me3-18 analogue clock faces - commondrive.pbworks.com
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Measurement Teacher’s Guide Workbook 3:2 1 Copyright © 2007, JUMP Math For sample use only – not for sale.
ME3-18 Analogue Clock Faces Goal: Students will order the numbers on clock faces.
Prior Knowledge Required: Familiarity with clocks
Understanding of ordinal numbers
Vocabulary: clock, analogue, quarters, sequence, before, after, first, second, third
ASK: What is a clock? How do we use clocks? What does a clock measure? Record the students’ ideas.
Draw a circle on the board or on chart paper with boxes where the numbers on a clock would be. (See
below for initial example.) Ask students to tell how many numbers are usually on a clock’s face. Show
students exactly what part of the clock is referred to as its face. Explain that the clock face is divided into
four parts called quarters. The easiest way to draw a clock face is to first put the numbers 12, 3, 6, and 9 in
the proper places. Pointing at the box where the 12 should be, ask students to tell which number fits into
that spot. Have a volunteer come to the board and write in the 12. Repeat with the numbers 3, 6, and 9, in
any order.
Next, show a similar clock face where the 12 and the 6 have been added, but the 3 and the 9 are missing.
Have another volunteer insert the missing numbers.
Finally, remove all four “key” numbers and encourage a volunteer to use the preceding clocks and the clock
in the classroom (if there is one) to fill in all four missing numbers.
Now ask students what numbers come before and after the 3. Write those numbers on the clock face.
Repeat for the 6 and the 9. Ask students what comes before the 12. Fill in the 11. Now discuss with
students what number usually comes after the number 12. Most should say 13. Some will say 1, based on
their prior knowledge of clocks. Explain that the clock face shows only 12 hours and then starts again. You
may wish to explain at this point that a day consists of 24 hours and that it is divided into two periods called
a.m. and p.m. (a.m. starts at midnight and ends at noon, while p.m. starts at noon and ends at midnight).
Before moving on to the next lesson, ensure all students understand that a clock tells time sequentially—
one hour follows another.
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Measurement Teacher’s Guide Workbook 3:2 2 Copyright © 2007, JUMP Math For sample use only – not for sale.
Activities:
1. Brainstorm with students everything they know about time. Record all information on a chart.
2. Working in small groups, have students search through magazines to find and cut out pictures of
watches, clocks, timers, etc. They can use the pictures to create a collage. Remind students to give
their collage a title. Students who are ready to read and write the time could write the time shown on
each clock underneath the picture.
3. The BLM “Analogue Clock Faces” shows the clock face divided into quarters, with 15-minute intervals
noted for students who need an extra visual support.
4. http://www.learningplanet.com/act/tw/index.asp?contentid=410
In this interactive online activity, students can fill in the missing numbers on the clock face.
Extensions:
1. Students can research the origins of the clock and why it measures time in 12-hour increments.
2. Challenge students to order times on the half-hour! Show clock faces with these times: 2:30, 4:30, 1:30,
12:30.
3. Challenge students to order times on the hour and the half-hour. Clock faces might show 12:00, 1:30,
5:30, 3:00, and 11:30.
Journal:
Describe a clock (what it looks like and how it works). Draw a picture to go along with your explanation.
Measurement Teacher’s Guide Workbook 3:2 3 Copyright © 2007, JUMP Math For sample use only – not for sale.
ME3-19 Hands on an Analogue Clock Goal: Students will identify the hour and the minute hands on an analogue clock.
Prior Knowledge Required: Familiarity with a clock face
Familiarity with the hands on a clock
Vocabulary: clock face, clock hands, hour, minute
Show students a clock and draw their attention to the two hands. ASK: How are the hands the same?
How are they different? Do you know what each hand is called? You can use a graphic organizer, such
as a Venn diagram, to record students’ answers. Once all ideas have been recorded, summarize key
points for the class. Make sure students understand the key difference—the minute hand is longer than the
hour hand.
Next, show the hands at different positions on the clock, and have students identify which hand is pointing
where. Ask questions such as: Which hand is pointing at 12, minute or hour? Which hand is pointing at 3?
Now put the minute hand at the quarter hours only (12, 3, 6, and 9) and ASK: What number is the minute
hand pointing at? Once students are comfortable with these basics, show the minute hand at different five-
minute intervals. Keep the hour hand at 12 while you change the position of the minute hand.
Activity: Students can make their own clock. Each student will need a paper plate, some sturdy paper
and a paper fastener.
