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Lake Elsinore Unified School District

Instructional Module To Enhance the Teaching of Envision Math – CA Edition

WORK IN PROGRESS

Grade 3

Module 6 Time and Measurement

Revised September 2014

3rd Mathematics Sequence 2014-2015

Trimester Module/Topic

(based on Dana Center)

Envision Lessons Approximate Days

1st Trimester

Unit 1 Exploring Equal

Groups as Foundations for Multiplication and

Division

6-1, 6-2, 6-3,8-1,8-2, 9-1,9-2, 10-2, 14-3 Online - 4-1, 4-2, parts of 4-4 & 4-5, 5-1, 5-5, 6-2, 6-3, 7-1, 7-2, 7-5, 7-6, 8-1*

12 days

Unit 2 Developing Conceptual

Understanding of Area

Old – 18-3, 18-4, Online –4-3, 14-1,14-2,14-3,14-4,14-6

12 Days

Unit 3 Number & Base Ten

Operations Developing Strategies

for Addition and Subtraction

Old – 1-1, 1-2, 1-3, 1-6,

2-1*(intro round) All topic 3&4,

18-1(perimeter) Online- All topic 1

& 3, 2-1, 2-2, 2-3, 2-4, 2-5,

13-1 (perimeter)

15 days

Unit 4

Understanding Fractions

Old-12-1,12-2, 12-3,

Online- 9-1 to 9-6, 11-6, 11-7, 11-8

12 days

Unit 5

Using Fractions in In Measurement and

Data

Old – 12-4, 16-2 Online- 9-7 &

Review of topic 9* from unit 4, 16-1,

16-2

12 days

2nd Trimester

Unit 6 Solving Addition and Subtraction problems

involving Measurement and

Time

Old -16-7,16-8, 16-9, 17-3, 17-4 Online - 12-1, 12-2,12-3, 12-4, 12-5, 15-2,15-3

12 days

Unit 7

Understanding the Relationship Between

Old –7-2, 8-1 to 8-6, 10-1, 10-2

(review from 1) 10-3, 10-4, 10-5,

12 days

2nd Trimester

Multiplication and Division

10-6 Online only- 6-2, 6-3, 6-4,

8-1*(Rev. from 1), 8-2, 8-3, 8-4, 8-6,

8-7, 8-8 Unit 8

Investigating Patterns in Number

and Operations/Rounding

Old-2-1*(rev. from 3), 2-2,

6-5, 11-3, 11-4, 14-1, 20-5

Online only – 2-5*(rev. from 3),2-6, 2-7, 2-9, 5-2 to 5-6, 8-5, 9-8, 16-3, 16-4,

16-5

12 days

Unit 9

Developing strategies for Multiplication and

Division including Area

Old – 6-2, 14-3*(rev. from 1) 14-4, 18-3*,18-4*(rev. from 2) Online-4-1* &

4-2*(rev. from 2) 4-3, 4-4, 4-5,

6-1, 9-8, 14-3*(rev. from

2), 14-5, 14-7

12 days

Unit 10 Understanding

Equivalent Fractions

Old- 12-6, 12-7, 12-8

Online – 10-5 to 10-9

12 days

3rd Trimester

Unit 11 Comparing Fractions

Old- 12-5, 12-7 Online 10-1 to

10-4

12 days

Unit 12

Solving Problems Involving Area

6-2*(rev. from 1), 7-2, 7-3

Online-4-3*(rev. from 2), 6-1*(rev. from 9),14-5*(rev.

from 9), 14-8 to 14-10

12 days

Unit 13

Solving Problems Involving Shapes

Old- 5-5 to 5-8, 18-1, 18-2, Online – 13-2 to 13-5, 11-

1 to 11-5

12 days

Unit 14

Using Multiplication and Division to solve

Old - 14-3(rev. of 1 &9) All topic 10 review, 17-3, 17-4

12 days

Measurement Problems

Online – All of topic 15, 4-4, 4-5,

8-6*(rev. of 7) Unit 15

Demonstrating Computational

Fluency in Problem Solving

Old-7-2*(rev. of 1), 7-5, 14-4*(rev. of 9) 15-1, 15-2,

17-6 Online- 3-3 to

3-10*(rev. from 3), Review of

topics 5,6 and 8

12 days

3rd Grade Module 6 at a Glance

Some lessons may take more than one day.

