Kindergarten: Comparing Length and Weight
Using Sentence Frames
![Picture](/uploads/9/2/4/5/9245768/3106022.jpg?864)
Objectives: By the end of the lesson, the student should be able to correctly describe and compare common objects by using the words taller, shorter, longer, heavier, and lighter.
Common Core Standards Addressed:
K.MD1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
Materials:
Pencil
Paper
Sentence cards with pictures (Found at Here and Here)
Envelopes
Items from the cards
Pencils, erasers, tape measures, tissue boxes, string or yarn, rulers, books, paper clips, stapler, crayon box, glue sticks, juice boxes, cups, milk cartons, blocks, markers, feathers, oranges, apples, marbles, numeral cards.
Procedure:
1. Cut the attached sentence cards and laminate them. Put one color set in each envelope and paste a copy of the whole sentence frame on the outside of the envelopes.
2. During math centers time, have a small group of students (up to five, one for each envelope) come over to a large table where they can each have their own space.
3. Show the students that the sentence frame should look like it does on the front of the envelope and the blanks are where they put the pictures to compare.
4. Remind the students what a sentence is supposed to look like.
5. Have objects that match the pictures on the cards
6. Show them how to use the objects to compare- have them feel the difference between the weight using one object in each hand, have them hold the objects next to each other to see which ones are taller, longer, or shorter.
7. Have the students practice writing their sentences down and read them to a partner. Have them compare the answers they got with their partner and see if there are any similarities or differences between their answers and why they may be that way.
8. Finally have the students pick two different items they haven’t worked with yet and write a sentence with it and then draw a picture to show what they’re saying in the sentence.
Assessment:
Talk to the students while they’re working and see where they’re struggling and where they’re excelling. Focus them more on the ones they’re struggling with. Read they’re sentence structures and look at the pictures to make sure they go together. Ex. If the sentence is The pencil is longer than the paperclip., make sure the picture shows a larger pencil and a smaller paperclip.
Differentiation:
Help the students read the words.
Have only one size of each object to make it easier to compare.
Have many sizes of each object to make it more complex. ex: a small pencil and a large pencil, two different types of tape measures, etc.
Have the students compare one object to two others. ex: The pencil is shorter than the stapler. The pencil is longer than the eraser.
Talk about what jobs you may needs these skills for.
Common Core Standards Addressed:
K.MD1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
Materials:
Pencil
Paper
Sentence cards with pictures (Found at Here and Here)
Envelopes
Items from the cards
Pencils, erasers, tape measures, tissue boxes, string or yarn, rulers, books, paper clips, stapler, crayon box, glue sticks, juice boxes, cups, milk cartons, blocks, markers, feathers, oranges, apples, marbles, numeral cards.
Procedure:
1. Cut the attached sentence cards and laminate them. Put one color set in each envelope and paste a copy of the whole sentence frame on the outside of the envelopes.
2. During math centers time, have a small group of students (up to five, one for each envelope) come over to a large table where they can each have their own space.
3. Show the students that the sentence frame should look like it does on the front of the envelope and the blanks are where they put the pictures to compare.
4. Remind the students what a sentence is supposed to look like.
5. Have objects that match the pictures on the cards
6. Show them how to use the objects to compare- have them feel the difference between the weight using one object in each hand, have them hold the objects next to each other to see which ones are taller, longer, or shorter.
7. Have the students practice writing their sentences down and read them to a partner. Have them compare the answers they got with their partner and see if there are any similarities or differences between their answers and why they may be that way.
8. Finally have the students pick two different items they haven’t worked with yet and write a sentence with it and then draw a picture to show what they’re saying in the sentence.
Assessment:
Talk to the students while they’re working and see where they’re struggling and where they’re excelling. Focus them more on the ones they’re struggling with. Read they’re sentence structures and look at the pictures to make sure they go together. Ex. If the sentence is The pencil is longer than the paperclip., make sure the picture shows a larger pencil and a smaller paperclip.
Differentiation:
Help the students read the words.
Have only one size of each object to make it easier to compare.
Have many sizes of each object to make it more complex. ex: a small pencil and a large pencil, two different types of tape measures, etc.
Have the students compare one object to two others. ex: The pencil is shorter than the stapler. The pencil is longer than the eraser.
Talk about what jobs you may needs these skills for.
1st Grade: Let's Measure Our Shoes!
![Picture](/uploads/9/2/4/5/9245768/3568059.jpeg?138)
Objectives:
Student should be able to measure using cubes with no gaps or overlapping.
Common Core Standards Addressed:
1.MD2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object is being measured is spanned by a whole number of length units with no gaps or overlaps.
Materials:
Connecting cubes
Paper
Markers
Procedure:
1. Have the students work with a partner to trace each other’s right shoe onto a piece of paper.
A. Do an example to go along with each of their steps
2. Then use connecting cubes to measure how big the shoe is.
3. Record the answer by drawing out the cubes on the shoe.
4. Give them other items to measure with like paper clips and erasers.
5. Make a graph as a class taking the data they gathered from their cubes to see who has the biggest and smallest shoe size.