The plate is the face of your clock. Draw or paint the numbers on the plate. Cut out a large and a small
arrow for the hands. Use a paper fastener to affix them to the centre of the clock. The clock can be used to
show different times during this and the next lessons.
Extensions: Project:
Which non-digital clocks do not have hands? (Examples for students to investigate: hourglass, sundial,
water clock) Choose one of the clocks without hands. How does it show time? Where was it used and why?
Journal:
The hour and the minute hands are similar and different because…
Measurement Teacher’s Guide Workbook 3:2 4 Copyright © 2007, JUMP Math For sample use only – not for sale.
ME3-20 Telling Time The Hour Hand Goal: Students will identify hours on an analogue clock.
Prior Knowledge Required: Familiarity with a clock face
Familiarity with the hands on a clock
Ability to differentiate the two hands on a clock
Vocabulary: clock face, clock hands, hour, minute
Review the previous lesson. Draw two clock faces—one with the hour hand pointing at 2, and one with the
hour hand pointing at 3 (leave off the minute hand). Ask students which comes first (assuming they are
focusing only on a 12-hour period), two o’clock or three o’clock. Repeat with six o’clock and five o’clock.
Continue with more examples until students can readily identify which time comes first. Finish with twelve
o’clock and one o’clock.
Next, draw three clock faces without the minute hand, showing three, two, and one o’clock, and have
volunteers determine which came first. Ask them to order the times using 1st, 2
nd, and 3
rd. Repeat with more
sets of three times.
Remind your students that the hour hand shows the hour. Ask your students to tell you what hour it is in the
clocks you have drawn. Write the answers in two forms: “The hour is 3” and “3:00.”
ASK: How do people answer the question, What time is it? Record the answers students have heard on the
board in 2 columns—times “past the hour” and times “to the hour”
EXAMPLES:
Ten minutes after three Twenty minutes before two
Quarter past five Five to ten
Half past one Quarter to eight
Eight thirty-five
…and so on
Start with the times “past the hour.” ASK: The time is twenty minutes after three. Which hour has just
passed? (three o’clock) So the hour is 3. Is it 3:00? No, it’s after three, so the minutes are different. Where
is the hour hand pointing? Explain that the hour hand is not pointing directly at 3; it has already started
moving towards 4. Draw an analogue clock without the minute hand and with the hour hand pointing
between 3 and 4. Draw several more clock faces without the minute hand and with the hour hand pointing
between hours. Ask your students to write the hour for each time in two ways: Hour:___ and ___: .
Repeat the exercise, but draw the minute hand as well. Students do not need to write the minutes yet.
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As a challenge, you might draw several clock faces without the hands, give several times in verbal form
(e.g., five past ten) and in digital form (e.g., 4:15), and ask your students to draw the hour hand for the
times. Students can also use the clocks they created during the activity in ME3-19.
Extension: The time is ten minutes before two. Is it already two o’clock? Which hour has passed? What
is the hour?
Write the hour for these times:
Five minutes to ten
Twenty minutes before two
Fifteen before twelve
Five minutes to nine
Measurement Teacher’s Guide Workbook 3:2 6 Copyright © 2007, JUMP Math For sample use only – not for sale.
ME3-21 Telling Time Five-Minute Intervals Goal: Students will identify minutes (in five-minute intervals) on an analogue clock.
Prior Knowledge Required: Familiarity with a clock face
Familiarity with the hands on a clock
Ability to differentiate the two hands on a clock
Skip counting by 5s
Vocabulary: clock face, clock hands, hour, minute
Review skip counting by 5s. Draw a close-up of part of a clock face on the board so that students can see
the minutes clearly. Let students count the number of minutes between each pair of numbers.
Remind your students that when a minute hand moves from one number to the next, five minutes have
passed. Ask your students where the minute hand points at the round hour, that is, when it is exactly three
o’clock or four o’clock (or any o’clock). Draw a minute hand pointing at 1 and ASK: How many numbers did
the minute hand move from the round hour? How many minutes have passed since the round hour? Write
“5” outside the clock face, beside the 1, and continue moving the hand and skip counting by 5s until you
reach 60. Explain to your students that there are 60 minutes in one hour, so when one hour ends and a new
hour begins, we start back at 0 minutes.
Draw several clocks with only a minute hand pointing at different numbers. Ask your students to skip count
by 5s around the clock, writing down the minutes as they go, until they reach the position of the hand. Ask
your students to tell you how many minutes have passed since the round hour on each clock.
Draw several clocks with both hands and ask your students to tell how many minutes past the hour it is, and to write that down in this form: :45.
