2.2 Time Intervals of 5 COMMON CORE STATE STANDARD
Solve problems involving measurement and estimation 3.MD.A.1 – Measurement and Data 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 Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.A.2 – Number and Operations in Base Ten Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
BIG IDEA
Students will relate skip-counting by 5 on the clock and telling time to a continuous measurement model, the number line.
Standards of Mathematical Practice Informal Assessments □ Make sense of problems and persevere in □Math journal solving them Cruising clipboard Reason abstractly and quantitatively □ Construct viable arguments and critique the □ Foldable reasoning of others □ Checklist Model with mathematics Use appropriate tools strategically Exit ticket □ Attend to precision Response Look for and make sure of structure Boards □ Look for and express regularity in repeated reasoning Problem Set Class Discussion
PREPARING FOR THE ACTIVITY MATERIALS □ Photocopy Tape Diagram and 2 Clocks Analog clock Template back to back. Response boards Tape Diagram 2 Clocks Template Centimeter ruler Problem Set 2.2 Exit Ticket 2.2 VOCABULARY Interval Point Plotting Analog clock AUTOMATICITY TEACHER NOTES
Source: http://www.engageny.org/resource/grade-3-mathematics-module-2 Grade 3 Unit 2: Block 2 Procedures Group counting reviews Group Counting interpreting multiplication 1. Direct students to count forward and backward using the as repeated addition. following suggested sequences, occasionally changing the Counting by sevens, eights, sequence of the count. and nines in this activity a. Sevens to 35, emphasizing the transition of 28 to anticipates multiplication 35 using those units in Unit 3. b. Eights to 40, emphasizing the transition of 32 to 40. SETTING THE STAGE TEACHER NOTES Procedures These activities review the Grade 2 standard Tell Time on the Clock of telling and writing time to the nearest 5 minutes. It prepares students to count by 5- Display an analog clock. 1. minute in Exploring the Concept. Students 2. Let’s start at 12 and count by 5 minutes also practice group counting strategies for on the clock. Move finger from 12 to 1, multiplication in the context of time. 2, 3, 4, etc., as students count. 3. Distribute response boards. I’ll show a time on the clock. Write the time on your board. a. Show 3:05, 2:35, etc. varying the hour and 5-minute interval so that students read and write a variety of times to the nearest 5 minutes. Minute Counting 1. How many minutes are in 1 hour? (60) How do you know? (If I count each minute around the clock, I will get 60 minutes. When the minute hand moves once around the clock it is 1 hour.) 2. Let’s count by 5 minutes to 1 hour. As students count, record the minutes in a list. When students get to 60 minutes, write 1 hour next to it. 3. How many minutes are in a half-hour? (30) How do you know? (Half of 60 is 30; halfway around the clock is at the 6 which is 30 minutes). 4. Let’s count again by 5 minutes to 1 hour. This time, say half-hour when you get to 30 minutes. 5. Repeat the process using the following sequences: a. Count by 6 minutes to the hour and half hour b. Count by 3 minutes to a quarter past the hour and half hour c. 10 minutes, counting up to 1 hour d. 9 minutes, counting to 45 and Source: http://www.engageny.org/resource/grade-3-mathematics-module-2 Grade 3 Unit 2: Block 2 emphasizing the transition of 36 to 45
Today, we will explore how to measure time on a number line. EXPLORE THE CONCEPT TEACHER NOTES Procedures This problem activates prior knowledge 1. Display the following from Grade 2 about math with minutes. problem. Have students use the Twelve is a new factor. If students are RDW process to solve. Discuss unsure about how to multiply 12 groups of student responses. 5, encourage them to solve by skip- counting. They can also use the distributive property, 10 fives + 2 fives or 6 fives + 6 Christine has 12 math problems fives. Students use the solution to this for homework. It takes her 5 problem as a springboard for modeling 12 minutes to complete each intervals of 5 minutes on the number line problem. How many minutes does in the lesson. it take Christime to finish all 12 problems? 2. Distribute and display Tape Diagram in personal response boards. 3. Model the problem using the tape diagram on the template. 4. Guide discussion so that students articulate the following: the tape diagram is divided into 12 parts, each part represents the time it takes Christine to do 1 math problem, the tape diagram represents a total of 60 minutes. Part 1: Draw a number line and relate skip-counting by fives to skip-counting intervals of 5 minutes. 1. A different way to model this problem is to use a number line. Let’s use our tape diagram to help us draw a number line that represents a total of 60 minutes. 2. Draw a line a few centimeters below the tape diagram. Make it the same length as the tape diagram. Make tick marks on the number line where units are divided on the tape diagram. Model each step as students follow along. 3. What do you notice about the
