ME3-18 Analogue Clock Faces - commondrive.pbworks.com

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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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.


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…


ME3-20 Telling Time The Hour Hand Goal: Students will identify hours on an analogue clock.



Ability to differentiate the two hands on a clock


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.


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


ME3-21 Telling Time Five-Minute Intervals Goal: Students will identify minutes (in five-minute intervals) on an analogue clock.




Skip counting by 5s


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.


ME3-22 Telling Time Putting It Together! Goal: Students will tell time (in five-minute intervals) on an analogue clock.




Skip counting by 5s


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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ME3-23 Digital Clock Faces Goal: Students will tell time (in five-minute intervals) using both digital and analogue clocks.




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


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.


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


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


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.


ME3-25 Intervals of Time Goal: Students will express time intervals in different units.



periods of 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


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


ME3-26 Estimating Time Intervals Goal: Students will estimate various time intervals.



periods of 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?


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?


ME3-27 Cumulative Review

This worksheet is a review worksheet for time and money. Review the basic concepts of money before

assigning it.


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.


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….


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.


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


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


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?


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


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.

Documents

ME3-18 Analogue Clock Faces - commondrive.pbworks.com