Activity: Each student will need two dice and a clock face with moveable hands (e.g., the play clock
made in the activity in ME3-19). Each student rolls the dice, adds the results, and points the minute hand
towards the sum. For example, if a student rolls 3 and 4, he should set the minute hand pointing at 7,
i.e. 35 minutes. Then the student writes down the minutes past the hour given by the minute hand.
Measurement Teacher’s Guide Workbook 3:2 7 Copyright © 2007, JUMP Math For sample use only – not for sale.
ME3-22 Telling Time Putting It Together! Goal: Students will tell time (in five-minute intervals) on an analogue clock.
Prior Knowledge Required: Familiarity with a clock face
Familiarity with the hands on a clock
Ability to differentiate the two hands on a clock
Skip counting by 5s
Vocabulary: clock face, clock hands, hour, minute
Review the previous two lessons. Tell your students that today they will tell both the hour and the minutes,
like grown-ups. Explain that, to tell time, we look at the hour hand first and then the minute hand. Draw
many clock faces showing various times (five-minute intervals only) and ask students to say and to write the
time. The should write the time in both digital form (using numbers) and verbal form (using words).
Encourage your students to say the time in various ways, such as “five past three,” “ten minutes after
twelve,” and “four and twenty-five minutes”.
Assessment:
What time is it? Write each time in digital and in verbal form: What time is it? Draw the hands on an analogue clock and write these times in verbal form: 12:50 2:45 1:05
Activities:
1. Each student will need two dice and a clock face with moveable hands (e.g., the play clock made in the
activity in ME3-19). The student rolls the dice, adds the results, and sets the hour hand pointing at the
sum. The student rolls the dice again, adds the results, and sets the minute hand pointing at the sum.
Then the student writes down the time. For example, if a student rolls 7 at the first roll and 9 at the
second roll, the clock should be set at 7:45.
2. Each pair of students will need a die and a clock face with moveable hands (e.g., the play clock made in
the activity in ME3-19). Player 1 rolls the die three times. He or she adds the results of the first two rolls
and writes them down as the hour, then multiplies the result of the third roll by 10 and chooses whether
or not to add 5 for the minutes. (If the third roll is 4, the minutes could be :40 or :45. If the third roll is 6,
the player should write :00 or :05 instead of :60 or :65.) Player 2 has to set the play clock to this time.
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Measurement Teacher’s Guide Workbook 3:2 8 Copyright © 2007, JUMP Math For sample use only – not for sale.
ME3-23 Digital Clock Faces Goal: Students will tell time (in five-minute intervals) using both digital and analogue clocks.
Prior Knowledge Required: Familiarity with a clock face
Familiarity with the hands on a clock
Ability to differentiate the two hands on a clock
Skip counting by 5s
Vocabulary: clock face, clock hands, hour, minute, digital, analogue
Show students an analogue and a digital clock (perhaps an alarm clock). ASK: How are these clocks
similar? How are they different?
Next, review the two ways students have learned to write time. Have volunteers write various times using
numbers (e.g., 12:00) and words (e.g., twelve o’clock). Sample times: 12:30, 12:15, 3:45, 2:50, 6:10.
Ask students to look at the digital clock face again, and to compare it to the times they’ve written. What
does the time on the digital clock face look like? (The time on the digital clock faces matches one of the
ways students have learned to write time.)
Show one o’clock on an analogue clock. Ask a volunteer to show what the time would look like on a digital
clock. Repeat with several times, to give students opportunities for practice. Then do the reverse: state and
write digital times and have students show the times on the analogue clock.
Activities:
1. Draw the following table and have students fill in the blanks.
2. On the BLM “Time: Digital Clock Faces,” students are asked to match the digital time to the
analogue clock.
3. Use the BLM “Time Memory Game” to play a game. Directions: Arrange the cards face down in a
rectangular array. Players take turns turning over pairs of cards. If the times on the cards match, the
player lays the pair aside. If the times do not match, the cards are turned face down again. The player
with the largest number of pairs wins.
1 hour ago now 1 hour later
3:15
7:45
11:30
1:45
8:00
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Extensions:
1. Ask students to calculate how much time passed between the given times (assume the times are both
a.m. or both p.m.).
a) 7:20 and 7:25 b) 10:30 and 10:45 c) 8:20 and 8:40
d) 1:10 and 1:30 e) 3:45 and 3:50 f) 2:00 and 2:20
g) 3:15 and 3:55 h) 11:05 and 11:40 i) 10:15 and 10:45
HARDER:
j) 5:40 and 6:05 k) 6:45 and 7:20 l) 8:30 and 9:20
2. At various times during the day, ask your students to record the time on the classroom analogue clock
digitally. At the end of the day, ask them to calculate the amount of time that passed between each
reading.