Source: http://www.engageny.org/resource/grade-3-mathematics-module-2 Grade 3 Unit 2: Block 2 relationship between the tape diagram and the number line? (The lines are in the same place. They have the same number of parts). 4. What part of the tape diagram do the spaces between the tick marks represent? (The units; The time it takes to do each math problem; They each represent 5 minutes.) 5. We know from yesterday, that time doesn’t stop. It was happening before Christine started her homework, and it keeps going after she finished. To show that time is continuous, we’ll extend our number line on both sides and add arrows to it. Model as students follow. 6. Let’s label our number lines. The space between 2 tick marks represents a 5 minute interval. Write 0 under the first tick mark on the left. Then skip- count by fives. As you count, write each number under the next tick mark. Stop when you’ve labeled 60. (Model, students follow along.) 7. The space between 2 marks represents one 5 minute interval. How many minutes are in the interval from 0 to 10? From 0 to 60? From 15 to 30? (From 0 to 10 is 10 minutes, from 0 to 60 is 60 minutes, and from 15 to 30 is 15 minutes). 8. Let’s use the number line to find You need not use 1 p.m.–2 p.m. as the how many minutes it takes Christine to interval; pick an hour that’s relevant to your class. As students determine the number of do 4 math problems. Place finger at 0. 5 minute intervals on the number line, some Move to 5, 10, 15, and 20 as you count may count tick marks instead of spaces and 1 problem, 2 problems, 3 problems, 4 get an answer of 13. Watch for this problems. It takes Christine 20 minutes misconception and guide students to make a to do 4 math problems. Use the word distinction between tick marks and intervals if necessary. interval to explain to your partner how I used the number line to figure that out. Allow students to turn and talk. 9. Work with students to determine how long it takes for Christine to solve 7, 9, and 11 problems. Extend discussion by inviting students to Part 2: Use a number line to tell time to discuss whether or not 12:55 p.m. and 2:15 Source: http://www.engageny.org/resource/grade-3-mathematics-module-2 Grade 3 Unit 2: Block 2 the nearest 5 minutes within 1 hour. p.m. can be plotted on this number line. Help them reason about their answer and think 1. Distribute ruler. Use your ruler to about where the times might be plotted, draw a 12cm number line. Model as given the continuity of time. students follow. 2. How many 5 minute intervals will the number line need to represent a Activate prior knowledge about the minute total of 60 minutes? (12) hand and hour hand learned in Grade 2, Module 2. Review their difference in purpose, 3. Marking 12 equally spaced as well as in length. intervals is difficult! How can the ruler help do that? (It has 12 centimeters. The centimeters show us where to draw tick marks). 4. Use the centimeters on your ruler to draw tick marks for the number line. Model as student follow. 5. Just like on the first number line, we’ll need to show that time is continuous. Extend each side of your Problem 10 is likely to pose the biggest challenge. It requires understanding the number line and make arrows. Then difference between a.m. and p.m. This skip-count to label each 5 minute concept was introduced in Grade 2. One interval starting with 0 and ending with option would be to review it with students 60. Model while students follow along. before they begin the Problem Set. Another option would be to allow them to grapple 6. How many minutes are labeled with the question and support understanding on our number line? (60 minutes). through the Reflection. 7. How many minutes are there between 1:00pm and 2:00pm? (60 minutes) How do you know? 8. Let’s use the number line to model exactly when we will do the activities on our schedule that happen between 1:00 p.m. and 2:00 p.m. Below the 0 tick mark, write 1:00 p.m. Where would we write 2:00pm? How do you know? (Below the 60 tick mark). Have students follow as you model. 9. Now this number line shows the hour between 1:00 p.m. and 2:00 p.m. We start recess at 1:10 p.m. Is that time between 1:00 p.m. and 2:00 p.m.? 10. How will I find where 1:10 would be on this number line? (Allow students discussion to guide you to put your finger on 1:00 and move it to the right as you skip-count intervals until you