Lesson Number Lesson Focus

1 Relating number line and clock

2 Time to the half and quarter hour

3 Time to the minute

4 Adding intervals of time

5 Elapsed time on a number line

6 Elapsed time on a number line

7 Mass in grams and kilograms

8 One step word problem involving mass

9 Making sense of liquid volume - metric

10 Using drawings to show liquid volume

3rd Grade Unit/Module Overview

Unit 6 – Time and Measurement

Standards –

3. MD.A1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

3. MD.A2 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 units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Materials Provided: Materials Needed: Sentence strips

Large construction or chart paper

Laminated 1” number cards (2 sets: 1-12, 0-60 by 5s) on different colored paper

General classroom or office supply items for weighing

Circus Manager paper (used over two lessons)

Balance scales w/gram and kg weights (*found in HM 3rd grade science kit)

Master with 3 number lines

Counting manipulatives (base 10 blocks, Unifix cubes, two sided counters)

Master with 1 number line

2 empty water bottles (L and .5L)

Visual aide pictures (3 Mod 6.8) Eye dropper for each student (found in HM 3rd grade science kit)

1 empty 236 mL (8 oz) water bottle for each group (label removed)

Bowl of water (1 for each group)

Optional Materials: Hula hoops (1 per group of 4-5 students), chalk, markers, hour and minute hand made of construction paper

Routines during the unit-

Hours in the day, minutes in an hour, days in a week, skip counting / multiplication (esp. by 5s)

Online lessons needed (homework) –

Reteach and Practice pages for lessons: 12-1, 12-2, 12-4, 15-3

Envision Workbook lessons needed (homework) –

Reteach and Practice pages for lessons: 16-7, 17-3, Quick Check 17-3

Connecting Mathematical Practices and Content Grade 3

The Standards for Mathematical Practice (MP) are developed throughout each grade and, together with the content standards, prescribe that students experience mathematics as a rigorous, coherent, useful, and logical subject that makes use of their ability to make sense of mathematics. The MP standards represent a picture of what it looks like for students to understand and do mathematics in the classroom and should be integrated into every mathematics lesson for all students Although the description of the MP standards remains the same at all grades, the way these standards look as students engage with and master new and more advanced mathematical ideas does change. Below are some examples of how the MP standards may be integrated into tasks appropriate for Grade 3 students. Standards for Mathematical Practice

Explanation and Examples from Mathematics Framework

MP.1 Make sense of problems and persevere in solving them.

In third grade, mathematically proficient students know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Students may use concrete objects, pictures, or drawings to help them conceptualize and solve problems, such as “Jim purchased 5 packages of muffins. Each package contained 3 muffins. How many muffins did Jim purchase?” or “Describe another situation where there would be 5 groups of 3 or 5 × 3.” Students may check their thinking by asking themselves, “Does this make sense?” Students listen to other students’ strategies and are able to make connections between various methods for a given problem.

MP.2 Reason abstractly and quantitatively.

Students recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. For example, students apply their understanding of the meaning of the equal sign as “the same as” to interpret an equation with an unknown. When given 4 × ? = 40, they might think: • 4 groups of some number is the same as 40 • 4 times some number is the same as 40 • I know that 4 groups of 10 is 40 so the unknown number is 10 • The missing factor is 10 because 4 times10 equals 40.

Teachers might ask, “How do you know” or “What is the relationship between the quantities?” to reinforce students’ reasoning and understanding.

MP. 3 Construct viable arguments and critique the reasoning of others.

Students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions that the teacher facilities by asking questions such as “How did you get that?” and “Why is that true?” Students explain their thinking to others and respond to others’ thinking. For example, after investigating patterns on the 100s chart, students might explain why the pattern makes sense.

MP.4 Model with mathematics.

Students represent problem situations in multiple ways using numbers, words (mathematical language), drawing pictures, and objects. They might also represent a problem by acting it out or by creating charts, lists, graphs, or equations. For example, students use various contexts and a variety of models (e.g., circles, squares, rectangles, fraction bars, and number lines) to represent and develop understanding of fractions. Students use models to represent both equations and story problems and can explain their thinking. They evaluate their results in the context of the situation and reflect on whether the results make sense. Students should be encouraged to answer questions, such as “What math drawing or diagram could you make and label to represent the problem?” or “What are some ways to represent the quantities?”

Connecting Mathematical Practices and Content -Grade 3

Connecting Mathematical Practices and Content Grade 3

MP.5 Use appropriate tools strategically

Mathematically proficient students consider the available tools (including drawings or estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table and determine whether they have all the possible rectangles. Students should be encouraged to answer questions such as, “Why was it helpful to use…?”

MP.6 Attend to precision.

Students develop mathematical communication skills as they use clear and precise language in their discussions with others and in their own reasoning. They are careful to specify units of measure and to state the meaning of the symbols they choose. For instance, when calculating the area of a rectangle they record the answer in square units.

