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Measurement UnitGrade 2

Created by:Ilianna Givelos,

Lillian Papel,Waheda Hofioni,

Sarah Gibson,Tania Decaudin-Prendergast

Overall Expectations:Grade 2: -estimate, measure and record length, perimeter, area using non-standard units and

standard units-compare, describe and order object, using attributes measured in non standard and standard units

Specific Expectations:-choose benchmarks to help them perform measurement tasks-estimate and measure length, height and distance, using standard units and non-standard units-record and represent measurements of length, height and distance in a variety of ways-select and justify the choice of a standard unit and a non standard unit to measure length-estimate, measure and record the distance around objects, using non-standard units-estimate, measure and record area through investigation using a variety of non-standard units-describe, through investigation the relationship between a size of unit of area and the number of units needed to cover a surface

Mirian Small’s Key Ideas:-a measurement is a comparison of the size of one object with the size of another-the same object can be described by using different measurements-the numerical value attached to a measurement is relative to the measuring unit-the use of standard measurement units simplify communication about the size of objects-knowledge of the size of benchmarks assists in measuring-measurement formulas allows us to rely on measurements that are simpler to access to calculate measurement that are more complicated to access

Success Criteria: Misconceptions:-I can measure objects using my foot, paper clips, markers etc…. (non standard units)-I can use my ruler (standard units) instead of paper clips (non-standard units) to measure my desk -I can use a meter stick (standard units) instead of my feet (non-standard units) to measure the hallway or classroom -I can choose the biggest/smallest tool to help me measure something tall, short, wide, thin, long-I can use the appropriate unit of measurement to calculate area.-I can use the appropriate unit of measurement to calculate the distance around an object -I can measure length and height by lining the objects next to each other -I can choose the best unit of measurement to the measure the length and height of an object

Refer to individual lessons.

Culminating Task:

Hook: Students will design a playground for our school. They will measure the perimeter and area of the playground and surrounding fence.

Success Criteria:

-I can draw a playground with a surrounding fence on chart paper

- I use snap cubes and rulers to measure the perimeter of the fence and the area of my playground structure.

- I know how to find the perimeter of my fence, the area of my structure, and can explain my work using snap cubes and rulers.

- I can use math words (cm/m, length, width, tall, short, perimeter, area) to describe my playground.

Assessment:

Rubric (See attached)Anecdotal Notes

Name:_____________ Date:______________

Measurement Culminating Activity: Design Your Own Playground!

Level 1 Level 2 Level 3 Level 4

ThinkingUses planning skills effectively to develop a playground with a surrounding fence and one structure.

With a lot of assistance, I can draw a playground with a surrounding fence on graph paper.

With some assistance, I can draw a playground with a surrounding fence on graph paper.

With little assistance, I can draw a playground with a surrounding fence on graph paper.

Independently, I can draw a playground with a surrounding fence on graph paper.

Knowledge and UnderstandingDemonstrates an understanding of the concept of area and perimeter by selecting standard (cm/m) and non-standard units of measurement.

With a lot of assistance, I use snap cubes and rulers to measure the perimeter of the fence and the area of my playground structure.

With some assistance, I use snap cubes and rulers to measure the perimeter of the fence and the area of my playground structure.

With little assistance, I use snap cubes and rulers to measure the perimeter of the fence and the area of my playground structure.

Independently, I use snap cubes and rulers to measure the perimeter of the fence and the area of my playground structure.

ApplicationApplies knowledge and skills effectively to:-calculate and record the perimeter of the fence using appropriate units.-calculate and record the area of the playground structure using appropriate units

With a lot of assistance, I know how to find the perimeter of my fence, the area of my structure, and can explain my work using snap cubes and rulers.

With some assistance, I know how to find the perimeter of my fence, the area of my structure, and can explain my work using snap cubes and rulers.

With little assistance, I know how to find the perimeter of my fence, the area of my structure, and can explain my work using snap cubes and rulers.

Independently, I know how to find the perimeter of my fence, the area of my structure, and can explain my work using snap cubes and rulers.

CommunicationUses mathematical conventions, vocabulary, and terminology (cm/m, length, width, tall, short, perimeter, area) effectively to describe a playground.

With a lot of verbal prompts, I can use math words (cm/m, length, width, tall, short, perimeter, area) to describe my playground.

With some verbal prompts, I can use math words (cm/m, length, width, tall, short, perimeter, area) to describe my playground.

With few verbal prompts, I can use math words (cm/m, length, width, tall, short, perimeter, area) to describe my playground.

With no verbal prompts, I can use math words (cm/m, length, width, tall, short, perimeter, area) to describe my playground.

Measurement Introductory Lesson PlanLesson 1: Non Standard Units By: Ilianna GivelosCurriculum Expectations: Overall: estimate, measure and record length, perimeter, area using non-standard units and standard unitsGr. 2 Specific: -choose benchmarks to help them perform measurement tasks-estimate and measure length, height and distance, using standard units and non-standard units

Task/ProblemTo understand nonstandard measurements and how we use different nonstandard measurement objects to measure various items.

