# SFUSD Mathematics Core Curriculum Development · PDF fileSFUSD Mathematics Core Curriculum,...

### Transcript of SFUSD Mathematics Core Curriculum Development · PDF fileSFUSD Mathematics Core Curriculum,...

1

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

SFUSD Mathematics Core Curriculum Development Project

2014–2015

Creating meaningful transformation in mathematics education

Developing learners who are independent, assertive constructors of their own understanding

2

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Grade 3

Unit 3.11 Volume and Weight

Number of Days

Lesson Reproducibles Number of Copies

Materials

½ Entry Task What Do You Know About Weight and Volume? 1 per student

3 ½

Lesson Series 1

Day ½ HW: Measuring Weight With Paperclips Day 1 HW: Weight in Kilograms Day 1 HW: Weight and Mass Worth the Weight (2 pages) Day 2 HW: Units for Measuring Day 3 HW: Reading a Digital Scale

1 per student 1 per student 1 per student 1 per student 1 per student 1 per student

Per group: Balance, Spring scale, Gram pieces (10-15), Kilogram pieces (3-5 per group), Wood chip, Plastic chip, Metal chip (From 3rd Grade Foss Kit Matter & Energy)

1 Apprentice Task

Going to the Market (2 pages) HW: Story Problems About Weight and Mass HW: Measuring Weight Part 2 (2 pages)

1 per student 1 per student 1 per student

2 Lesson Series 2

HW: Containers (2 pages) HW: Volume (2 pages)

1 per student 1 per student

Per group: Beaker, Vial, Graduated cylinder (From 3rd Grade Foss Kit Matter & Energy)

1 Expert Task Car Wash (2 pages) HW: Measurement Story Problems

1 per pair 1 per student

2 Lesson Series 3

More Punch, Please! (2 pages) HW: Solving One Step Word Problems (2 pages) Solving One Step Word Problems (2 pages) Exit Slip: Weights HW: Weight Problems (2 pages)

1 per pair 1 per student 1 per student 1 per student 1 per student

1 liter bottle per group 3-5 pieces of Construction paper per group Whiteboard - 1 per student

1 Milestone Task

Weighing and Measuring Problems Sheet 1 per student

3

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Unit Overview

Big Idea

Volume and mass are attributes that can be estimated and measured using appropriate standard units.

Unit Objectives

● Students will be able to measure and estimate liquid volumes and masses of objects using the standards units of grams, kilograms and liters. ● Students will be able to solve one-step word problems involving masses or volumes that are in the same units using addition, subtraction,

multiplication, or division.

Unit Description

In this unit, students will continue to build their understanding of measurement expanding it to include the topics of Volume and Mass. Students will find exact and estimated measurements using liters when measuring volume, and grams/kilograms when measuring weight. Students will use all four mathematical operations applying their understanding of volume and weight to solve one-step word problems.

CCSS-M Content Standards

3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same unit, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Progression of Mathematical Ideas

Prior Supporting Mathematics Current Essential Mathematics Future Mathematics

In second grade, students recognized the need for standard units of measure (centimeter and inch) and used rulers and other measurement tools with the understanding that linear measure involves an iteration of units. They recognized that the smaller the unit, the more iterations they will need to cover a given length.

Third grade is students’ first exposure to the measurement of mass and volume. Students will measure and estimate volume and mass, using grams, kilograms, and liters. They will also use multiplication, division, addition, and subtraction to solve one-step problems.

In fourth grade, students will understand the relative sizes of measurement units within one system specifically: grams, kilograms, and liters. Within this system of measurement, students will gain practice in converting units from grams to kilograms and kilograms to grams

4

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Unit Design All SFUSD Mathematics Core Curriculum Units are developed with a combination of rich tasks and lessons series. The tasks are both formative and summative assessments of student learning. The tasks are designed to address four central questions: Entry Task: What do you already know? Apprentice Task: What sense are you making of what you are learning? Expert Task: How can you apply what you have learned so far to a new situation? Milestone Task: Did you learn what was expected of you from this unit?