MP.7 Look for and make use of structure.

Students look closely to discover a pattern or structure. For instance, students use properties of operations (e.g., commutative and distributive properties) as strategies to multiply and divide. Teachers might ask, “What do you notice when…?” or “How do you know if something is a pattern?”

MP.8 Look for and express regularity in repeated reasoning.

Students notice repetitive actions in computations and they look for “shortcut” methods. For instance, students may use the distributive property as a strategy to work with products of numbers they do know to solve products they do not know. For example, to find the product of 7 × 8, students might decompose 7 into 5 and 2 and then multiply 5 × 8 and 2 × 8 to arrive at 40 + 16 or 56. Third grade students continually evaluate their work by asking themselves, “Does this make sense?” Students should be encouraged to answer questions, such as “What is happening?”

Connecting Mathematical Practices and Content -Grade 3

Instructional Strategies Used in K-7 Instructional Modules

Taken from the CA Mathematics Framework and 5 Practices for Orchestrating

Productive Mathematics Discussions by Peg Smith and Kay Stein

POSE THE PROBLEM

Simply pose the problem, without suggesting or allowing other students to suggest any particular mathematical strategy to solve the problem.

INDEPENDENT Students work independently and quietly, often for the purpose of letting students think about their own reasoning and informal assessment.

THINK-PAIR-SHARE Students get time to think quietly, then share their thoughts with a partner and listen to their partners’ thinking.

TABLE TALK THINK-PAIR-SHARE with more than 2 students.

WHOLE GROUP Focus is on pulling the whole class together.

CONSENSUS Students share their individual ideas and come to an agreement within the group to share with the whole class.

MONITOR

Teacher pays close attention to students’ mathematical thinking and solution strategies as they work on a task, for the purpose of using their observations to decide what and whom to focus on during the class discussion that follows.

SELECT The teacher, through monitoring, selects student work samples or strategies to display or have students present.

SEQUENCE

The teacher purposefully chooses the order in which student strategies are displayed and/or discussed, often beginning with the more concrete strategies moving to more abstract.

CONNECT

The teacher helps students draw connections between their solutions/strategies and others’ solutions/strategies for the purpose of connecting their thinking to the mathematics we want them to learn

DISPLAY The teacher shows student work to the rest of the class for the purpose of allowing students to analyze the students’ strategies.

CAROUSEL-MUSEUM WALK

Each group posts sample work on the wall while students rotate around the room to analyze other students’ work. A leader from each group may, but does not need to stand near his/her own group’s work.

Grade 3 Module 6, Lesson 1

Lesson Focus Relating the clock and the number line. PLC Notes

Lesson Purpose

Students will understand that a clock is made up of two different number lines (hour and minute) in order to tell time to the nearest minute.

Content Standards


Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. ☒ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.

☒ Use appropriate tools strategically. ☐ Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials *Sentence strip (1 per student)

Give each group or student (if available) a small clock to explore and discuss. What do you know about this? (a clock, used to tell time, has hours and minutes, has numbers and hands) Can you make a clock on a straight line? (yes, a number line) Think independently and call on students for possible answers. If no one comes up with number line, direct the students to look at the numbers on a clock. Then show a ruler. How are the numbers on a clock and a ruler different? Display a blank sentence strip.

TABLE TALK How do you display the numbers on a number line?

Investigate

Materials

Laminated 1” number cards

with the numbers 1-12 on them and

another set 0-60 by 5’s

Give each group a blank sentence strip and their number cards for 1-12 and 0-60 (by 5’s). Have them think of the sentence strip as 1 hour (whole). MONITOR Teacher is monitoring and clarifying (not correcting) student understanding while students are preparing their number lines for their hour number #’s 1-12( teachers remember that 0 & 12 overlap on a clock) placement. If this is an hour what else can we call it? (60 mins) If students finish early, they can add the numbers for their minute placement (0-60 counting by 5’s). When students are happy with their number placement they can write it on their sentence strip. SELECT During this time the teacher is selecting the group examples to present to class and students are preparing their presentations. As students make presentations discuss number spacing and why even spacing is important to show the passing of time.

Optional Practice

Quick Write: Why aren’t clocks straight like a number line?

Summarize

34T

WHOLE GROUP How does the number line relate to a clock? Pass out individual sentence strips so students can create their own time number line. THINK-PAIR-SHARE How do we find the half way point? (folding it into equal parts) Have students label this point with a line. What do we call these equal parts? (halves, 30 mins (How do you know it’s 30 mins?)) Are there any other points we can name or identify? (fourths, quarters, 15 mins) Finish labeling the number line using one color for the hours, and another color for the minutes.

