Measurement
The main focus of this unit is to introduce and explore
measurement as non-standard units can be used to measure
objects
Mass is a measure of how heavy an object is. Mass can be
measured using non-standard units. Students can make
comparison statements.
The activities and problems presented will give the teachers
opportunities to assess students’ knowledge of linear
measurement and mass. Students will be engaged in
opportunities to communicate their understandings individually
and with others, develop and apply strategies to measure objects
and make connections to prior knowledge, justify their thinking
and represent their understanding in a variety of ways.
Assessment Methods or Strategies
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Whole class/ group observations-checklists
Individual anecdotal observations- sticky notes
Individual interviews- with those who need intervention
Journals or learning logs-written communication and
representation- Class Journal on Measurement
 “Show What You Know” or Exemplar Problems to score
using a rubric from NCTM
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These outcome indicators are for grade two and will be used only for this lesson as I launch the
unit on Measurement. I will gather information of prior knowledge and use of proper vocabulary
before evaluating the outcome below.
Grade Two
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Measures length and height
using non-standard
measurements/ Compares,
Orders
Makes Statements of
Comparison using proper
mathematical language
SS2.1 Demonstrate understanding of non-standard units for linear measurement
by:
• describing the choice and appropriate use of non-standard units
• estimating
• measuring
• comparing and analyzing measurements
A Three-Part Format for Problem-Based Lessons
Lesson 1- Introduction to Linear Measurement
Curriculum Outcomes:
Shape and Space
SSK.1 Use direct comparison to compare two objects based on a single attribute, such as • length including height • mass •
volume • capacity.
a) Compare the length or height of two objects and explain how they compare using the words shorter, longer, taller, or
almost the same.
b) Compare the mass of two objects and explain how they compare using the words lighter, heavier, or almost the same.
c) Compare the volume of two objects or capacity of two containers and explain how they compare using the words less,
more, bigger, smaller, or almost the same.
SS1.1 Demonstrate an understanding of measurement as a process of comparing by:
• identifying attributes that can be compared
• ordering objects
• making statements of comparison
• filling, covering, or matching
SS2.1 Demonstrate understanding of non-standard units for linear
measurement by:
• describing the choice and appropriate use of non-standard units
• estimating
• measuring
• comparing and analyzing measurements
SS3.3. Demonstrate an understanding of linear measurement (cm and m) including:
selecting and justifying referents
generalizing the relationship between cm and m
estimating length and perimeter using referents
measuring and recording length, width, height, and perimeter
constructing 2-D shapes with a given perimeter or given lengths.
Math Word Wall:
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measurement
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non-standard unit
Materials:
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various lengths of yarn/lots of string/craft sticks/giant gingerbread man/recording
sheet
Before: Opening Warm-up “Compare Yarn Lengths”
Have students take a piece of yarn from the basket and compare their yarn length with that
of their partners. Encourage students to compare their pieces with questions and statements
such as, whose is longer? Whose is shorter? Discuss findings. Have students make statements
about their comparison findings. Share in full group.
“Samantha’s yarn is longer than my yarn. My yarn is shorter than Samantha’s yarn.”
__________________________________________________________________________
Guided Discussion
Display giant gingerbread man
ASK:
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About how many craft sticks tall do you think this gingerbread is?
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How could we measure to find out?
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Lay the cut-out on the floor.
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Lay some craft sticks out with spaces between “How’s this, have I done it right?”
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Rearrange sticks now with overlap. “How’s this, have I done it right?”
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Lay the sticks end to end in a crooked line. “How’s this, have I done it right?”
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Have a volunteer show how to place the sticks to measure you may even want to use a
metre stick to get a straight line.
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Discuss what to do when you get close to the end
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“About how many craft a stick tall is the gingerbread man? How do you know?
Tape the gingerbread man to the wall.
How tall is the gingerbread man now? How do you know? How could we measure to check?
Show a roll of yarn or string. “How could the string help us?”
Demonstrate how to record the height on line master 8. Provide students with string, scissors,
and craft sticks.
Think Pair Share:
How will you measure your height with the string? Think of the answer to yourself. Now turn
to a partner and discuss. Full group: Does anyone want to share?
How will you decide how many craft sticks you will need? Think of the answer to yourself.
Now turn to a partner and discuss. Full group: Does anyone want to share?
Are there any questions before you begin?
__________________________________________________________________________
During: STUDENTS WORK
Today you will solve a problem of measurement.
The gingerbread factory wants to build life size gingerbread cookies of the students in this
classroom. The cook needs to know how many craft sticks tall each of you are.
With a partner, you will work together to measure how tall you are in craft sticks. Begin by
measuring your height using the string.
Record your work.
Who is the tallest? Is it you, your partner or the ginger giant?
Assessment during task: Observational Notes- Assessment Master 3.2 Grade 2 Lesson 3
This is when you give the student a problem based task- work in partners or small group.