Learning Goal:I will be able to choose the appropriate non-standard unit to measure certain objects. Write “I will be able to explain non-standard units and I will be able to choose which non standard units to use when measuring” on the white board visible to the students (to be continued into lesson 2).

Part 1 Before, Minds On or Activate Prior Knowledge

Diagnostic: Before – Read the title “How Big Is A Foot?” and ask the students what they feel the book is about based on the title. Read up until page 16; identifies the kings measurements of feet (3 feet wide and six feet long – see questions below). Do not show the students the picture with the Queen lying with the surrounding feet as students have to discuss how to properly trace 3 feet wide and 6 feet long. (Only show to groups that seem to be struggling with the concept and need the support however do not explain)

Questions:What is wide?What is long?When do we use wide/long to explain? Ask students to give an example of when we use wide and long to explain something. Why is the king using his feet? Could the King use a paper clip?What could we use that may be more exact?

*Determine which students may require more assistance throughout the Hands-On when determining width and length

Student Success Criteria:

I can measure objects using my foot, paperclips, markers etc…. (non standard units)

I can choose the biggest/smallest tool to help me measure something tall, short, wide, thin, long

I can use math language to explain and describe why I chose certain objects

I can explain wide and long and when I use those math words

Part 2- During, Work on It or Hands OnLet’s split up into groups and try to figure out how big the bed was for the queen (flexible groupings).

Guided Flexible Groupings by Teacher – choose the students with the smallest feet, largest feet and myself to be traced in the individual groups in order to show the students how the feet sizes effect the size of the queens bed.

Questions:How will you use your feet to measure? What strategy will you use when tracing your feet?How close will you place your feet together on the paper and why?(Have a student model how they place their feet on the paper for tracing – Discuss why this is the best way)

Strategies: Place your foot, trace it and then place your

other foot right beside your traced foot (Have a student model this)

Trace one foot place your foot beside it and trace the other foot

Tools: Book “How Big is A Foot?” Long Craft Paper Markers

Part 3 – After, Consolidation, Congress, Bansho or Gallery WalkConsolidation – we finish the rest of the story and then have the students flip over their work to see the difference in sizes and understand WHY the bed did not fit the queen initially.

Congress Questions:How do you know that this is not the right way of measuring? We all have different sized feet.What CAN we use to measure things? (e.g. ruler, etc…)

How did you use the non standard measurement (feet) to create your bed? What made it easier?How did you place your feet on the paper when tracing? What made it easier?Should we use non-standard units to build houses? Why might that be a problem?Should we only use ONE person’s foot when measuring objects? Why might that be a problem?What can we use that is STANDARD or helps us measure? Does anybody know anything that helps them measure or has anyone seen

Misconceptions: Does not understand the concept non standard

units (that it is not how we measure things) Leaving gaps or overlapping when using non

standard units Does not understand how to trace his/her foot Lifts foot off the paper before tracing and draws

freehand

their parents use anything? Answer: Ruler, Measuring tape etc… (This is just to have the students understand the concept of NON STANDARD and why it is called NON-standard vs. STANDARD).Resources:

A Guide to Effective Instruction K-3- MeasurementOntario Curriculum Mathematics, 2005 RevisedHow Big Is A Foot by Rolf Myller

Measurement Lesson PlanLesson 2: Non Standard Units Con’tBy: Ilianna GivelosCurriculum Expectations: Overall: estimate, measure and record length, perimeter, area using non-standard units and standard unitsGr. 2 Specific: -choose benchmarks to help them perform measurement tasks-estimate and measure length, height and distance, using standard units and non-standard units

Task/Problem

To understand nonstandard measurements and how we use different nonstandard measurement objects to measure various items.

Learning Goal:

I will be able to choose the appropriate non-standard unit to measure certain objects. “I will be able to explain non-standard units and I will be able to choose which non-standard units to use when measuring” on the white board visible to the students.


Questions:What non-standard units of measurement did we use last lesson? Answer: FeetWhy is this considered non-standard unitsWhat is wide?What is long?When do we use wide/long to explain? Remind students of the previous lesson and how we used wide and long to describe the bed the King made for the QueenWhat could we use that may be more exact?

On the Smart Board have the students view a series of pictures of items that are tall, short, wide, long, thing to familiarize them selves with math language (Buildings compared to people, families, dogs compared to people, tall grass compared to ants etc…). As students are stating describing words that we use write on chart paper)

Compare teacher to a student; if possible compare a student to another student being careful of students who may be sensitive to this. Have one student describe their family using words such as tall, thing, shorter etc… in order for all students to understand that we use math words every day.


I can measure objects using paperclips, markers and meter sticks (not the actual measurement just as a non-standard item), (non standard units)

I can choose the biggest/smallest tool to help me measure something tall, short, wide, thin, long

I can use math language to explain and describe why I chose certain objects

I can explain wide and long and when I use those math words

*Determine which students may require more assistance throughout the Hands-On when determining what non-standard units to use.