Source: http://www.engageny.org/resource/grade-3-mathematics-module-2 Grade 3 Unit 2: Block 2 reach 1:10.) 11. What are we counting by as we find 1:10? (Fives) 12. Model the process as students follow along. Draw a dot on the spot where the tick mark and number line make cross and label it R for recess. The dot shows the location of a point. Finding and drawing a point is called plotting a position on the number line. 13. Guide students through the same procedure to plot other events that happen between 1:00 and 2:00 p.m. labeling points B, C, etc. 14. How does the number line you’ve labeled compare to the analog clock on the wall? (The minutes count by fives on both. The clock is like the number line wrapped in a circle). Part 3: Relate the number line to the clock and tell time to the nearest 5 minutes. 1. Distribute clock templates and display clock templates in personal boards. We counted by fives to plot minutes on a number line, and we’ll do the same on a clock. 2. How many 5-minute intervals show 15 minutes on a clock? (3 intervals) 3. We started at 0 on the number line, but a clock has no 0. Where is the starting point on a clock? (The 12). 4. Let’s count each 5-minute interval and plot a point on the clock to show 15 minutes. Model as students follow. 5. Plot 30 minutes, 45 minutes, and 55 minutes using the process above. 6. Model drawing hands on the clock with 10:20 a.m. 7. Write 9:15 a.m., 3:30 p.m., and 7:50 a.m. on the board as they would appear on a digital clock, or say the
Source: http://www.engageny.org/resource/grade-3-mathematics-module-2 Grade 3 Unit 2: Block 2 time rather than write it. Students copy each time, plot points, and draw hands to show that time. 8. Distribute Problem Set 2.2 and allow students to complete. REFLECTION TEACHER NOTES Procedures Consider allowing students to use a math journal to record their response to any of 1. Guide students in a conversation these questions. to debrief the Problem Set and process the lesson. You may choose any combination of questions to guide the discussion. a. In Problem 8, what information was important for plotting the point on the number line that matched the time shown on each clock? b. Each interval on the analog clock is labeled with the numbers 1– 12. Compare those with our labels from 0 to 60 on the number line. What do the labels represent on both tools? c. How does multiplication using units of 5 help you read or measure time? d. Students may have different answers for Problem 10 (11:25 p.m. may come before or after 11:20 a.m.). Allow students with either answer a chance to explain their thinking. e. How did our minute counting and time telling activities in today’s fluency help you with the rest of the lesson? f. Look at the number line used for Problem 2. Where do you think 5:38 would be? (This anticipates Lesson 3 by counting by fives and then ones on a number line.) 2. Distribute Exit ticket 2.2 and allow students to complete.
Source: http://www.engageny.org/resource/grade-3-mathematics-module-2 Grade 3 Unit 2: Block 2 Name: ______Date: ______
Problem Set 2.2 – page 1
Directions: Follow the directions to label the number line below.
1. Ingrid gets ready for school between 7:00 a.m. and 8:00 a.m. Label the first and last tick marks as 7:00 a.m. and 8:00 a.m.
2. Each interval represents 5 minutes. Count by fives starting at 0, or 7:00 a.m. Label 0, 5, and 10 below the number line up to 8:00 a.m.
3. Ingrid starts getting dressed at 7:10 a.m. Plot a point on the number line to represent this time. Above the point write D.
4. Ingrid starts eating breakfast at 7:35 a.m. Plot a point on the number line to represent this time. Above the point write E.
5. Ingrid starts brushing her teeth at 7:40 a.m. Plot a point on the number line to represent this time. Above the point write T.
6. Ingrid starts packing her lunch at 7:45 a.m. Plot a point on the number line to represent this time. Above the point write L.
7. Ingrid starts waiting for the bus at 7:55 a.m. Plot a point on the number line to represent this time. Above the point write W. Problem Set 2.2 – page 2
8. Label every 5 minutes below the number line shown. Draw a line from the clocks to the points on the number line showing their time. Not all the clocks have matching points.
9. Noah uses a number line to locate 5:45 p.m. Each interval is 5 minutes. The number line shows the hour from 5:00 p.m. to 6:00 p.m. Label the number line below to show his work below.
10.Tanner tells his little brother that 11:25 p.m. comes after 11:20 a.m. Do you agree with Tanner? Why or why not? Name: ______Date: ______
Exit Ticket 2.2
The number line below shows math class from 10:00 a.m. to 11:00 a.m. Use the number line to answer the following questions.
a. What time do Sprints begin? ______
b. What time do students work on the Exit Ticket? ______
c. How long is math class? ______
Name: ______Date: ______
Exit Ticket 2.2
The number line below shows math class from 10:00 a.m. to 11:00 a.m. Use the number line to answer the following questions.
a. What time do Sprints begin? ______
b. What time do students work on the Exit Ticket? ______c. How long is math class? ______
Tape Diagram
2 Clocks Template