1/2 3 1/2 1 2 1 2 1

Total Days: 11

5

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Entry Task What Do You Know About Weight

and Volume?

Apprentice Task Going to the Market

Expert Task Car Wash

Milestone Task Weighing Objects

CCSS-M Standards

3.MD.2

3.MD.2 3.MD.2 3.MD.2

Brief Description of Task

Students will be asked to identify and explain why one object might weigh more than another and why one object holds more liquid than another. They demonstrate knowledge of appropriate tools to measure weight and volume.

Students will read scales using standard units of measurement for weight (g and kg). They will apply knowledge of scales and balances to solve one-step addition and subtraction word problems involving measurement of weight.

Students will read liquid volume using standard units of measurement for volume (L). They will solve one-step word problems involving measurement of volume using addition, subtraction, multiplication, or division.

Students will apply their knowledge of measuring in grams and liters to solve one-step word problems using multiplication, division, addition, and subtraction.

Source SFUSD Teacher Created Adapted from Engage NY Adapted from Engage NY Adapted from Braingenie.com

Lesson Series 1

Lesson Series 2

Lesson Series 3

CCSS-M Standards

3.MD.2

3.MD.2 3.MD.2

Brief Description of Lessons

Students will use nonstandard (large and small paperclips) to measure the weight of an object and discuss the importance of using standard units (grams and kilograms) to measure weight.

Students will use nonstandard units (different sized vials) to measure the volume of a liquid and discuss the importance of using standard units (liters) to measure volume.

Students will use their knowledge of weight and volume to solve one-step word problems, using addition, subtraction, division, and multiplication.

Sources

Foss Matter and Energy Unit georgiastandards.org

Foss Matter and Energy Unit Engage NY georgiastandards.org

6

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Entry Task

What Do You Know About Weight and Volume?

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Assess students’ prior knowledge in concepts of weight(how much an

object weighs and volume (how much liquid a container holds). ● Assess student knowledge of choosing appropriate tools to measure

weight and volume. CCSS-M Standards Addressed: 3.MD.2 Potential Misconceptions

● An object weighs the same if it is the same size. ● Objects are only measured linearly (1-D), just length. ● One tool is used for all measurements. ● Students might confuse the word ‘volume’ with ‘sound volume’.

Launch: ● Remind students they learned how to measure length of objects in

second grade. ● Brainstorm when they might have have measured how heavy

something is or how much liquid a container holds in real life. ● Remind students they already have some knowledge about weight and

volume from life experiences. During:

● Student complete the Entry Task individually. Closure/Extension:

● After teacher reviews entry task to assess what students already know, teacher may choose to review it as a whole class.

What Do You Know About Weight and Volume?

How will students do this?

Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. Structures for Student Learning: Academic Language Support:

Vocabulary: weight, volume, heavy, liquid, container Sentence frames: The bowling ball is heavier than the balloon because ________. The balloon is heavier than the bowling ball because ________. The swimming pool contains more liquid than the water bottle because______________. The water bottle contains more liquid because _______________.

Participation Structures (group, partners, individual, other): Partner/ Group discussion, then individual work

7

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Lesson Series #1

Lesson Series Overview: Students will use nonstandard (large and small paperclips) to measure the weight of an object and discuss the importance of using standard units (grams and kilograms) to measure weight. CCSS-M Standards Addressed: 3.MD.2 Time: 3 ½ days

Lesson Overview - Day ½ (second half after Entry Task) Resources

Description of Lesson: Students will be introduced to mass as the amount of stuff in an object. The terms we often use are heavy or light. Students will then measure objects using nonstandard units (small and large paperclips). Notes: This lesson is included in the Foss unit Matter and Energy. Materials are included in the FOSS kit. Today the focus will be on the 1st part of the Matter Lesson pgs. 140-142, parts 1-9

