Mathematics – Grade 5
Unit of Study: Measurement
Third Grading Period – Weeks 1 – 4 (17 days) CURRICULUM OVERVIEW
Big Idea / Unit RationaleUnderstanding measurement is an integral component of fifth grade mathematics. One of the primary focal points is comparing and contrasting lengths, areas, and volumes of two- or three-dimensional figures. In fifth grade, students will perform simple conversions within the same measure system, connect models for perimeter, area, and volume with their respective formulas, and select appropriate units to measure length, perimeter, area and volume. They will also solve problems involving changes in temperature and elapsed time. / Students should understand that:
· Objects may be compared to customary units of length, such as inches or yards or metric units of length, such as meters or centimeters.
· Volume and capacity are both terms for the size of 3-dimensional figures. Volume refers to the number of cubic units needed to fill a solid figure.
· The formula for volume involves multiplying the area of the base by the height.
· The basic units in the metric system are meter (length), liter (capacity), and gram (mass). The prefix used indicates the multiple of the basic unit.
· To convert larger units to smaller units, multiply; to convert larger units to smaller units, divide.
· Conversions in the metric system is like moving form one place value to another, multiplying or dividing by ten or a power of ten.
· Elapsed time is the amount of time that passes between the beginning and the end of an event.
· Fahrenheit is the customary temperature scale.
· Celsius is the metric temperature scale.
TEKS / TEKS Specificity - Intended Outcome
Concepts / 5.10 Mearsurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems. The student is expected to:
5.10(A) perform simple conversions within the same measurement system (SI (metric) or customary);
5.10(B) connect models for perimeter, area, and volume with their respective formulas; and
5.10(C) select and use appropriate units and formulas to measure length, perimeter, area, and volume.
5.11 Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius). The student is expected to:
5.11(A) solve problems involving changes in temperature; and;
5.11(B) solve problems involving elapsed time. / ” I CAN” statements highlighted in yellow should be displayed for students.
I can:
· Perform conversions within the same measurement system using models and graphic organizers (5.10A)
· Connect models for volume with the formula (5.10B)
· Select appropriate units and formulas to measure volume (5.10C)
· Solve problems involving changes in temperature (5.11A)
· Solve problems involving elapsed time (5.11B)
Skills / 5.14 Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
(A) identify and apply mathematics to everyday situations;
(B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. / I can:
· identify mathematics in everyday situations; (5.14A).
· use a problem-solving model to solve problems (5.14B).
Evidence of Learning
At least 80% of the time, students will demonstrate on paper or use models to show that they can:
1. perform simple conversions within the same measurement system
2. connect models for volume with the formula
3. select and use the appropriate units and formula to measure volume
4. solve problems involving changes in temperature
5. solve problems involving elapsed time
Mathematics – Grade 5
Unit of Study: Measurement
Third Grading Period – Weeks 1 – 4 (17 days) CURRICULUM GUIDE
Essential Questions / Essential Pre-requisite Skills· How do you change one unit of length to another?
· How do you change one unit of capacity to another?
· How do you convert customary units of weight?
· Can you think of a strategy to help covert from one metric unit to another by showing the relationship between units?
· What fraction of a liter is 750 milliliters?
· What is the relationship between hours and minutes? Between minutes and seconds?
· Would -20˚C be colder or warmer than 20˚C?