Letting go is the most important and also can be very difficult.
During this time you may want to walk around and observe and evaluate by using rubrics or
anecdotal records.
You may provide hints but not solutions.
Find out what your students KNOW, HOW THEY THINK AND HOW THEY APPROACH THE
TASK GIVEN.
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Let go!
Listen carefully.
Provide guided questions.
Observe and assess.
After: CLASS DISCOURSE
Ask students who are taller than, shorter than, and the same height as the gingerbread
giant.
Invite students to share their measurement strategies. How did you decide who is the tallest?
Be sure you have at least 20 minutes for this portion of your lesson.
This is a time for the class to show and share their ideas and to have a class discussion. Be
sure that students explain their answer. Often a child that may have made a mistake will find
and correct their own error during their explanation.
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Accept student’s solutions without evaluation.
Conduct a discussion as students justify and evaluate results and methods.
Practice/Extra Support/Extension - you may want to reinforce concepts with paper and
pencil at this time.
Journal writing or follow-up
Your job is to write a letter to the cook at the Giant
Gingerbread Factory. The cook needs to know how
many craft sticks tall each of you are in the
classroom. You may also include other information or
requests such as decorations for the gingerbread
giants.
Be creative.
How are you going to gather and organize your results
so the cook can easily read and understand the height
of each student?
What information are you going to need to get started?
What materials will you need?
*This is an individual assignment that can be evaluated using a rubric.
What criteria do you expect? You may want to establish the criteria with students before they
begin.
How could you modify this assignment for a few of your students?
Today you will be working with a partner to measure the Ginger Giant’s footprint.
You will have a variety of non-standard units to measure with.
You will need to choose one unit and estimate how many it would take to measure the
length of the Ginger Giant’s footprint. Your estimate may be different from that of your
partner’s estimate.
Record your estimate and then measure using the unit you chose. Remember you need to
use the same unit to measure the length of the footprint. Always measure twice to check
your work!!!
Continue on choosing a different unit. Always begin with an estimate.
Have Fun!
http://www.storyit.com/Borders/christginbreadmanbw.htm
Today you will solve a problem of measurement.
The gingerbread factory wants to build life size gingerbread
cookies of the students in this classroom. The cook needs to
know how many craft sticks tall each of you are.
With a partner, you will work together to measure how tall
you are in craft sticks. Begin by measuring your height
using the string.
Record your work.
Who is the tallest? Is it you, your partner or the ginger
giant?
My partner’s
name:__________
Height _________ My height ______
My partner’s
height: _________
List the heights from greatest to least.
______________ _______________ ______________
Who is the tallest? ____________________
Show how you measured and compared heights
Grade 2 Linear Measurement
SS2.1 Demonstrate understanding of non-standard units for linear measurement by:
• describing the choice and appropriate use of non-standard units
• estimating
• measuring
• comparing and analyzing measurements
SS3.3. Demonstrate an understanding of linear measurement (cm and m) including:
selecting and justifying referents
generalizing the relationship between cm and m
estimating length and perimeter using referents
measuring and recording length, width, height, and perimeter
constructing 2-D shapes with a given perimeter or given lengths.
Before: Open ended problem. This has many ways to enter the problem. It is a safe way for all students
to be a part of the discussion.
Unit: paper clip or p.c.
Desktop
Mrs.
12 p.c.
Mrs. Muir
19 p.c.
We both used paperclips. Why do you think our
measurements are not the same?
------------------------------------------Show students a paper clip. Talk with students about how they measured using this paper clip. How did
they record their unit? EX. 5 p.c. pc meaning paper clip
We labeled the unit with a symbol so that everyone would know we used the unit paper clip.
Now hand out a smaller paper clip. What would happen in Mrs. and I we asked to measure the desk
using paper clips? We would both use paper clips because we know that we need to use the same unit
in order to get the same measurement. If I used this small paper clip and Mrs. used the large paper
clip tell me about our measurements?
Grade 3:
(This is where the concept of Standard Measurement comes into the lesson. What do you think standard is? Why is it important to have
standard units?)
A centimetre is a standard unit used to measure length. It is about the length of the width of your small fingernail. Pass out base ten blocks ones
and tens. Have the students examine these math materials and ask what they notice about them?
A “one” is a cm cube. It has a length, width and height of one centimetre.
What about the “rod” or ten stick? What would the dimensions be of it? How could we use a ten rod to measure length?
Have students take out their ruler.
Demonstrate using the SMART board how to measure lining up with the zero mark on their ruler.
Pass out a worksheet for students to practice measuring using the unit centimetre.
Talk in large group their measurements.
During
Introduce a game called “Sketch the Line”
Materials needed:
Paper, cm ruler, two dice for each pair of students, pencil
Rules:
1.
