablecloth that she bought was 50 inches by 70 inches. Would it fit?
(Note: Students would have to look up the sizes of tablecloths.)
Students write: 4 ft. = x in., 5 ft. = x in.
Answer: Yes, because 4 ft = 48 in. and 5 ft = 60 in. A tablecloth that measures 50 in. ( 70 in. would cover a table that measures 48 in. ( 60 in.
Activity 11: Graphing Measurement Data (GLE: 36; CCSS: 4.MD.4, SL.4.1c)
Materials: Graphing Data BLM, Graphing Measurement Cards BLM, paper, pencils, rulers
Provide students with the Graphing Data BLM and introduce them to bar graphs, pictographs, line graphs, and line plots. Discuss the characteristics of each type. Ask questions such as the following to guide the discussion. Does the graph have a scale? If so, what is it? Does the graph need horizontal and vertical axes? Does the graph need a number line? Does the graph show trends? Does the graph show frequencies? Does the graph show changes over time?
Give students the Graphing Measurement Cards BLM. Have the students cut out the cards and shuffle them. Working in pairs, have students decide on the type of graph that could be used for each card. Have the students create the graph for the card. After students have had the opportunity to create several graphs, have the students present one of their graphs to the class discussing how they decided which graph to use, how they created the graph, and what the graph represents.
Sample Assessments
General Assessments
• Maintain portfolios containing samples of students’ graphic organizers, tables, grid drawings, etc.
• Record anecdotal notes on students as they complete tasks.
• Give prompts such as the ones that follow, and have students record their thoughts in their personal math journals.
o Do rectangles that have the same area also have the same perimeter? Why or why not.
o Mary has a gallon of lemonade. Does she have enough for each of the 23 children in her room to have a cup? Explain your answer.
o Terrell and Tyrisha ran a race. Terrell ran 2 miles in ¼ of an hour. Tyrisha ran 2 miles in 18 minutes. Who ran the faster? Explain your answer.
Activity-Specific Assessments
• Activity 1: Have students create a book of measurement problems about their school with questions such as:
o How long and wide are our halls?
o What is the length and width of the door to the classroom?
o What are the dimensions of each floor tile?
o How much does my math textbook weigh?
• Activity 3: Give students a variety of different grid-paper rectangles. Have students calculate the perimeter and area of each of the rectangles. Give students the perimeter and area of a rectangle and have them draw the rectangle based on the perimeter and area measurements.
• Activity 6, 7, 8, 9: Give students a variety of measurement problems using different measurement units. Have the students identify the tools, units, and abbreviations used in the problems. Make sure that some of the problems require conversions.
• Activity 11: Give students a set of measurement data. Have the students determine the type of graph to use, graph the data, and answer questions based on the data.
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