Homework Take home their personal number line. Explain to someone/something (teddy bear, dog, etc.) at home why this number line relates to a clock. Write your explanation on another piece of paper or on the back of your time number line.


Lesson Focus Telling time to the half hour and quarter hour. PLC Notes

Lesson Purpose

Practice telling time to the half and quarter hour.

Content Standards


Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. ☐ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.

☒ Use appropriate tools strategically. X Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials

Previous day’s number line, small student

clocks or 3Mod 6.1c

Review the number line from the previous lesson (half & quarter). When we are talking about time, we use terms that represent the hours and the minutes like 2:00, 4:30, 7:05. There are also many other terms used with time that use fraction terms that we know. (half, quarter) POSE THE PROBLEM Ricky got a message to meet his friend at a quarter past seven for the movies. Ricky is unsure of what time to show up. How can you help Ricky figure out what time to meet his friend at the movie?

Investigate

Materials

34T

THINK-PAIR-SHARE How can they help Ricky? (divide the clock into quarters, divide into 4 equal pieces) Have 3 Mod 6.1c, small clocks, and their time number lines available for use, if needed. THINK-PAIR-SHARE What time does Ricky need to meet his friend? How do you know? MONITOR Look for ones that use the time number line, as well as, the clock model. SELECT Teacher selects partner samples to share out. Compare number line and clock models. Discuss how the half and quarter look different. Students display their reasoning for determining what time Ricky needs to meet his friend. CONNECT Teacher highlights strategies used to determine a quarter of an hour and how time connects with prior knowledge of fractions.

Optional Practice

1.) Ricky just got a new message that the movie time changed to

half past 7. What is the new time Ricky needs to meet his friend?

2.) Oh no! Another change has happened. The movie you were going to originally sold out. The next show is at a quarter to 9.

Summarize

34T

CONSENSUS Class comes to a consensus on how to determine a quarter of an hour. Connect this to the half hour and a quarter til. THINK-PAIR-SHARE Look at how the numbers are placed on the clock. How do we know where the half way and quarter points are. The two paper plate activity can be used as a teacher demonstration to show the relationship between the hours and minutes on the clock. It may also be a lesson extension based on teacher evaluation of the students’ needs. See diagram below.

Homework Online Envision page Reteach 12-1 and Practice 12-1


Lesson Focus Telling time to the minute. PLC Notes

Lesson Purpose

Practice telling time to the minute on an analog clock.

Content Standards


Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. X Construct viable arguments and critique the reasoning of others. X Model with mathematics.

☒ Use appropriate tools strategically. X Attend to precision. ☒ Look for and make use of structure. ☒ Look for and express regularity in repeated reasoning.

Introduce

Materials

34T

Today we will actively practice telling time to the minute. You can use this activity during math time or PE time. This activity will take roughly about an hour.

Investigate

Materials

Hula hoops (1 per group of 4-

5 students), chalk, markers,

hr and min hand made of construction

paper

Have students put their Hula Hoops on the playground or floor of your room (as weather permits) and start by labeling 12, 3, 6, and 9 o’clock. Instruct them to fill in the missing numbers for the hours. Allow for enough space to put the minute intervals in between each of the numbers. (To represent minutes math tiles or strips of paper can be used.) Teachers check the placement of the numbers. Teacher calls out a time and students place the hands in the corresponding spots. Group checks for consensus if the hands are in the correct positions. Make sure enough times, to the minute, are called out so that each student gets an opportunity to show the time.

Optional Practice

Students come up with their own times and place the hands on the clocks. Groups can rotate to read the other clocks.

Summarize

34T

Discuss the different tools used to tell time; hula hoops, clock, small clocks, number lines THINK-PAIR-SHARE Was there a difference in using a Hula Hoop vs. a paper clocks or a number line? Review re-teach side of 12-2 (homework). Clarify any language issues.

Homework Online Envision 12-2 re-teach and practice.


Lesson Focus Adding intervals of time. PLC Notes

Lesson Purpose

Students will be able to add time.

Content Standards


Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. ☐ Construct viable arguments and critique the reasoning of others. X Model with mathematics.

☒ Use appropriate tools strategically. X Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials

Small clocks, number lines, 3

Mod 6.4a

Review several addition and subtraction facts and 2-3 examples showing time on a clock. Work in groups to solve this problem that has more than one step. Your family went to the circus last weekend. You stood in line for 15 mins to get your tickets. It took you 5 mins to find your seat. The first part of the show was 30 mins, followed by a 15 min intermission, then the second part of the show was 40 mins. After that, you went back to your car and headed home. How long did you spend at the circus?