· What formula would you use to determine the volume of a rectangular prism? Why? / Grade 3
· Use linear measurement tools to estimate and measure lengths using standard units (3.11A)
· Use standard units to find the perimeter of a shape (3.11B)
· Use concrete and pictorial models of square units to determine the area of two-dimensional surfaces (3.11C)
· Identify concrete models that approximate standard units of weight/mass and use them to measure weight/mass (3.11D)
· Identify concrete models that approximate standard units for capacity and use tem to measure capacity (3.11E)
· Use concrete models that approximate cubic units to determine the volume of a given container or other three-dimensional geometric figure (3.11F)
· Use a thermometer to measure temperature (3.12A)
· Tell and write time shown on analog and digital clocks (3.12B)
Grade 4
· Estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary (4.11A)
· Perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system (4.11B)
· Use concrete models of standard cubic units to measure volume (4.11C)
· Estimate volume in cubic units (4.11D)
· Explain the difference between weight and mass (4.11E)
· Use a thermometer to measure temperature and changes in temperature (4.12A)
· Use tools such as a clock with gears or a stopwatch to solve problems involving elapsed time (4.12B)
The Teaching Plan
Instructional Model & Teacher Directions
The teacher will… / so students can…. / Resources
Holiday – MLK Day / Holiday – MLK Day / Holiday – MLK Day
Staff Development/WorkDay / Staff Development/WorkDay / Staff Development/WorkDay
Days 1-17:
Step 1: Problem Solving: Follow the Problem Solving Checklist and the strategies that were studied in the Lane County Mathematics Project. Since only 10 minutes are allotted each day for problem solving, it will take more than one day to complete the checklist. Steps 1 through 4 should be completed on 1 day and step 5 on another. Two problems will be provided for every week. The extra day can be used to extend a problem or complete a problem that took longer than two days to finish. These problems align to TEKS 5.6 and are an identified district weaknesses for 5th grade based on 2006-2008 TAKS data.
Week 1 – Reteach and review week
Week 2 – Problem Solving Task 1 Topic 11 pp. 249 # 16
Problem Solving Task 2 Topic 11 pp. 254 # 6
Week 3 – Problem Solving Task 1 Topic 11 pp. 254 # 2
Problem Solving Task 2 Topic 11 pp. 254 # 3
Week 4 – Problem Solving Task 1 Topic 11 pp. 255 # 10
Problem Solving Task 2 Topic 11 pp. 255 # 12 / Step 1: Problem Solving
· Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness (5.14B)
· Select or develop an appropriate problem-solving plan or strategy (5.14C) / Step 1: Problem Solving
· Problem Solving Checklist
· Probing Questions
· enVision Math Topic 11.
· Student math journals – students need either a spiral notebook or a section in their binder for math journal.
Days 1-3:
Reteach and review opportunity: Complete or review content from the 2nd 9 weeks of instruction. / Reteach and Review Opportunity: Complete or review content from the 2nd 9 weeks of instruction. / Reteach and Review Opportunity:
Complete or review content from the 2nd 9 weeks of instruction.
Day 4: enVison Math Topic 17 Converting Measurement Lesson 17-1
Step 2: Interactive learning:
· Give each group of students a strip of paper to measure in yards, feet, and inches.
· Have groups discuss and record the relationship between yards, feet, and inches pictorially and numerically.
· Have students work with a partner to find the relationship between 3 other linear measurements (customary).
· NOTE: Instruct students to record the relationships between the customary units of measurement using pictorial models. / Step 2: Interactive Learning
· Students will use a strip of paper and create a concrete model showing the relationship between customary units of linear measurement (5.10A).
· Students will create pictorial models showing the relationship between customary units of linear measurement (5.10A).
· Students will translate the concrete and pictorial models into number sentences that show the relationship between customary units of linear measurement (5.10A). / Step 2 Interactive Learning
· enVision Math Topic 17 Converting Measurements
· Lesson 17-1, pp. 372B
Additional Materials
· Ruler (yardstick, inch), Teaching Tool 30, two different colored markers, strips of paper 1 yard long (1 per group)
Step 3: Visual Learning and Practice:
· Show students the Visual Learning Bridge.
· Complete two exercises from the Do You Know How section and all the exercises from the Do You Understand section of the Guided Practice.
· Assign 5 problems from the Independent Practice. NOTE: As you monitor student work, ask student’s questions about what operation they would use to convert the measurement and why they choose it. See if they can talk about it in terms of the relationship from one unit of measure to another.
· Grouping students in pairs, assign 4 problems from the TAKS problem solving section. NOTE: Do not assign problem 27 or 28 as the content has not been covered yet.