Assessment:
Make sure the students are drawing their cubes the same size as the ones they’re using so the picture is accurate.
See if they’re connecting the cubes all the way/ putting the other items as close as they can go.
Be sure they’re counting the number of cubes correctly.
Differentiation:
Have them compare their shoe size to the number of cubes they used.
Have extra shoes of different sizes and types
Student should be able to measure using cubes with no gaps or overlapping.
Common Core Standards Addressed:
1.MD2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object is being measured is spanned by a whole number of length units with no gaps or overlaps.
Materials:
Connecting cubes
Paper
Markers
Procedure:
1. Have the students work with a partner to trace each other’s right shoe onto a piece of paper.
A. Do an example to go along with each of their steps
2. Then use connecting cubes to measure how big the shoe is.
3. Record the answer by drawing out the cubes on the shoe.
4. Give them other items to measure with like paper clips and erasers.
5. Make a graph as a class taking the data they gathered from their cubes to see who has the biggest and smallest shoe size.
Assessment:
Make sure the students are drawing their cubes the same size as the ones they’re using so the picture is accurate.
See if they’re connecting the cubes all the way/ putting the other items as close as they can go.
Be sure they’re counting the number of cubes correctly.
Differentiation:
Have them compare their shoe size to the number of cubes they used.
Have extra shoes of different sizes and types
2nd Grade: Estimation Station
![Picture](/uploads/9/2/4/5/9245768/6089025.png?545)
Objectives:
· The student will be able to estimate the length of an object by looking at it and choosing the closest length possible as to what length they think that object is.
· The student will be able to measure their chosen object by selecting an appropriate tool to measure it with and accurately reading that chosen tool.
Common Core Standards Addressed:
· 2.MD Measure and estimate lengths in standard
units.
- Estimate lengths using units of inches, feet,
centimeters, and meters.
- Measure the length of an object by selecting
and using appropriate tools such as rulers,
yardsticks, meter sticks, and measuring
tapes.
Materials:
- Rulers
- Pencils
- Yardsticks
- Measuring Tapes
- Estimation Worksheets
Procedure:
1.Review of measurement. (inches, centimeters, yards) The students will answer questions asked by the teacher. How long is a ruler? (1 foot/12 inches/30 ½) How many inches are on a ruler? (12) How many centimeters are on a ruler? (30 ½) How long is a yardstick? (1 yard/36 inches) How many inches are on a yardstick? (36)
2.Review what it means to estimate. An estimation is your best guess at what you think the length will be. Tell the students that it is not a right or wrong answer but they should try to make an educated guess.
3.Ask students some real life questions to get them connecting the content to themselves. Some examples could be having them estimate how long they think certain things are that relate to their lives. Examples could be "Can you think of something that is the length of a yard/foot/inch/centimeter?" or "How long do you think this classroom is?" etc. Use this to get the students to understand how to estimate using their best educated guess. Encourage the students to guess a number that is as close as possible to the number they think it is. Encourage the students that estimating is not random guessing and they need to make their best guess.
4.The students will listen to the rules of the activity that we will be playing. The teacher will demonstrate and model an example for the students.
5.The students will go on to choose objects around the room, estimate their length, then measure them and complete the worksheet on their own. The teacher will be walking around the room and checking for student understanding during this time. The students can use a variety of units to measure during this activity including inches, centimeters and yards.
6.Ask students questions such as "Why did you chose the ruler to measure this object?" or "Do you think that was the best tool to use to measure your chosen object?"
7.When students finish the worksheet, come together as a group to talk about it. Have students share some of the items that they estimated and measured. Students will share what item they chose and explain why they chose the tool they chose and what they estimated. Then ask the class if anyone else measured the same item and what they estimated for it. Talk about why they estimated the way they did and then what they discovered after measuring. Then have the groups that measured it share what answer they got and compare the answers. Ask students if the estimating became easier as they continued through the activity.
8.Close with asking students to share 3 challenges that they ran into during the activity or something they learned today.
Assessment:
· The assessment will be done through observation of the following and questioning throughout the activity.
· Was the student able to look at an object and know which tool would be an appropriate tool to measure their chosen object? (ex. to measure the
chalkboard it makes more sense to choose the measuring tape or yardstick instead of the ruler.)
· Was the student able to use their best-guess to estimate the length of their chosen object?
· Did the student fill out the entire worksheet? The worksheet will serve as an assessment tool to see if the students are able to grasp the content of
the lesson. Is the child able to fill out this worksheet accurately or not? (i.e. label units of measure, make educated guesses, and choose accurate
tools to measure the object with.)
· Ask students questions throughout the activity to enhance student understanding. Get the students to think deeper about what they are estimating
and why they are choosing certain tools.