Morning Routines need to include: hrs in a day, mins in an hr, days in a week,

Investigate

Materials

34T

Table Talk on how to solve the problem. How would you start? What tools would you want to use and why would that tool help? In partners, work to solve the problem.

MONITOR Encourage multiple representations to confirm their results. (Do not correct if students are only putting answers in minutes) SELECT Look for students showing their answers on a clock, a number line, and computations only. Hope for students using the half and quarter hours as fractions.

SEQUENCING Basic computation (with no hour conversion), using a clock without fractional parts (recognizing a half and quarter hour), using a clock with fractional parts, then a number line, computation with hour conversion – discuss 60 mins = 1 hr DISPLAY Allow time for students to analyze for strategies. Discuss their learning.

Optional Practice

If you left your house at 6:00pm and it took you 30 mins to get to the circus. What time did you get home? Tessa spends 34 minutes washing her dog. It takes her 12 minutes to shampoo & rinse her dog. The rest of the time was spent trying to get her dog in the tub! How much time did it take Tessa to get her dog into the tub?

Summarize

Small clocks, number lines

Students should be learning: • There’s more than one way to add time (numbers, clocks, time

line). • Time is not counted up to 100. • 1 hr = 60 mins • Time can be recorded by solely minutes or hours and minutes

Demonstrate how the problem would look on a time line if no student come up with it. Circus Manager (independent practice)-save for next lesson

SBAC emphasizes number line for time problems

Homework Old Envision 16-7 (connects to morning routines- continues to next lesson)

3 Mod 6.4a Your family went to the circus last weekend. You stood in line for 15 minutes to get your tickets. It took you 5 mins. to find your seat. The first part of the show was 30 mins., followed by a 15 min intermission, then the second part of the show was 40 mins. After that, you went back to your car and headed home. How long did you spend at the circus? Your family went to the circus last weekend. You stood in line for 15 minutes to get your tickets. It took you 5 mins. to find your seat. The first part of the show was 30 mins., followed by a 15 min intermission, then the second part of the show was 40 mins. After that, you went back to your car and headed home. How long did you spend at the circus? Your family went to the circus last weekend. You stood in line for 15 minutes to get your tickets. It took you 5 mins. to find your seat. The first part of the show was 30 mins., followed by a 15 min intermission, then the second part of the show was 40 mins. After that, you went back to your car and headed home. How long did you spend at the circus?

3 Mod 6.4b Circus Manager NAME

1. Congratulations! You are the new manager for the Crazy Circus. Your first job is to inform each act the amount of time that they will perform. To do this you need to look at the schedule and calculate the elapsed time, or duration, in the table below.

ACTIVITY START TIME FINISH TIME DURATION

Ringmaster Introduction

3:00 p.m.

3:15 p.m.

Acrobatics

3:15 p.m.

3:25 p.m.

Juggling

3:25 p.m.

3:35 p.m.

Trapeze

3:35 p.m.

3:52 p.m.

Intermission

3:52 p.m.

4:10 p.m.

Clowns on Unicycles

4:10 p.m.

4:20 p.m.

Contortion

4:20 p.m.

4:34 p.m.

Tightrope

4:34 p.m.

5:07 p.m.

Farewell

5:07 p.m.

5:25 p.m.

2. How much time will the entire circus performance take, not including intermission?

© 2011 National Council of Teachers of Mathematics http://illuminations.nctm.org

http://illuminations.nctm.org/


Grade Module 6, Lesson 5

Lesson Focus Elapsed time on a number line PLC Notes

Lesson Purpose

To show elapsed time on a number line. (Use only the number line because this is the standard being addressed.)

Content Standards


Practice Standards

X Make sense of problems and persevere in solving them. ☒ Reason abstractly and quantitatively. ☐ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.

X Use appropriate tools strategically. X Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials

Circus Manager

paper from previous lesson (3 Mod 6.4b), master with 3 time lines on it (3 Mod 6.5a), master with 1 time line on it, (3 Mod 6.5b)

“In the previous lesson, you figured out the times for each performance to fit within the time schedule. Some of you may have noticed that it used the term duration on the chart. We also use the term elapsed time, or how much time has gone by.” (Adjust wording to suit teacher style) THINK-PAIR-SHARE Teacher passes back “Circus Manager” paper. All students Pair-Share their answers for accuracy. Any discrepancies should be discussed and resolved. WHOLE GROUP How can we display the information from the Circus Manager paper on a time line? (A timeline is a specialized number line to display time)