Part 2- During, Work on It or Hands On

Classroom Scavenger Hunt:We will now partner up and will be provided with clipboards and you will walk around the room finding objects and deciding what NON STANDARD UNITS you would use to measure objects in the classroom. Think about why you are using those non-standard units and why it is better to use them for the object you chose.

Have 2 students model a tall object and explain what unit they are using and have another student model a short object and what non-standard unit they are using and why. Have students raise their hands and think of things they can measure in the class (desks, chairs, computers, books, pencils etc…)

Questions:How will you determine what non-standard unit you will choose?Will you choose a non standard unit bigger than the object you are trying to measure or smaller? Why?

Walk around the room taking anecdotal notes and have students answer the above questions, ask them why they are using the items they are using. Show them possibilities, model the way of measuring if needed.

Strategies: Use the materials (paper clips, markers, meter

sticks) to measure the objects and see what is easier

Tools: Paper clips Meter sticks Markers Clipboards Worksheet with a table separating paper clips,

markers and meter sticks Classroom

Part 3 – ConsolidationConsolidation – All students come back to the mat and place their clip boards in front of them. Students will now all share their answers and teacher will write them on the board.

On Chart Paper is a bigger version of the worksheet with the word bank that the students created on top (tall, thin, short, wide, long etc…). Fill it out with the class so they are able to see what they are comparing when answering questions.

Misconceptions: Does not understand the concept non standard

units (that it is not how we measure things) Leaving gaps or overlapping when using non

standard units Does not understand how to place the items on

the object when measuring Does not understand the concept of tall, thin,

short, wide

Congress Questions:What items did you use the paper clips to measure? Why? What items did you use the markers to measure? Why?What items did you use the meter stick to measure? Why?Would you use a meter stick to measure a book? Why?Would you use a paper clip to measure how tall the door is? Why?

Have students look around the room and remind them to use their math words. Model an example such as “I used paper clips to measure marker which is much shorter than the leg of this desk”. Have students compare the various items of this room using math words.

Resources:

A Guide to Effective Instruction K-3- MeasurementOntario Curriculum Mathematics, 2005 RevisedSmart Board (Images taken from Google or taken by teacher)

Lesson Plan for Standard Measurement (centimetres)By: Tania Décaudin

Curriculum Expectations: Overall: estimate, measure and record length using standard unitsGr. 2 Specific: -estimate and measure length, height and distance, using standard units (i.e., centimetre, metre,)-choose benchmarks-in this case, personal referents-for a centimeter Task/ProblemTo understand the importance of standard measurements and how and when we use centimeters to measure various items.

Learning Goal: I will be able to choose the appropriate

standard unit to measure certain objects. (cm) I will know that I can use centimeters to

measure small objectsPart 1 Before, Minds On or Activate Prior KnowledgeInvite students to sit in a circle on the carpet with their feet facing towards the middle of the circle. Ask them to estimate whose feet are longer, shorter or the same length as theirs. Once the students come up with the word centimeters, measure each child’s foot with a ruler and record it on chart paper. Take the opportunity to show how to line up the end of the ruler with the object. Questions:What else measures around 1 cm? (the width of my finger) How would you measure each foot? What unit of measurement would be the best tool? How do you know which one is longer, shorter or the same as yours?If you wanted to borrow someone’s shoes, whose would fit you best? How do you know?


I know that centimeters are used to measure small objects

I know that one centimeter measures about the same as the width of my finger

I can use a ruler to measure certain objects I can describe my mathematical thinking using

words such as length and height

= 30 cm

Part 2- During, Work on It or Hands OnIn pairs, using a ruler, have the students find objects in the classroom that measure around the same amount as their shoe. Ask them to estimate first. They will record their answers on a chart. Problems:

Find an object that is longer than your shoe

Find an object that is shorter than your shoe

Find an object that is the same length as your shoe

Strategies: Start at zero when measuring with the metre

stick

Questions:What is this measuring tool called?How long is a centimetre?What else measures around 1 centimeter?How do you know without measuring it?What do you need to measure a centimetre?

Tools: rulers Centimeter cubes Classroom objects to measure Chart paper and markers shoes

Part 3 – After, Consolidation, Congress, BanshoCome together as a group. Students present their findings to the class. Questions:Is it easier to measure an object using centimeters and meters rather than a non-standard unit (i.e., your foot)?Why is it better?If 2 people measured the same object, would their answers be the same?When is it better to measure with a ruler than with your finger, for example?