Matter and Energy Binder (Weighty Matters pgs. 140-142, parts 1-9) Materials: Per group: Balance, Spring scale, Gram pieces (10-15), Kilogram pieces (3-5 per group), Wood chip, Plastic chip, Metal chip (From 3rd Grade Foss Kit Matter & Energy) Homework Measuring Weight With Paperclips

Lesson Overview - Day 1 Resources

Description of Lesson: After students have had experience measuring with nonstandard units and its inefficiency, students will now learn how to measure with a standard unit and the fact that it leads into reliable, consistent answers. They will then measure with grams, and eventually create a kilogram to measure object with more mass. Notes: This lesson is included in the Foss unit Matter and Energy. Materials are included in the FOSS kit. Today the focus will be on the 1st part of the Matter Lesson pgs. 140-142

Matter and Energy Binder (Weighty Matters pgs. 143-145, parts 10-20, stop at breakpoint) Matter and Energy Foss Kit Homework Measuring Weight with Kilograms Weight and Mass

8

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Lesson Overview - Day 2 - 3 Resources

Description of Lesson: Worth the Weight: In this task, students will experiment with gram and kilogram weights. They will select objects to weigh, estimate their weight, and then use a spring scale to determine the actual weight. Day 1 – complete Part I Day 2 – complete Part II Notes: Spring Scales are available in the 4th Grade Foss Kit

https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_3_Unit6Framework.pdf TECHNOLOGY CONNECTION http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathHunt Is a link to a classroom video of this task. Teachers may want to view this video to see how one teacher implemented this task in his classroom. Homework Day 2 From Engage NY Unit 3.2 lesson 7 Units for Measuring Weight and Mass Homework Day 3 From Engage NY 3.2 Lesson 6 Reading a Digital Scale

9

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Apprentice Task

Going to the Market

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will read scales using standard units of measurement. ● Students will apply knowledge of scales and balances to solve one-

step addition and subtraction word problems involving measurement of weight.

CCSS-M Standards Addressed: 3.MD.2 Potential Misconceptions

● Students might not understand that each hash mark between numbers on a scale represent one.

● Students might not know that balancing the scale means that both sides have the same amount of weight.

Launch: Remind students they have been practicing measuring weight using nonstandard and standard units of measurement. Tell them they will be solving some real life problems involving reading the measurement of weight on a scale and solving problems with that information. During: The task should be completed in pairs with partner discussion and individually written. Closure/Extension: Have a class discussion on real life applications of weight measurement in students’ and families’ daily lives. Homework Story Problems About Weight and Mass & Measuring Weight part 2

Going to the Market

How will students do this?

Focus Standards for Mathematical Practice: 2. Reason abstractly and quantitatively. & 6. Attend to precision. Structures for Student Learning: Academic Language Support:

Vocabulary: almonds, raisins, broccoli, lettuce, carrots, balance, scale Sentence frames: She needs ____ watermelons to balance the scale because_______.

Differentiation Strategies: ● Have partners or groups discuss their ideas before students complete the task individually

Participation Structures (group, partners, individual, other): partners, individual

10

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Lesson Series #2

Lesson Series Overview: Students will use nonstandard units (different sized vials) to measure the volume of a liquid and discuss the importance of using standard units (liters) to measure volume. CCSS-M Standards Addressed: 3.MD.2 Time: 2

Lesson Overview - Day 1 Resources

Description of Lesson: In this lesson, students will estimate and measure volume using nonstandard units (vials and spoons) and standard units- liters and milliliters (beakers). Notes: Foss Matter and Energy Unit (A Matter of Volume pgs. 149-154- Parts 1-8). Do the parts until the break point.

Foss Matter and Energy Unit (A Matter of Volume pgs. 149-153- Parts 1-8). Homework Containers Adapted from EngageNY Unit 3.2 Lesson 9 Homework

Lesson Overview - Day 2 Resources

Description of Lesson: In this lesson, students will estimate and measure volume using liters and milliliters, using a syringe and graduated cylinder Notes: Delete sections 14-17. It is not necessary to teach capacity in this math unit.