Investigate

Materials

3 Mod 6.5a

Table Talk what is a number line for time? What do you know? Whole Group share out (pull out info that it’s more than an hour) “How many hours is it?” (more than 2) “So, if it’s more than 2 hours, how many time lines will we need?” (3) “I have a tool I think we can use.” Pass out the master with 3 time lines on it. (Each number line represents 1 hour) 3 Mod 6.5a “Where would you start?” (3:00, at the top left of the first number line) Partner up to work on this assignment. Each group should figure out how to label their time lines (in increments of 5 mins) Teacher monitors groups watching for the time line being used in an unexpected way (only using 1 of the lines to represent the whole time). **Misconceptions: students mislabel the time lines not using the increments as 5 mins or not using the whole time line. Re-group and correct any labeling misconceptions. Transition group back into partners and have them continue displaying all of the activities on their time lines. As teacher monitors suggest possible use of different colors to show the activities for clarity. Teacher will select work samples to share, showing a variety of presentations. (using beginning and ending points, hopping, brackets, mountains) As students display their work, teacher encourages them to make connections between each one, looking for representations that make the data easily understood.

Optional Practice

Turn the 3 time lines into one showing all of the data. Use the 1 time line master. 3 Mod 6.5b

Summarize

34T

When time has passed from one time to another it’s called elapsed time. Time does not always start at 0. We need a way to be able to show how this time has passed. A number line is a good tool. Students share what the differences are between the Schedule Circus chart and number line.

Homework Online Envision 12-4


Lesson Focus Elapsed time problem solving strategies PLC Notes

Lesson Purpose

To expand understand of elapsed time on a number line, including starting from the ending time.

Content Standards


Practice Standards

X Make sense of problems and persevere in solving them. ☒ Reason abstractly and quantitatively. ☐ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.

X Use appropriate tools strategically. X Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials

master with 1 number line on it (3 Mod 6.5b)

“In the last lesson, we looked at recording time on a time line to show that time has passed. We called this elapsed time. Today we are going to look at what time we need to start an activity when given the time it ends.” Review how to find the duration of time when given a start and end time with the following problem. Pass out number line (3 Mod 6.5b). Table Talk Austin goes to the movies with his friend. The movie starts to 7:45 and ends at 9:17. How long did the movie last? (Accept any problem solving strategies without value judgment) Groups share out their answers. Teacher demonstrates on a number line and all students should have one at this point. POSE THE PROBLEM “If it takes Austin’s mom 24 minutes to get to the theater to pick him up, what time does she need to leave the house to get him?”

Investigate

Materials

34T

INDIVIDUALLY Using the same number line as above the teacher lets the students work on the problem. MONITOR See how students approach the problem. Do they start from the end and go backwards? Do they put mom’s drive in a different color? SELECT Subtracting the time with numbers (correct and incorrect examples), time line (showing new problem above or below prior problem), clocks (student drawn) ** Possible Misconceptions: adding the 24 minutes to the end of the movie time, adding the 24 to the start time of the movie, if subtracting they could regroup an hour to 100 mins. instead of 60 mins Sequence should not go from incorrect to correct. Samples should be displayed as a representations (all clock together), time line should be displayed last.

Optional Practice

You get to see a double feature (2 movies in a row). Each movie is 1 hr and 35 mins. It will be 8:30 pm when the second movie ends. What time did the double feature start?

Summarize

34T

Explore other ideas for solving elapsed time problems – clocks, t-chart, repeated subtraction. “We’ve looked at different ways to show elapsed time. Think-Pair-Share Which way was the easiest way for you to understand?” Give time for students to look at the samples left up to make their arguments. “In your math journals, reflect on the strategy that is the easiest for you and explain why you feel that way.” Teacher can choose to have a few students to share out.

Homework My Day (3 Mod 6.6a)


3 Mod 6.6a My Day NAME

1. Practice elapsed time by creating your own daily schedule. Fill in

your own start times for each activity. The first activity has been done for you.

ACTIVITY START TIME DURATION FINISH TIME

Breakfast

7:00 a.m.

20 minutes

7:20 a.m.

Trip to School

7:20 a.m.

School

Trip Home

Homework

Play

Dinner

Get Ready for Bed

Go to Bed

2. You need to wake up tomorrow morning at 7:00 a.m.. Using the time you go to bed as your

start time, how much time will you be sleeping tonight?



Grade 3 Module 6-7, Lesson: Mass of objects

Lesson Focus Estimate and measure masses of objects using standard units of

grams (g), kilograms (kg) PLC Notes

Lesson Purpose

To estimate and discover the mass of objects using grams and kilograms

Content Standards

MD3. 2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters.