Literature Connection:
Telling Time: How to tell time on digital and analogue clocks by J. Older
This book introduces the how and why of analogue and digital clocks. Read this as an introduction to time
and to the relationship between digital to analogue.
Journal:
List the differences and similarities between how we record digital and analogue times.
Measurement Teacher’s Guide Workbook 3:2 10 Copyright © 2007, JUMP Math For sample use only – not for sale.
ME3-24 Timelines Goal: Students will find elapsed time using number lines.
Prior Knowledge Required: Thorough understanding of the concept of time
Ability to differentiate between long periods of time and short
periods of time
Understanding of hours and minutes
Ability to write the time
Knowledge of the number line
Vocabulary: passed, elapsed, hours, minutes
Draw this number line on the board:
Ask students to tell what they know about number lines and how they have used them in the past. (Adding,
subtracting, skip counting, and measuring are some of the possible answers.)
Draw a leap starting at nine o’clock and ending at ten o’clock:
ASK: How many hours have passed? How can you tell? Add another leap from ten o’clock to eleven o’clock
and repeat the question. Continue until students are comfortable using the number line to count the number
of hours that have passed.
Next, using the same number line, draw a leap from eleven o’clock to noon. Ask students how many hours
have passed. Add a leap to one o’clock. Repeat the question. Point out that although the numbers are not
sequential, the hours are. (The number 1 does not follow the number 12, but one o’clock comes after twelve
o’clock.) Students should focus on the number of leaps to help them determine how much time has passed.
Draw a new number line using half-hour increments. Ask how much time has passed with this leap:
Students should reply a half-hour or thirty minutes. Repeat the exercise, adding to the number of leaps
incrementally. Then use a different starting time, such as 10:30, and repeat the exercise to ensure that
students are using the leaps to help them count the half-hour increments that have passed.
9:00 10:00 11:00 12:00 1:00 2:00 3:00 4:00 5:00
9:00 10:00 11:00 12:00 1:00 2:00 3:00 4:00 5:00
9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30 1:00
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3:50 3:55 4:00 6:00 8:00 9:00 9:05 7:00 5:00
Finally, repeat the exercises with five-minute increments. Let your students tell how much time passed from
9:15 to 9:40, from 9:45 to 10:05, from 9:55 to 10:25, and so on.
Assess the understanding before proceeding to more complicated number lines. Do not continue until all
students are able to find elapsed time by counting forward using an equally divided number line.
Assessment:
Sindi played hockey from 9:45 to 10:20. How long did she play?
Draw this number line:
Tell students you want to calculate how much time passed between 3:50 and 9:05. Ask your students to
count by 5s until they get to the hour. How much time elapsed? (10 minutes) Draw a leap from 3:50 to 4:00
and label it “10 min.” Ask a volunteer to count by hours from 4:00 to 9:00. Draw another leap from 4:00 to
9:00 and label it “5 hours.” Ask another volunteer to draw a third leap from 9:00 to 9:05 and to label the arrow
“5 min.” Ask a volunteer to add up the labels to get the total time that passed from 3:50 to 9:05. Students will
need more practice with problems of this type.
SAMPLE PROBLEMS:
• Rita worked from 8:00 to 4:05. How long did she work?
• Sam’s birthday party started at 12:45 and ended at 3:10. How long was his birthday party?
Make sure all students are able to find longer period of elapsed time using number lines with leaps of
different length before proceeding to the next material.
Show 7:15 on a play clock or a clock drawn on the board. SAY: This is the time Eve wakes up. She eats
breakfast at 7:40. How much time passes between the time Eve wakes up and the time she eats breakfast?
Turn the hand slowly and ask a volunteer to count the minutes on the clock by 5s. Give your students several
practice questions, such as:
Eve brushes her teeth at 7:30 and gets to school at 8:15. How much time elapsed?
Eve arrived at school at 8:15. The math lesson started at 9:05. How much time elapsed?
Let your students solve such problems by counting by 5s or by drawing number lines marked off in five-
minute intervals. For harder questions involving times with two different hours (e.g., 4:15 and 5:35), suggest
that students use number lines. Invite volunteers to present their solutions.
9:40 9:45 9:50 9:55 10:00 10:05 10:10 10:15 10:20 10:25 10:30
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SAMPLE PROBLEMS:
• Eve put a cake in the oven at 7:55. The cake should bake for 25 minutes. When should she take the
cake out?