Misconceptions: Does not understand the concept that

standard units are the best way to measure objects (everybody understands the same thing, speaks the same language)

Misaligns the ruler with the beginning of the object

Resources: A Guide to Effective Instruction in Mathematics; Kindergarten to Grade3, Measurement 2007Ontario Curriculum Mathematics, 2005 Revised

Lesson Plan for Standard Measurement (metres)By: Tania Décaudin

Curriculum Expectations: Overall: estimate, measure and record length using standard unitsGr. 2 Specific: -estimate and measure length, height and distance, using standard units (i.e., centimetre, metre,)-record and represent measurements of length, eight and distance in a variety of ways (i.e., written, pictorial, concrete)

Task/ProblemTo understand the importance of standard measurements and how and when we use meters to measure various items.

Learning Goal: I will be able to choose the appropriate

standard unit to measure certain objects. (cm or meters)

I will know that 100 cm is the same as 1 metrePart 1 Before, Minds On or Activate Prior KnowledgeGive students each a card that has a measurement on it. (2cm, 35cm etc…) Ask the students to order themselves from smallest to biggest. One student will have the 100 cm card and one student will have the 1 metre card. Begin the discussion around how much is a metre and do the 2 students have equal value.Introduce the game: The meter stick race!Play the game against the class (teacher vs whole class). Each team picks a card and moves the centicube along the meter stick according to the number on the card. The first team that reaches 100 cm wins. Take this opportunity to show students how to count accurately. Questions:What is this measuring tool called?How much is a centicube?How many centicubes do you need to make a metre stick?How many centimetres are in a meter stick?


I know that 1 metre is 100 cm I know that one centicube measures 1 cm. I can use a metre stick to measure certain

objects I can describe my mathematical thinking using

words such as length and height

Part 2- During, Work on It or Hands OnAfter the game: In pairs, have students solve the following problems. Ask them to record answers on a piece of chart paper.

Strategies:

For the game, count aloud when the moving the cube along the metre stick

Make sure the centicube is lined up against the number that you count

Start at zero when measuring with the metre stick

Problems: Describe and compare a metre to a

centimetre. Compare a metre to an object in the

classroom. Using math words, describe how you know. (I estimated and then measured the object using a metre stick)

Using a string that measures about 1 metre, find an object that is shorter than a metre, about the same length as a metre, and longer than a metre.

Questions:What is this measuring tool called?How long is a metre?What else measures around 1 metre?How do you know without measuring it?What do you need to measure a metre?

Tools: Meter sticks (1 per group) Centimeter cubes 1 centimeter ruler Classroom objects to measure Chart paper and markers Cards and a coin String scissors

Part 3 – After, Consolidation, Congress, BanshoConsolidation – Students post and present their findings to the class. Pairs have a chance to explain their different strategies.Remind students that 1m=100cm.Questions:Is it easier to measure an object using centimeters and meters rather than a non-standard unit (i.e., your foot)?Why is it better?If 2 people measured the same object, would their answers be the same?When is it better to use a meter instead of a centimetre?

Misconceptions: Does not understand the concept that

standard units are the best way to measure objects (everybody understands the same thing, speaks the same language)

Leaving gaps or overlapping when counting the centimeters

Loses track of count during the game Does not know that it is better to use 1 metre

to measure big objects and centimetres when measuring smaller objects.

Resources: Math Now 2 by Molly Larin and Judy Onody GTK Press, Toronto 2008 Ontario Curriculum Mathematics, 2005 Revised

Grade 2: Measurement, Length (Non-Standard Units)By: Sarah Gibson

Curriculum Expectations: Overall: -estimate, measure and record length using non-standard -compare, describe and order objects, using attributes measured in non-standard unitsSpecific: -estimate and measure length using non-standard units-record and represent measurements of length in a variety of ways -select and justify the choice of a non-standard unit to measure lengthTask/ProblemTo explore how to measure length using a variety of different non-standard units of measurement and to select the best fitting unit.

Learning Goal:I will be able to measure and show the length of a person’s arm using different non-standard units of measurement and explain which unit works best.

Part 1- Minds OnRead the poem “Hug-‘o-War” by Shell Silverstein. Ask for a volunteer to stand in front of the class and stretch his/her arms out. Co-create a chart with students on the board listing a variety of non-standard units.Have students estimate the length of one of the volunteer’s arms in non-standard units (from the tip of the middle finger to the shoulder).Jot student’s estimations down on chart paper.

Questions:What type of non-standard units could we use to measure the length of ________ arm?Is there one unit that might be easier to use over another?How can we check to see if our predictions are correct?

Student Success Criteria:I know that length is a measurement of an object from one end to another (from the tip of the middle finger to the shoulder).

I can measure the length of an object using non-standard units (ie. Manipulatives)

I need to use the same non-standard unit when measuring an object.

The length of an object can be described differently when using different tools to measure (snap cubes vs. hand prints)

I use math language (more than/ less than, bigger/smaller) to explain and describe why I chose to use certain units of measurement

Part 2- Hands-OnSuggest to students that longer arms give bigger hugs.Invite students to play “Hug-‘o- War”.In partners, students will estimate whose arms are longer (from tip of middle finger to shoulder).Each student will then measure the length of their partner’s arm using non-standard units of measurement. “If I were to measure _____’s right arm using non-standard units, which tool might be best for the job? Why?”Whoever has the longer arms wins!Questions:What units of measurement did you use?How do you know you measured correctly?