Practice Standards

☒ Make sense of problems and persevere in solving them. ☒ Reason abstractly and quantitatively. ☐ Construct viable arguments and critique the reasoning of others. ☐ Model with mathematics.

☒ Use appropriate tools strategically. ☒ Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials: Large

construction or chart paper Classroom

items in desk or general

office supplies made available

POSE THE PROBLEM The principal told us we need to move classrooms, the custodian will move the heavier items, but we can move the lighter things. Your task is to sort classroom items into two categories of heavy and light items. TABLE TALKS Allow students to work in table groups to create a t-chart(on large construction paper or chart paper) of heavy and light items. Students should sort no more than 10 items per group. MONITOR Teacher monitors group work, posing questions and probing for explanations as to” How did you decide to place the items in the groups?”

SELECT

Select individual students to share select items and explain reasoning for the placement in the category of light and heavy. (How do you know this item is heavier than another?)

Investigate

Materials

Balance scales with gram and

kilogram weights(one per group) Available in

HM 3rd grade science kits, 3

Mod 6.7a

After sharing and discussing reasoning introduce a balance scale including the weights to the class. THINK-PAIR-SHARE: How can this tool could be used to help us in our sorting task? (students might reply: put two objects on it and see which one is heavier, use the weights to make the sides even) Distribute one balance scales to each group. Write sentence frames on the board to direct their thinking and conversation of the weight of items that they choose to weigh. _____________is lighter than _____________. _____________ is heavier than _____________________. ___________________weighs ___________grams. __________is equal to _________________grams. Distribute attached recording sheet (3 Mod 6.7a) for groups to complete as they weigh the items on the balance scale. MONITOR Teacher will monitor student work posing probing questions relating to the difference in weight among the light objects. Example: ”How are both these items considered light but this one weighs more than the other?” SELECT Select students to share and explain findings when complete. (For lesson 6.8 might want to include weighing of food items from a lunch)

Optional Practice

34T

Summarize

34T

Using examples of student’s weights on recording sheet, teacher will check and review weights of items for accuracy to demonstrate to students to proper weighing and balancing technique by showing weighing of items on a scale under the ELMO. Teacher will also review questions at the bottom of recording sheet for discussion and strategies used to solve. Use page 42-43 Reteaching and Practice 17-4 enVision workbook. Discuss and review reteaching side pg. 42 as a whole class, bring attention to the comparison of 1 kilogram equal to 1,000 grams.

Homework Envision workbook pg. 43


Lesson Focus One step word problems involving mass PLC Notes

Lesson Purpose

To develop a conceptual understanding of measuring mass.

Content Standards

MD 3.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.74

Practice Standards

☒ Make sense of problems and persevere in solving them. ☒ Reason abstractly and quantitatively. ☒ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.

☒ Use appropriate tools strategically. ☒ Attend to precision. ☒ Look for and make use of structure. ☒ Look for and express regularity in repeated reasoning.

Introduce

Materials If available, use actual

items listed for the lunch in the problem,

Balance scales (optional)

Today we are looking at packing a healthy lunch in a brown paper bag for school. Pose the problem: The manufacture says the total capacity of the lunch bag is 70 grams. I need to pack my kids’ lunch. I want to give them an apple, cookies, juice box, gogurt, sandwich, and chips. Will their bag carry all these items without breaking? If not, what items should I keep and why? (Teacher discretion: you can allow students to use scales again from previous lesson to weigh actual items you provide, or allow students to estimate weight based on what they remember from previous lesson or give students the weight of the items to work with.)

Apple is about 20g Cookies about 5g Gogurt about 7g Sandwich about 10g Chips about 4g Juice Box about 30g

Investigate

Materials

Familiar counting

manipulatives (base 10

blocks), visual aide pics (3

mod 6.8)

THINK-PAIR-SHARE or SMALL GROUP Students will work in pairs or small groups with problem solving recording sheet* or white boards to represent and solve problem using manipulative, drawings or balance scale. MONITOR Teacher will circulate the room to pose probing questions as students work on solving the problem. “What do your items add up to?” “How did you know to choose those items?” “Do you have any space left over in your bag?” “Can you substitute a different item? How did you determine it’s weight?” **Possible extension: Is your lunch a healthy lunch? What makes a healthy lunch? Misconceptions: Students may look at label on items and mistake liters for the weight of items. If they say “Yes, they will all fit” then they probably added incorrectly.

Optional Practice

What is the best way to pack their lunch bag so, none of the lunch items in the bag get damaged?