• The art lesson starts at 1:30 and lasts for 55 minutes. When does it end?
• The TV show is on from 8:15 till 8:55. How long is the show?
Assessment: Cyril has to catch a school bus at 8:25. He woke up at 7:40. How much time does he have before the
bus leaves?
Bonus:
A witch is cooking a potion. The potion turns purple at 3:45. Twenty minutes after it turns purple, the witch
has to add snake heads. When should the witch add the snake heads? The snake heads should stay in the
potion for 35 minutes. Then the witch should stir the potion quickly 7 times clockwise, remove the heads,
and let the potion boil for 35 minutes more. After this, the potion will be ready. When should the witch take
the cauldron from the fire?
Activity:
http://www.shodor.org/interactivate/activities/ElapsedTime/
This website illustrates skip counting in “See” mode and lets students check their own skip counting in
“Guess” mode.
Extension:
Ask students to calculate how much time passed between the given times.
a) 7:25 a.m. and 11:25 a.m. b) 10:05 a.m. and 11:45 a.m. c) 4:20 p.m. and 8:50 p.m.
d) 3:10 p.m. and 8:30 p.m. e) 1:45 a.m. and 7:50 a.m. f) 2:00 p.m. and 8:20 p.m.
g) 9:00 p.m. and 1:30 a.m. h) 11:15 a.m. and 3:15 p.m. i) 11:00 p.m. and 3:35 a.m.
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ME3-25 Intervals of Time Goal: Students will express time intervals in different units.
Prior Knowledge Required: Thorough understanding of the concept of time
Ability to differentiate between long periods of time and short
periods of time
Understanding of hours and minutes
Ability to write the time
Vocabulary: passed, hours, decade, century, centuries
Ask your students to suppose that a relative is coming to visit in two weeks and two days. How many days is
this? Students might reason as follows: A week is 7 days long, so in 2 weeks there are 7 + 7 = 14 days. The
relative is coming in two weeks and two days; since 14 + 2 = 16, the relative will arrive in 16 days. Give your
students more time intervals to express in days, such as 3 weeks and 4 days, 4 weeks and 1 day, and 6
weeks and 5 days.
Suggest that your students use models, such as dots grouped in 7s, to find out how many weeks are in 19
days. Students can draw 19 dots and circle sets of 7 dots to see that there are 2 full sets (2 weeks) and 5
dots (5 days) left over.
Ask your students to convert the following time intervals into weeks and days:
14 days 17 days 21 days 24 days 29 days 27 days
ASK: How many minutes are in one hour? In two hours? Three hours? Record the numbers in a table. Write
two time intervals and ask your students to tell which one is longer. Start with simple pairs of intervals, such
as 20 minutes and two hours, 40 minutes and one hour, 65 minutes and one hour, 60 minutes and two
hours. Continue with harder pairs, such as 90 minutes and one hour, 90 minutes and two hours, 130
minutes and two hours. Ask your students to explain how they know which interval is longer. Explain to your
students that when they compare two measurements in different units, it is convenient to convert both
measurements into smaller units. For example, to compare 145 minutes to 2 hours and 10 minutes,
students should convert the second time interval to minutes: 2 hours + 10 minutes = 120 minutes + 10
minutes = 130 minutes). As a final series of challenges, ask your students to compare more such pairs of
intervals.
SAMPLE INTERVALS:
1 hour and 40 minutes and 2 hours
3 hours and 50 minutes and 225 minutes
three periods of 45 minutes and 2 hours
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Explain to your students that longer periods of time are measured not only in years, but also in decades and
centuries. Write the singular and plural forms of “decade” and “century” on the board. Explain that a decade
is 10 years long, and a century is 100 years long. Ask your students to give an example of a period of time
that is measured in decades or in centuries (e.g., age of a country, age of a tree, time since the Middle
Ages). List several periods of time and ask your students to write them in centuries and/or decades.
SAMPLE PROBLEMS:
50 years = _____ decades 110 years = _____ decades
90 decades = _____ years = _____ centuries 1 century = _____ decades
300 years = _____ centuries = _____ decades 210 years = _____ centuries + _____
decades
Assessment:
Convert:
7 weeks = _____ days
31 days = _____ weeks and _____ days
50 decades = _____ years = _____ centuries
2 centuries = _____ decades = _____ years
500 years = _____ centuries = _____ decades
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ME3-26 Estimating Time Intervals Goal: Students will estimate various time intervals.