Strategies:Drawing picturesMeasuringCountingAddingMaking comparisons

Tools:Variety of manipulatives (string, snap cubes, handprints, straws, etc)PencilsPaper

Part 3 – ConsolidationInvite the volunteer from the beginning of the lesson to return to the front of the classroom. Prior to measuring the volunteer’s arm, have students adjust their prior estimations and discuss which non-standard units of measurement were most successful.

Questions:After using different measuring units, how have your estimations changed?What sort of non-standard measuring tools did you use?Which units of measurement were faster, or easier to use?How did you know your measurements were accurate?

Misconceptions:

Length is not the same as height.

Students tend to measure in full units only, forgetting about fractional measurements (Based on Marian Small’s). Example: My arm is 14. 5 snap cubes long.

Resources:Ontario Curriculum Mathematics, 2005 RevisedMaking Math Meaningful to Canadian Students K-8 by Marian Small.Math Makes Sense 3- Teacher’s Resource, Unit 9: Length, Perimeter, and Area.

Name:_____________________ Date:____________________

Hug ‘o War!

My partner is:_________________________________

Estimate (in non-standard units):

I think his/her right arm is ______________________________________ long.

Total (in non-standard units):

I know his/her right arm is ______________________________________ long.

Who has the longer arm? ______________________________________

___________________________________________________________________________________________

If I were to measure ______________________’s right arm using a variety of non-standard units, which tool would be best for the job? Why?

Grade 2: Measurement, Height (Standard Units)By: Sarah Gibson

Curriculum Expectations: Overall: -estimate, measure and record height using standard units-compare, describe and order objects, using attributes measured in standard unitsSpecific: -measure height using standard units-record and represent measurements of height in a variety of ways-select and justify the choice of a standard unit to measure heightTask/ProblemTo explore how to measure height using a variety of standard units of measurement and to select the best fitting unit.

Learning Goal:I will be able to measure and show the height of a person using different standard units of measurement and explain which unit works best.

Part 1- Minds OnPoint out two students of similar heights sitting on the carpet.Have the class predict who is taller, and take a vote. Co-create a chart with students on the board listing a variety of standard units.Have students estimate the height of each volunteer using the different standard units came up with. Jot student’s estimations down on chart paper.Encourage students to use the language “more/less, bigger/smaller, tall/taller/tallest, etc.”

Questions:What type of standard units could we use to measure the height of a person?Is there one unit that might be easier to use over another?How can we compare the two students’ heights, to see who is taller?How can we check to see if our predictions are correct?

Student Success Criteria:I know that height measures how tall something is (from the ground to the top of the object)

I can measure the height of an object using standard units (ie. centimeters)

I need to use the same tool (ruler) when measuring an object.

The height of an object can be described differently when using different tools to measure (meters vs. centimeters)

I use math language (more than/ less than, bigger/smaller, taller/shorter) to explain and describe why I chose to use certain units of measurement

Part 2- Hands OnChallenge students to silently line themselves up against a clear wall from tallest to shortest.Place a piece of tape above each student’s head to mark their heights. “If you were to measure your own height using standard units, which unit would be best for the job? Why?”

Strategies:MeasuringCountingAddingMaking comparisons

Provide students with rulers, meter sticks, cm cubes, measuring tape. Each student will measure their own height using various standard units and mark them on a name tag that will go above their marked heights. Questions:What units of measurement did you use?How do you know you measured your height correctly?Is there a unit of measurement that you would use to measure your height, and not the length of your arms?

Tools:cm cubesRulersMeter StickMeasuring tapePencilsPaperTape

Part 3 – Gallery WalkAs a class, tour along the “Wall of Height” that the students created. Pay particular attention to the two students pointed out at the beginning of the lesson. Refer to estimations taken at the beginning of class.

Questions:What do you notice about the units of measurement as we walk up and down the wall? (They grow bigger/smaller in number) How close were the estimations?What types of standard units did students use?Was there a unit of measurement that was easier, or fast to use?How did you know your measurements were accurate?

Misconceptions:Height is not the same as length.

When measuring height with a ruler, students start at the end of the ruler, instead of at the zero.

Students leave spaces when lining up their measuring tool.

Students tend to measure in full units only, forgetting about fractional measurements (Based on Marian Small’s) Example: I am 100.5 cm tall.

Students have difficulty measuring lengths greater than 1m, using only 1 meter stick.

Resources:Ontario Curriculum Mathematics, 2005 RevisedMaking Math Meaningful to Canadian Students K-8 by Marian Small.Math Makes Sense 3- Teacher’s Resource, Unit 9: Length, Perimeter, and Area.