Summarize

34T

SELECT & SEQUENCE Teacher will select and sequence student answers to be shared with class. Look for different representations of answers: added items then subtract from the bag capacity, use repeated subtraction starting with the bag capacity, base 10 blocks, pictures with the weight label. Show correct and incorrect representations to allow for discussions. Things weigh different amounts. There is more than one way to measure the weight of an object. Let students know that 1 kg = 1000 g. Brainstorm what would you measure in kilograms? (Car, backpack, person, desk) “What was the easiest way to understand?”

Homework Online Envision 15-3

3 Mod 6.8

_____________________ _______________

_______________________ __________________

______________ _________________


Lesson Focus Making sense of measuring liquid volume- metric PLC Notes

Lesson Purpose

To reason about appropriate tools involving liquid measurement.

Content Standards


Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. X Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.


Introduce

Materials

2 empty water bottles (L) and

(.5L), eye dropper for

each student, 1 empty 236 mL (8 oz) water

bottle for each group with the label removed,

sharpie per group, bowl of

water per group

“We just finished measuring mass using weight. Today we are going to look at measuring volume (the liquid capacity of a container)” Pose the problem: Approximately how many eyedroppers does it take to fill up a mini water bottle? Each student in your group will fill and empty their dropper five times. Have one person tally the number of times each person empties their dropper. After everyone has emptied their dropper five times then another person will mark the bottle equal to the top of the water line then write the number of droppers it took to get to that line.

Investigate

Materials

34T

Students will take turns emptying their droppers five times each, mark their line and label how many droppers are in the bottle. While waiting for the other groups to finish, students will clean up their area putting the droppers away and dumping the extra water in the bowl. Students will draw a picture of the bottle on their white boards, indicating the current water level. Based on what they have already filled up, students will try to figure out how many total eyedroppers it will take to fill the bottle. Use picture to help. Record group estimations and post where visible. (These will be used in optional practice and summary.) MONITOR Teacher is monitoring how each group is doing. Asking probing questions “Can you find half way? Where have we done that before?” **Hope that someone takes out a ruler and measures the bottle to find the halfway point. **Misconceptions: they will give you how many more, not the total amount.

TABLE TALK How would you explain your reasoning for your group’s answer. All table members need to be prepared to present the groups findings- reach consensus. SELECT & SEQUENCE Start with estimation then, move to more concrete example for finding half way.

NOTE: Bottle shape irregularity is part of the problem solving challenge.

Optional Practice

Fast finishers can add the total numbers from the individual groups on the board.

Summarize

34T

Students present their findings and make connections between each one. Teacher acknowledges effective and ineffective strategies. Teacher also acknowledges positive group interactions. “Now that we’ve found approximately how many droppers it takes to fill a tiny water bottle let’s find out approximately how many droppers it will take to fill a .5L water bottle.” Remember the tiny bottles are not full. Note how many droppers are transferred. “Are out predictions correct?” Good T-chart opportunity. *Optional Exploration 1: Teacher pours all of the tiny bottle amounts into a .5L to see how far it fills it. * Optional Exploration 2: How many full tiny bottles will it take to fill the .5L bottle (500mL). How many would it take to fill the 1L bottle? (1000mL) Extension: Envision 16-4 Reteach and Practice (Standard)

Homework Envision 17-3 Reteach and Practice (Metric)


Lesson Focus Using drawing to show liquid volumes in word problems. PLC Notes

Lesson Purpose

Using drawing to show liquid volumes in word problems.

Content Standards


Practice Standards

☒ Make sense of problems and persevere in solving them. ☐ Reason abstractly and quantitatively. X Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.


Introduce

Materials

Pose the Problem: “You have a punch bowl that holds 2,000mL of punch. You fill four glasses with punch. Each glass holds 200mL. How much punch remains in the bowl? Show 2 different ways of how to solve this problem.”

Investigate

Materials

34T

Think-Pair-Share How can you approach this problem? What do you do first? Students work together to persevere in solving this problem. Teacher monitors partners as they work. **Probing questions: “Where did you start? How much liquid is in 4 glasses? How can you show me how much liquid has been taken away? What does that number represent? How much is used or how much is left?” Look for students showing a variety of different approaches (repeated subtraction, adding then subtracting, multiplying then subtracting, figure out how many glasses in whole bowl then subtract). Teacher selects samples that show multiple representations for the problem.

u

Optional Practice

1. Try solving this problem with base 10 blocks (picture or actual blocks) 2. How many total glasses can be filled by the amount of punch in the bowl?

Summarize

34T

Teacher calls up students to explain and make connections as their strategies show relationships between multiplication and division. Show how to transition these numbers into equal groups. 2,000mL into equal groups of 100. Then bundle as 200, skip count by 200.

Homework Envision 17-3 Quick Check

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