Prior Knowledge Required: Thorough understanding of the concept of time
Ability to differentiate between long periods of time and short
periods of time
Understanding of hours and minutes
Ability to write the time
Vocabulary: decade, century (centuries), hour, minute, second, week, month
Ask your students to name some units people use to measure time. Record the answers on the board. Ask
students which units they would use to measure these intervals of time:
• the length of Christmas holidays
• the length of summer holidays
• the age of a person
• the length of a music lesson
• the length of a movie
• the age of a baby that is not yet one month old
Next, ask students if they know what unit of measurement is used to count an amount of time smaller than a
minute. Students may say seconds, nanoseconds, milliseconds, etc. Accept all correct answers. Explain
that seconds are a very short amount of time. There are sixty seconds in one minute and sixty minutes in
one hour. Draw a long line on the board and tell student that it represents one hour. Ask a volunteer to draw
a line that represents one minute, and ask another volunteer to draw a line that represents one second. The
final drawing may look something like this:
An hour _____________________________________________________
A minute ____
A second _
Ask a volunteer to clap 5 times, to do 5 sit-ups, and to run around a desk. Measure the time each activity
takes with a stopwatch, to help students develop a better understanding of how long one second is.
Divide your students into 7 groups. Give each group a sheet of paper, and assign each group a unit for
measuring time from the vocabulary for this lesson. Ask each group to list 10 time intervals that would
normally be measured in their unit. To decide in which order the lists will be shared with the class, ask a
volunteer to order the units of time from least to greatest.
Ask your students to estimate the time it takes to do various daily activities, such as sleeping, washing,
brushing teeth, eating, studying, walking a dog, etc. To help students estimate the time, you might ask
questions like: When do you go to bed? When do you get up? How much time elapsed?
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Activities:
1. Ask students to estimate how long it will take to…
a) write 100 words
b) walk up a flight of stairs in the school
c) read a chapter of a book
d) count to 50
e) clap your hands 30 times
f) sing the national anthem
g) do 20 jumping jacks
(Students should check some of their estimates using a clock with a second hand.)
2. Students can use the BLM “Time: How Long is a Minute?” to record activities that can be done in one
minute. Students will need a stopwatch to time themselves doing various activities.
Extensions:
1. How many…
a) seconds are in a minute?
b) minutes are in an hour?
c) hours are in a day?
d) days are in a week?
e) weeks are in a month?
f) years are in a decade?
2. How many…
a) seconds are in 3 minutes?
b) minutes are in 2 hours?
3. If a ones block (in base ten materials) represents 1 year, which block would represent…
a) a decade?
b) a century?
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ME3-27 Cumulative Review
This worksheet is a review worksheet for time and money. Review the basic concepts of money before
assigning it.
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ME3-28 Area Goal: Students will measure area in non-standard units.
Prior Knowledge Required: Concept of a surface
Concepts of size (big and small)
Spatial sense
Vocabulary: surface, area, big, small
ASK: What is a surface? How would you measure the size of a surface? Record and discuss students’
ideas.
Introduce the term “area” and explain that to measure the area of a surface, you can cover it with same-
sized units, such as squares, and count them. Draw a rectangle on the board and affix some squares to it,
so that many gaps are left. Ask your students if this is a good way to cover the shape. Repeat with
overlapping squares. Is this better? Repeat with squares that cover much more space than the shape itself.
Invite volunteers to affix the squares in the right way (close to but not overlapping one another and only on
the shape).
Draw this shape on the board or on graph chart paper.
ASK: What is the area of this shape in squares? (2)
Next, draw this shape and ask what its area is.
Ask students which shape has the larger area and have them explain how they know.
Put more and more complex shapes on the board, and challenge students to find their areas. Here are
some examples (see the worksheet for more):
For the more complex shapes, students will have to keep track of the squares they have counted. Ask
students how they can keep track. They may use the reading pattern, count in rows, check boxes off as
they count and tally, etc. The more methodical they are about the process, the easier it will be to find the
area of the more complex shapes.
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Repeat the sequence of exercises above for shapes made up of triangles. For each shape, ASK: What is
the area of this shape in triangles?
Draw a shape that is not divided into squares or triangles and ask your students to estimate how many
squares might cover the shape. Let them check and record the actual area. To help your students make
good estimates, draw a shape that can be covered by squares or triangles, ask your students to estimate
the area, then affix the squares or triangles one by one and ask your students after each shape is added if
they would like to revise their estimate. Continue until the whole shape is covered.
Draw two different shapes with the same area.