Perimeter Lesson -1 (Lillian Papel)

Measurement: Grade 2 -Using Non- Standard Units to Measure PerimeterCurriculum Expectations:

Overall: estimate, measure, and record length, perimeter, area, mass, capacity, time, and

temperature, using non-standard units and standard units; compare, describe, and order objects, using attributes measured in non-standard units

and standard units.

Specific: estimate and measure length, height, and distance, using standard units (i.e.,

centimetre, metre) and non-standard units record and represent measurements of length, height, and distance in a variety of ways estimate, measure, and record the distance around objects, using non-standard units select and justify the choice of a standard unit (i.e., centimetre or metre) or a

nonstandard unit to measure length

Task/ProblemTo use manipulatives to problem solve and investigate how to measure the perimeter of different polygons and shapes that are not polygons using non-standard units.

Learning Goal: I will be able to estimate and measure

the perimeter of different shapes using non- standard units.(snap cubes)


Duration: 15mins

Have a variety of cake pans in different shapes available. (rectangular, circular, square and others with unique shapes)

Students will be sitting in a circle.Ask students to describe the shape of the cake that would be made from each pan. Ask a student volunteer to select one and trace the cake pan on chart paper to show what the top of the cake would look like.

Place the chart paper in the center of the circle.

Invite the student to show with their hands (non-standard) how they would measure the distance around the shape. Share with the students that the total distance around the


I know that perimeter means the total distance around a shape.

I can measure around a shape with a string and then measure the string using snap cubes.

I can estimate and then find the perimeter of a shape by adding the lengths of the sides.

I can use diagrams to communicate and explain my mathematical thinking about perimeter.

I can apply strategies to solve the problem (ex. use addition to find out the distance of the cake pan in snap cubes)

I can work co-operatively in a small group.

shape is called the shape’s perimeter.

Ask: If X student put gummy bears the size of this sticker around the outside of this cake, estimate how many would he/she would need to measure the distance around the outside of the cake?

Think, Pair, Share- Students would share with their elbow partner how many stickers they think would be needed.

Student volunteer would then place stickers around the distance of the shape and record the measurement.

Questions:

What other strategy would you use to help solve this problem?

Does it matter where along the edge X student starts to measure? Why not?

Does it matter where X student starts and where X student stops measuring?

How do you make sure that the entire distance around the shape is covered?

Part 2- During, Work on It or Hands OnDuration: 20mins

Show students the cut outs of different cake pans and a string of licorice and ask “If I were to decorate each of these cakes with a licorice-string border. How much licorice would I need for each?

Divide students into groups of three and provide each group with snap cubes, a cake cut out, chart paper and string to represent the licorice.

Strategies:

Make a picture Use a manipulative Doubling or skip counting (if the polygon

is a square and each side is of equal length)

Addition Comparison Count the cubes Use logical reasoning

Questions:Pre-measuring: Can you estimate how much licorice you might need before measuring the perimeter?

How did you solve the problem?What strategy are you using to measure the perimeter of the shapes?What would you use to measure the distance around this shape? Why?How can you measure around the sides of the cake to find out exactly how much licorice-string is needed?

Tools: Variety of cake pans Cake pan cut outs Paper/pencil/markers Manipulatives (snap cubes, bears,etc) Chart paper Scissors String Stickers

Part 3 – After, Consolidation, Congress, Bansho or Gallery WalkDuration: 15-20mins

Math Congress – highlight 3 chosen pieces of work to show strategies for solving the problem

I would use the classroom Ipad to take photos of students work and project it onto the smart board to make it easier for students to observe and compare each other’s work.

Congress Questions:

What measuring tool did you use for this cake?Is this perimeter longer or shorter than that one?Which cake has the longest perimeter? The shortest? How do you know?How could we put the cakes in order from shortest to longest perimeter?

When might you need to measure the perimeter of something?

Misconceptions: Students may try to compare lengths

without aligning the objects first. Some students may think that length is determined by where an object ends, rather than by the distance from start to end.

Students may think that you use small units only to measure small items.

When students measure lengths by moving a single nonstandard unit along the distance, they may find it difficult to keep track of where one iteration of a unit ends and the next one begins. This leads to gaps or overlap between units and incorrect measurement.

Some students may not take curves into account when deciding which of two lengths is longer.

(Making Math Meaningful to Canadian Students K-8 by Marian Small)

Resources:A Guide to Effective Instruction K-3- MeasurementOntario Curriculum Mathematics, 2005 RevisedMaking Math Meaningful to Canadian Students K-8 by Marian Small.Nelson Mathematics 2- Teacher’s Resource, Chapter 5: Linear Measurement

Perimeter Lesson -2 (Lillian Papel)

Measurement: Grade 2 – Using Standard Units (Cm) to Measure PerimeterCurriculum Expectations:

Overall: estimate, measure, and record length, perimeter, area, mass, capacity, time, and

temperature, using non-standard units and standard units compare, describe, and order objects, using attributes measured in non-standard units

and standard units.