2.
3.
4.
Students will be with a partner.
Roll the dice. Add the numbers.
Both players try to sketch a line that is this many cm long.
Draw a line that is the correct length below each sketch.
Use a ruler.
5. The player whose sketch is closer to the correct measurement wins 1
point.
After
Talk to the students about the game. What did they find easy? Difficult? Why?
Grade 2
During
Introduce a game called “Sketch the Line”
Materials needed:
Paper, paper clips or other non-standard units, two dice for each pair of
students, pencil
Rules:
1.
2.
3.
4.
Students will be with a partner.
Roll the dice. Add the numbers.
Both players try to sketch a line that is this many paperclips long.
Draw a line that is the correct length below each sketch.
Use a ruler.
5. The player whose sketch is closer to the correct measurement wins 1
point.
After
Talk to the students about the game. What did they find easy? Difficult? Why?
Review and practice measuring using non-standard unit
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Work with a small group of grade 2 students that may not yet have a good
understanding of estimating and measuring using non-standard units. You could
use a variety of non standard tools and have students solve a problem. They
need to grasp the important concepts such as:
- Measuring properly from one end to the other with no overlap/ spaces, etc.
- Always use the same unit when measuring
- Are your estimates close? If no, why are they so off?
- How do you record your actual measurement.
- What happens if you measure the desktop using straws (larger unit) and also
using paper clips (smaller unit)? When using a longer unit it won’t talk as
many and therefore the measurement will be a smaller number.
http://www.smartkiddies.net/resource/allocation
Some students could be working on the tasks found at this site grade 2 or 3
under linear measurement.
Paper pencil tasks of measurement
SPARKLE BOX math mats- measuring using non-standard and standard units
Next lesson Ideas- Your lesson maybe the Problem or Exemplar that you will use to
evaluate non standard units
How can I plan my lessons using the Backwards Approach?
Identify the outcomes to be learned
SS2.1 Demonstrate understanding of non-standard units for linear measurement by:
• describing the choice and appropriate use of non-standard units
• estimating
• measuring
• comparing and analyzing measurements
Now that I have listed my outcome:
Determine how the learning will be observed
What will the children do to know that the learning has occurred?
What should children do to demonstrate the understanding of the mathematical concepts,
skills, and big ideas?
What assessment tools will be the most suitable to provide evidence of student
understanding?
How can I document the children’s learning?
Create your assessment tools before you create your lesson task.
Use the NCTM rubric to evaluate this question (assessment of learning)
See attached.
Plan the learning environment and instruction
What learning opportunities and experiences should I provide to promote the learning
outcomes?
What will the learning environment look like?
What strategies do children use to access prior knowledge and continually communicate
and represent understanding?
What teaching strategies and resources will I use?
How can I differentiate the lesson to challenge all students at their learning ability? How
will I integrate technology, communication, mental math, reasoning, visualization, etc into
this lesson? (7 Processes) Look at your outcomes to see which of the processes you should
be including.
Plan your lesson here: What lesson format will you use?
BEFORE-DURING-AFTER? Math PODS?
ETC.
Before:
Begin with a think pair share activity:
This will be an evaluation tool to get a feel for how students add numbers. Are they able to
see what makes ten? It also will demonstrate/model the Think Pair Share strategy. This
activity will also have students look at the concept of ‘total’ length.
4 Units long
2 Units Long
6 Units long
I have 3 lengths of Wool.
One piece is 4 units long, another is 2 units long and my last
piece is 6 units long.
The total length of my 3 pieces is 15 units long.
I want you to agree or disagree with me and tell my why.
Tell a story about finding earthworms, etc. Tell the students that:
Mrs. Muir has found 3 earthworms. They are all different lengths. The total length of all
three earthworms is 20 units long. What might the length of Mrs. Muir’s three
earthworms?
Solve together as teacher models recording on the graphic organizer.
During:
Students will now solve a problem.
This problem is about Henry catching fish and finding
the different combinations for the total length of his
fish. What is different is the amount of fish that
Henry caught as well the total length. It is in various
levels of difficulty. Grade one students can focus on
ordering their fish from greatest length to smallest
length or the focus could be on finding various
combinations to make 10.
Name: __________ Date:________
Henry caught 4 fish.
Two were the same length and two were
different lengths. Together they measured 30
units in total length.
What could have been the length of Henry’s 4
fish?
Explain your thinking using pictures, numbers
and words.
Name: __________ Date: ________
Henry caught 2 fish.
They were different lengths.
Together they measured 20 units in total length.
What could have been the length of Henry’s 2
fish?
Explain your thinking using pictures, numbers
and words.
Assess student learning and follow up
What conclusions can be made from assessment information?
How effective have instructional strategies been?
What are the next steps for instruction?
How will the gaps in the development of understanding be addressed?
How will the children extend their learning?