Invite a student to measure the area of one of the shapes with squares. Then ask your students to estimate
and then measure the area of the second shape. Record the measurements and the estimate. Students will
see that the shapes have the same area. Now provide your students with a different measurement unit,
such as a right-angled triangle that has half the area of the square. Ask a volunteer to measure the area of
the first shape with triangles. Record the area, so that your students have an opportunity to notice the
pattern (the area in triangles is twice the area in squares). ASK: What will be the area of the second shape
in triangles? Let your students check their predictions.
Activities:
1. Guide students to name or find objects in the classroom that they can use to illustrate an understanding
of area. EXAMPLES: “The blackboard has a big area.” “The cover of this book has a smaller area
than...” “The wall has a bigger area than...”
2. Students can choose a unit of measurement and prove that one object has a bigger area than another.
They can record this in their journals. Encourage them to use some form of graphic organizer, such as
a T-table with the headings “big area” and “small area,” to record their results.
Extensions:
1. Order the two shapes in QUESTION 8 on the worksheet according to their area in triangles. Does the
order change when you measure their area in rhombuses?
2. Have students draw a square with a perimeter of 12 cubes. Ask them to find the length of each side of
the square and then the area. Have them predict whether the area of a square with perimeter 12 cubes
would be the same as the area of a rectangle with perimeter 12 cubes. Have them check their
predictions.
Journal:
Area is….
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ME3-29 Area in Square Centimetres Goal: Students will measure the area of shapes on grids in square centimetres.
Prior Knowledge Required: Concept of a surface
Area
Concepts of size (big and small)
Spatial sense
Measuring and drawing lines with a ruler
Perimeter
Vocabulary: surface, area, big, small, centimetre, square centimetre, centimetres squared (cm2),
2-dimensional, perimeter, rectangle
ASK: What units do we use to measure length? Accept all correct answers. Draw a shape on the board and
ask students what units they would use to measure its length—metres, centimetres, or kilometres. Would
they measure the length in linking cubes? Suppose they have to explain how large the rectangle is to a
person that has never seen linking cubes. Would they still use linking cubes or would they prefer a more
standard unit? Ask your students if they think that there might be a standard unit for area as well.
Explain to your students that area is often measured in units called “centimetres squared” or cm2. Show
students an example of a square centimetre, that is, a square whose sides are all 1 cm long.
Draw several rectangles and other shapes (EXAMPLE: L-shape, E-shape) on the board and subdivide them
into equal squares (or draw the shapes on a grid on the board). Label the side length of one square “1 cm”
Ask volunteers to count the number of squares in each shape and write the area in cm2.
Then draw several more rectangles and mark their sides at regular intervals, as shown below.
Ask volunteers to divide the rectangles into squares by joining the marks using a metre stick. Ask more
volunteers to calculate the area of these rectangles.
Ask students to draw their own shapes on grid paper and to find the area and perimeter for each one.
Activities:
1. Students could try to make as many shapes as possible with area 6 units (or squares) on a geoboard.
For a challenge, students could try making shapes with half squares. For an extra challenge, require
that the shapes have at least one line of symmetry. For instance, the shapes below have area 6 units
and a single line of symmetry.
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2. Students work in pairs. One student draws a shape on grid paper, and the other calculates the area and
the perimeter.
Extension: Sketch the shape below (at left) on centimetre grid paper. What is its area in cm2? (16) Now
calculate the area using a different unit: a 2 cm × 2 cm square (see below right). What is its area in these
units? What happens to your measurement of area when you double the side lengths of the square you are
measuring with? (The area measurement decreases by a factor of 4.) If the area of a shape is 20 cm2, what
would its area be in 2 cm × 2 cm squares?
2 cm × 2 cm
square unit
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ME3-30 Half Squares Goal: Students will find the area of shapes built with whole squares and half squares (i.e., triangles).
Prior Knowledge Required: Division by 2
Area
Vocabulary: area
Before the lesson, cut a square into two triangles by cutting across the diagonal. Now you have 2 congruent
right triangles whose base and height are the same length. Hold up the 2 triangles and show students that
they are congruent. Then demonstrate how you can put the triangles together to form a square. SAY: If I
know that the base and height of the triangles is 2 cm, what is the area of the square? (2 × 2 = 4 cm2) What
part of the square does each triangle cover? (half) What area does it have? (2 cm2)
Draw this shape on the board:
Tell students the square has area 1 cm2. ASK: What is the area of the whole shape? How did you figure
that out? Invite students to draw another shape with the same area.