Specific: estimate and measure length, height, and distance, using standard units (i.e., centimetre,

metre) and non-standard units record and represent measurements of length, height, and distance in a variety of ways select and justify the choice of a standard unit (i.e., centimetre or metre) or a nonstandard

unit to measure length

Task/ProblemStudents will explore and compare ways to calculate the perimeter of an object with a distance of 60 cm.

Learning Goal:- I will be able to find different ways to

design a birthday card and calculate the distance around the card using appropriate standard units.(cm)


Duration: 15mins

Remind students of yesterday’s lesson and how we used non-standard units to measure the perimeter of the cake pans.

By this lesson in the unit students would have already been introduced to measuring with a ruler and meter stick, and use standard units including centimeter and meters.

Hand out a 30cm ruler, centimeter cubes and sheet of centimeter grid paper to each student.

Ask students:Draw two different shapes that have a perimeter of 12 cm.Questions:What measuring tool did you use to measure the perimeter? Why did you choose this tool?


I can estimate, measure and label each of the sides of my card using a ruler.

When measuring, I know how to start recording length at the zero mark on my ruler.

I can add up all the measurements together to find the perimeter.

I know that perimeter can be measured using non-standard units such as snap cubes and standard units such as centimeters or meters.

I can apply strategies to solve the problem and select the appropriate tools and best units to measure perimeter.

I can use diagrams to communicate about perimeter and explain my mathematical thinking.

How do you know that the perimeter is 12 cm?Are there other ways to draw a shape with a perimeter of 12 cm?


Kathryn is making a birthday card for her mom using construction paper. She has some left over ribbon in her art box and wants to use it to border her card. She measured using a ruler and only has 60 cm left of ribbon. What are the different ways that Kathryn can make the card using all the left over ribbon?

Questions:What strategy are you using to measure the perimeter of the card?Is the distance around the card longer or shorter than 1 metre? How do you know?

Is there more than one solution?

How do you know if you have enough ribbon to border the card?

Strategies:

Make a picture Doubling or skip counting Addition Comparison Use logical reasoning Use a manipulative ( ex. use construction

paper to make a card; use centimeter cubes)

Tools: Ribbon Construction paper Ruler String Centimeter cubes Scissors Grid paper

Part 3 – After, Consolidation, Congress, Bansho or Gallery WalkDuration: 15-20mins

Math Congress – highlight 3 chosen pieces of work to show strategies for solving the problemI would use the classroom Ipad to take photos of students work and project it onto the smart board to make it easier for students to observe and compare each other’s work.

Congress Questions:Would your card work if Kathryn only had 50 cm of ribbon? Why or why not?Could you use snap cubes to measure the perimeter instead of a ruler? Why or Why not?

Misconceptions: Students may mistakenly begin measuring

from points other than 0-cm mark on a ruler.

Students may sometimes forget to label all sides and to include the measures of the unlabelled sides in calculating perimeter.

Students may think that you use small units only to measure small items.

The object length stays the same size even if you use different measures and get different numerical values

(Making Math Meaningful to Canadian Students K-8 by Marian Small)

What do you notice about each of the solutions? ( ex. all cards are different shapes but same perimeter)

Extensions:Students can then use their diagrams to explore and compare area in the next lessons.Resources:

A Guide to Effective Instruction K-3- MeasurementOntario Curriculum Mathematics, 2005 RevisedMaking Math Meaningful to Canadian Students K-8 by Marian Small.Nelson Mathematics 2- Teacher’s Resource, Chapter 5: Linear Measurement

Area Lesson -1 (Waheda Hofioni)Measurement: Grade 2 -Using Non- Standard Units to Measure AreaCurriculum Expectations:

Overall: estimate, measure, and record area, using non-standard units compare, describe, and order objects, using attributes measured in non-standard units

Specific: estimate, measure and record area through investigation using a variety of non-standard units select and justify the choice of a non-standard unit to measure area describe, through investigation the relationship between a size of unit of area and the number of units

needed to cover a surfaceTask/ProblemTo use manipulatives to problem solve and investigate how to measure the area of your desk using 3 different non-standard units.

Learning Goal:I will be able to choose the best non-standard unit by comparing three different non-standard units to (cue cards, cd covers, chain links) to measure the area of my desk.


Duration: 15minsHave two different non-standard units (sticky notes paper, snap cubes) on the carpet.

Students will be sitting in a circle.Ask students to describe the non-standard units (shape, size).

Select a hard-cover book and place it in the middle of the circle.

Invite the students to share how they would measure (cover) the surface/front cover (area) of the book.

Ask students to: choose the best non-standard unit

(sticky notes, snap cubes). estimate how many of each non-

standard unit he/she would need to measure the surface (area) of the book.

Think, Pair, Share- Students would share with their elbow partner and discuss which is the best non-standard unit, and the amount of non-standards required to cover the drawing of the book.


I know that area means the total surface space of an object/shape

I can cover the surface of my desk and measure the area using different non-standard units.