· NOTE: Objective 2 TEKS 5.6 is an identified district weakness for 5th grade based on 2006-2008 TAKS data. Assign problem 1 from pp. 254 of the Student Edition during this time in place of one of the problems from the TAKS problem solving section as spiraled review.
· NOTE: E-tools can be referenced during any portion of Step 3. / Step 3: Visual Learning and Practice:
· Students will convert customary units of linear measurements to solve problems (5.10A).
· Students will identify the mathematics in everyday situations (5.14A). / Step 3 Visual Learning and Practice
· enVision Math Topic 17 Converting Measurements
· Lesson 17-1, pp. 372-273
· enVision Math Topic 11Patterns, Expressions, and Equations
Additional Resources:
· Visual Learning Animation CD
· www.pearsonsuccessnet.com
· e-Tools CD
Step 4: Differentiate/Assessment:
· Quick Check 17-1 (optional)
Suggested Homework: Note: To determine what level homework a student should receive, refer to the Differentiation section below.
Home School Connection Master pp. 19 Teacher Resource Masters Topic 17 & Leveled Homework.
Reteach, pp. 24 of Teacher Resource Masters Topic 17
Practice – Interactive Homework Workbook 17-1 or pp. 25 of Teacher Resource Masters Topic 17
Enrichment, pp. 26 of Teacher Resource Masters Topic 17 / Step 4: Differentiate/Assessment
· Students will convert customary units of linear measurements to solve problems (5.10A).
· Students will identify the mathematics in everyday situations (5.14A).
· For Differentiated Instructional Activities refer to the Differentiate section below in the Evidence of Learning. / Step 4 Differentiate/Assessment
· enVision Math Topic 17 Converting Measurements
· Lesson 17-1, pp. 373A-B
· Teacher Resource Masters Topic 17
Day 5: enVison Math Topic 17 Converting Measurements Lesson 17-2
Step 2: Interactive learning
· Using the measuring cup and empty containers have students fill in the recording sheet dealing with converting customary units of capacity.
· Have students expand with words and number sentences the relationship of equivalent units of capacity.
· Have students work with a partner to find the relationship between 3 other capacity measurements (customary). / Step 2: Interactive learning
· Students will use a liquid measuring cup and empty containers to find equivalent units of capacity (5.10A).
· Students will describe and write number sentences showing equivalent units of capacity (5.10A). / Step 2 Interactive Learning
· enVision Math Topic 17 Converting Measurements
· Lesson 17-2, pp. 374B
Additional Materials
· Interactive Learning Recording Sheet 23 (optional)
· Liquid measuring cup, empty containers (pint, quart, half-gallon, and gallon sizes), water (per group).
Step 3: Visual Learning and Practice:
· Show students the Visual Learning Bridge.
· Complete three exercises from the Do You Know How section and all the exercises from the Do You Understand section of the Guided Practice.
· Assign 6 problems from the Independent Practice. NOTE: As you monitor student work, ask student’s questions about what operation they would use to convert the measurement and why they choose it. See if they can talk about it in terms of the relationship from one unit of measure to another.
· Grouping students in pairs, assign 4 problems from the TAKS problem solving section. NOTE: Do not assign problem 29 or 31 as the content has not been covered yet.
· NOTE: Objective 2 TEKS 5.6 is an identified district weakness for 5th grade based on 2006-2008 TAKS data. Assign problem 5 from pp. 254 of the Student Edition during this time in place of one of the problems from the TAKS problem solving section as spiraled review.
· NOTE: E-tools can be referenced during any portion of Step 3. / Step 3: Visual Learning and Practice:
· Students will convert customary units of capacity measurements to solve problems (5.10A).
· Students will identify the mathematics in everyday situations (5.14A). / Step 3 Visual Learning and Practice
· enVision Math Topic 17 Converting Measurements
· Lesson 17-2, pp. 374-275
· enVision Math Topic 11 Patterns, Expressions, and Equations
Additional Resources:
· Visual Learning Animation CD
· www.pearsonsuccessnet.com
· e-Tools CD
Step 4: Differentiate/Assessment:
· Quick Check 17-2 (optional)