Draw several shapes made up of whole squares and half squares (i.e., triangles) on a grid and ask students
to calculate the shapes’ area in terms of whole squares. Then draw a shape with 3 half squares and ASK:
What is the area of this shape? (one and a half squares) Ask students to draw shapes using both whole
squares and half squares. They should swap their drawings with a partner and calculate the area of their
partner’s shapes. Students can then check each others’ area calculations.
Draw several shapes made with even an number of half squares, say four. Ask your students to find the
area in triangles. ASK: If you have a shape built from four half squares, what is its area in whole squares?
What did you do to calculate the area in whole squares? (divided the number of triangles by 2) What is the
area of a shape made of 10 half squares? 200 half squares? 100 half squares and 100 full squares?
Assessment Calculate the area of the shape.
Height 2
Base 2
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Bonus:
1. Calculate the area of the shape.
2. Write your name on grid paper using only squares and half squares. What is its total area? Compare
your name with a partner’s. Whose name has the greater area? Who in the class has the name with the
greatest area? The least area?
Activities:
1. Students use geoboards or dot paper (see the BLM “Dot Paper”) to create shapes with a given area
using whole squares. Then students make shapes that include a particular number of half squares.
(EXAMPLE: Build a shape that has an area of 8 squares and contains 8 half squares.)
2. Draw a 6 × 6 quilt pattern using whole squares and half squares. Use shading or colour to create a
design on your quilt. Calculate the area of the shaded or coloured squares. VARIATION: Use different
colours and calculate the area covered by each colour separately.
Extension: If it takes Sandra two seconds to colour one (triangle or half square). How long will it
take her to colour the whole shape from Bonus 1?
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ME3-31 Puzzles and Problems ME3-32 Investigating Units of Area These are review worksheets that can be complemented with the following activities and extension.
Activities:
1. Students can make up their own problems like those in QUESTIONS 2 and 3 on worksheet ME3-31.
Partners can use graph paper or a geoboard to solve each other’s problems.
2. A rectangle has area 6 cm2 and perimeter 10 cm. What is the length of the rectangle?
Extension:
History of Measurement: An Investigation
Weights and measures are some of the earliest tools invented by humans.
Length: The first measurements were based on lengths of parts of the human body (for example, the width
of a thumb) or distances between them (for example, the distance between the end of an outstretched arm
and the chin). The Egyptian cubit was based on the length of the arm from elbow to outstretched finger tip.
Roman soldiers measured marching distances by counting paces, the distance from the heel of one foot to
the heel of the same foot when it next touched the ground.
Capacity: To compare the capacities of containers such as gourds or clay or metal vessels, they were filled
with plant seeds which were then counted.
Mass: The first weights were seeds and stones. The Egyptians and the Greeks used a wheat seed as the
smallest unit of weight. Today's carat (used to measure the mass of gems) is based on the weight of a
carob seed, used by the Arabs. The Babylonians compared the weight of an object with a set of special
stones and used different stones for weighing different things.
Standard Units
People and seeds come in different sizes. For measurements to be useful, everyone
needs to be using exactly the same unit. The units need to be standard. Often, kings
or queens decided what a standard for a measurement would be. These standards
spread through trade and commerce.
Metric System
About 200 years ago, the French created the metric system. This system of
measurement is now used throughout the world. It includes measurements for
length, capacity, volume, and weight. The metric system is based on 10s. To
change a measurement from one unit to another, you just move the decimal point.
For example, 300 centimetres = 3.00 metres.
U N
I T
S
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1. With a partner, choose a part of the body (for example, length from elbow to fingertip, length of foot) as
a non-standard unit of measure for length. Write down a description for your measurement unit and
choose a name for your unit (e.g., the “stretch”: as far as you can stretch your thumb and index finger).
Choose 5 items to measure using your unit. Each partner will estimate the length of each item in their
unit of measurement, measure each item, and record the measurement (e.g., 4 stretches). Partners
should then compare their measurements.
2. Repeat the activity in Question 1 for capacity (for example, you could measure the capacity of a
container using ones blocks or linking cubes).
3. Repeat the activity in Question 1 for mass (for example, you could measure the mass of an object using
pennies or unsharpened pencils).
Class Projects:
1. Students can each measure a single length (for example, the width of the classroom) using a non-
standard measure, such as a cubit, then compare their measurements. They can then repeat the
activity using metres and centimetres.
2. Students can bring in stones of 3 approximate sizes—large (about 3 cm wide), medium (about 1 cm
wide), and small (3–5 mm wide)—and use them to measure the mass of various items. They can
construct a simple scale using a coat hanger with small foil pie plates hung from each end.