I can estimate and then find the area I can count the number of non-standard units needed

to cover the surface of my desk

Select two student volunteers to cover the book using different non-standard units provided.

Record this information on the board.

Questions:

What other strategy would you use to help solve this problem?

Does it matter which non-standard unit you should use?

Does the size of the non-standard unit affect the number of non-standard units needed to cover a surface?


Ask students to choose a partner. Ask the students to measure the area of their desk using the three non-standard units provided.

Ask the students to estimate how many non-standard units for each object in order to cover their desk.

Each group will determine the best appropriate unit to use to cover their desk?

Questions:Can you estimate how much licorice you might need before measuring the perimeter?

How did you solve the problem?What strategy are you using to measure the area of your desk?Which non-standard unit is the best to use to determine cover the surface of the desk?

Strategies:

Make a picture Use a manipulative Count the non-standard units

Tools: Desk Paper/pencil/markers Manipulatives (cue cards, cd cover, chain links)

Part 3 – After, Consolidation, CongressDuration: 15-20mins

Math Congress – highlight 3 chosen pieces of work to show strategies for solving the problem.

Misconceptions:

Leaving gaps or overlapping when using non-standard units

Does not understand the concept of non-standard

Congress Questions:

What non-standard unit did you use to measure the area of your desk?

Is this area more or less when you used another non-standard unit?

Which non-standard unit did you use the most of? The least? How do you know?

units (that it is not how we measure things) Does not understand that area means the space

inside an object (surface of the top of the desk) Does not understand to use the same non-standard

unit to measure the area Does not understand that the larger the non-standard

unit, the fewer the number of non-standard units required to cover the (area) surface of your desk

Resources:A Guide to Effective Instruction K-3- MeasurementOntario Curriculum Mathematics, 2005 RevisedMaking Math Meaningful to Canadian Students K-8 by Marian Small.

Area Lesson -2 (Waheda Hofioni)Measurement: Grade 2 -Using Non- Standard Units and converting to cm to Measure AreaCurriculum Expectations: Overall:

estimate, measure, and record area, using non-standard units compare, describe, and order objects, using attributes measured in non-standard units

Specific: estimate, measure and record area through investigation using a variety of non-standard units select and justify the choice of a non-standard unit to measure area

Task/ProblemTo measure two different gardens, using snap cubes and converting non-standard units into standard units (cm).

Learning Goal: I will be able to choose the appropriate non-

standard unit, and convert into centimeters.


Before – Show the students the front page of the book “The Busy Ants and the Lazy Ants?” Ask the students to predict what the story is about. Read up until page 4; and ask the following questions

Questions:Which garden is wide?Which garden is long?How might you determine which garden is bigger?Which garden do you think is bigger, the lazy ants or the busy ants?

Continuing reading up to page 10; ask the children the following questions:

Questions:Is there another way the busy ants could measure their garden without leaving any spaces? (after page 6)Why might the little rectangles take a longer time to cover the garden? (after page 9)Why might the lazy ants suggest that the triangle sandwiches are not the best way to measure the area of the garden? (Show students page 10, and point to the different sized sandwiches. Ask this question before


I can use the same non-standard unit (snap cubes) to measure the areas for both gardens

I know that one snap cube is equal to two cm I can use math language (wide, long, cm, equal

to) to explain and describe why I chose certain objects

the busy ants cover their garden. Once children have answered this question, read the rest of the page to see the response of the lazy ants).Now which garden do you think is bigger, the lazy ants, or the busy ants? How do you know?

Stop the story and ask children the following question:

The Lazy Ants and the Busy Ants were arguing about which garden was bigger? Help the ants solve their problem. Which garden is bigger? How do you know?Part 2- During, Work on It or Hands On

Divide students into groups of 3 to solve this problem.

Questions:How will you use the snap cubes to measure the area of each garden? What strategy will you use converting from non-standard units to standard?How close will you place your snap cubes and why?

Strategies: Draw a picture Use a manipulative Use addition to add up all the snap cubes Use a number line (to skip count by twos) Using multiplication Ruler to measure length X width

Tools: 2 different construction papers to represent the

gardens for each set of ants. (The square shape is for the busy ants and the rectangle shape for the lazy ants).

Markers Snap cubes Number line Ruler

Part 3 – After, Consolidation, Congress, Consolidation – Finish reading the story. Ask groups to present their work.

The Lazy Ants and Busy Ants garden is equal in size. The Busy Ants garden is a square while the lazy Ants garden is a rectangle.

Congress Questions:How do you know that the busy ant’s garden is equal to the lazy ant’s garden?

Could we have used standard units to measure the two gardens? Would we have got the same answer? How do you know?

How might leaving spaces or using different sizes of snap cubes change our answer?

Misconceptions: Does not understand the concept non-standard

units (that it is not how we measure things) Leaving gaps or overlapping when using non-

standard units Cannot convert one snap cube to 2 cm. Cannot skip count by twos. Uses different sizes of snap cubes to measure

the area.

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