Foss Matter and Energy Unit (A Matter of Volume pgs. 154-155 - Parts 9-13). Homework Volume Adapted from EngageNY Unit 3.2 Lesson 10

11

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Expert Task

Car Wash

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will determine liquid volume using standard units of

measurement. ● Students will solve one-step addition and subtraction word

problems involving measurement of volume CCSS-M Standards Addressed: 3.MD.2 Potential Misconceptions

● Students might round down instead of up when the liquid volume is between two different numbers. (For example, 2 ½ liters should be rounded up to 3 liters, not 2 liters.)

Launch: Remind students they have been practicing measuring volume using standard units of measurement. Tell them they will be solving some real life problems involving reading the measurement of liquid volume on containers and solving problems with that information. During: The task should be completed in pairs with partner discussion and individually written. Closure/Extension: Have a class discussion on real life applications of volume measurement in students’ and families’ daily lives. Homework: Measurement Story Problems worksheet

Car Wash

How will students do this?

Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 6. Reason abstractly and quantitatively. Structures for Student Learning: Academic Language Support:

Vocabulary: volume, liquid Sentence frames: One value size soaps has ____bottles of small soap because _____. I solved this problem by_________.

Differentiation Strategies: Partners may discuss how to approach the problem before writing the answers individually. Participation Structures (group, partners, individual, other): partner, individual

12

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Lesson Series #3

Lesson Series Overview: Students will use their knowledge of weight and volume to solve one-step word problems, using addition, subtraction, division, and multiplication. CCSS-M Standards Addressed: 3.MD.2 Time: 2 days

Lesson Overview - Day 1 Resources

Description of Lesson: More Punch Please: Students work with liquid volume to determine the amount of punch needed for a class party.

More Punch Please https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_3_Unit6Framework.pdf

Homework Solving One Step Word Problems From EngageNY Unit 3.2 Lesson 11

Lesson Overview - Day 2 Resources

Description of Lesson: Students will apply their knowledge of multiplication, division, subtraction, and addition to solve 1-step word problems involving weight and volume.

Lesson Adapted from Engage NY Module 2 Solving One Step Word Problems Exit Slip Homework Weight Problems From EngageNY Unit 3.2 Lesson 8

13

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Milestone Task

Weighing and Measuring

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will solve one-step measurement problems using

addition, subtraction, multiplication, and division. ● Students will measure weight in grams and volume in

liters. CCSS-M Standards Addressed: 3.MD.2 Potential Misconceptions

● The terms and abbreviations, g and L, may be confusing. ● Students may confuse the operations they should use for

each problem and forget the labels that distinguish weight and volume.

Launch: Remind students they have been practicing measuring weight and volume using grams and liters. They have also been using these measurements to solve one-step measurement problems. Tell them they will be solving some real life problems involving reading the measurement of weight on a scale and solving problems with that information. During: Students will solve the problems and explain their thinking individually. During this time, the teacher will walk around and note strategies students are using to solve their problems. Closure/Extension: Have a class discussion where students can share the strategies or misconceptions they had. Other students can explain their own strategies to clear up misconceptions. The teacher can also showcase some students’ work to model the grade-level math that was expected. This might be a good time to include a math talk based on some of the misconceptions collected during the observations and class discussion.

14

SFUSD Mathematics Core Curriculum, Grade 3, Unit 3.11: Volume and Weight, 2014–2015

Weighing and Measuring Objects

How will students do this?

Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. & 6.Attend to precision.

Structures for Student Learning: Academic Language Support:

Vocabulary: gram, weight, total, loaf/loaves, liters Sentence frames:

• The total weight is __________________. • _________ magnifying glasses would have the same weight as 1 iron. • The weight of the watering can is ___________. • I solved the problem by _____________. First, __________. Next, ____________. Then, _____________. Finally, __________.

Differentiation Strategies: 1. Have anchor charts created during the lesson, visible. 2. Can pull a small group to read text to students who are struggling with reading. 3. Post sentence frames so students can explain their thinking.

Participation Structures (group, partners, individual, other): Individual