Differentiation:
· For struggling students: Pair them with a more advanced student for this activity. There might be students who struggle with motor skills; I would have these students partner with a more advanced student. The advanced student would be able to measure the object and the struggling student could read how many inches or feet etc. Students who struggle with estimating would benefit from being with a partner also because they could work together to come to a consensus. Another thing I would do for struggling students would be assign objects to them instead of having them choose. Some students might have trouble narrowing it down to six items in a classroom full of tons of stuff. This would help them to stay a little more focused because they would have a task in mind and know exactly what to do. If the students still struggle I might even give them a sheet with an object and what to measure it with. This way I could just focus on the estimating part of the lesson with them instead of having so many components. If the student struggles with the content, the step before standard units of measure is using non-standard units of measure. I would go back to using non-standard units for them because it is easier for them to understand than using standard units. I would encourage them to use things such as paper clips, shoes, pencils etc. An example would be that I would just have them say how many paperclips an object is instead of how many inches. Then once they grasped this concept I would move forward with them to the standard units.
· For advanced students: I would have these students complete the worksheet and then I would assign them a length. They would then go around the room on a measure hunt finding as many objects as they could that were that length or very close to that length. They could write the objects down on the back of their sheet. Another way to get these students thinking more would be to have them measure each of their items using centimeters and inches (and even yards for large objects).
· The student will be able to estimate the length of an object by looking at it and choosing the closest length possible as to what length they think that object is.
· The student will be able to measure their chosen object by selecting an appropriate tool to measure it with and accurately reading that chosen tool.
Common Core Standards Addressed:
· 2.MD Measure and estimate lengths in standard
units.
- Estimate lengths using units of inches, feet,
centimeters, and meters.
- Measure the length of an object by selecting
and using appropriate tools such as rulers,
yardsticks, meter sticks, and measuring
tapes.
Materials:
- Rulers
- Pencils
- Yardsticks
- Measuring Tapes
- Estimation Worksheets
Procedure:
1.Review of measurement. (inches, centimeters, yards) The students will answer questions asked by the teacher. How long is a ruler? (1 foot/12 inches/30 ½) How many inches are on a ruler? (12) How many centimeters are on a ruler? (30 ½) How long is a yardstick? (1 yard/36 inches) How many inches are on a yardstick? (36)
2.Review what it means to estimate. An estimation is your best guess at what you think the length will be. Tell the students that it is not a right or wrong answer but they should try to make an educated guess.
3.Ask students some real life questions to get them connecting the content to themselves. Some examples could be having them estimate how long they think certain things are that relate to their lives. Examples could be "Can you think of something that is the length of a yard/foot/inch/centimeter?" or "How long do you think this classroom is?" etc. Use this to get the students to understand how to estimate using their best educated guess. Encourage the students to guess a number that is as close as possible to the number they think it is. Encourage the students that estimating is not random guessing and they need to make their best guess.
4.The students will listen to the rules of the activity that we will be playing. The teacher will demonstrate and model an example for the students.
5.The students will go on to choose objects around the room, estimate their length, then measure them and complete the worksheet on their own. The teacher will be walking around the room and checking for student understanding during this time. The students can use a variety of units to measure during this activity including inches, centimeters and yards.
6.Ask students questions such as "Why did you chose the ruler to measure this object?" or "Do you think that was the best tool to use to measure your chosen object?"
7.When students finish the worksheet, come together as a group to talk about it. Have students share some of the items that they estimated and measured. Students will share what item they chose and explain why they chose the tool they chose and what they estimated. Then ask the class if anyone else measured the same item and what they estimated for it. Talk about why they estimated the way they did and then what they discovered after measuring. Then have the groups that measured it share what answer they got and compare the answers. Ask students if the estimating became easier as they continued through the activity.
8.Close with asking students to share 3 challenges that they ran into during the activity or something they learned today.
Assessment:
· The assessment will be done through observation of the following and questioning throughout the activity.
· Was the student able to look at an object and know which tool would be an appropriate tool to measure their chosen object? (ex. to measure the
chalkboard it makes more sense to choose the measuring tape or yardstick instead of the ruler.)
· Was the student able to use their best-guess to estimate the length of their chosen object?
· Did the student fill out the entire worksheet? The worksheet will serve as an assessment tool to see if the students are able to grasp the content of
the lesson. Is the child able to fill out this worksheet accurately or not? (i.e. label units of measure, make educated guesses, and choose accurate
tools to measure the object with.)
· Ask students questions throughout the activity to enhance student understanding. Get the students to think deeper about what they are estimating
and why they are choosing certain tools.
Differentiation:
· For struggling students: Pair them with a more advanced student for this activity. There might be students who struggle with motor skills; I would have these students partner with a more advanced student. The advanced student would be able to measure the object and the struggling student could read how many inches or feet etc. Students who struggle with estimating would benefit from being with a partner also because they could work together to come to a consensus. Another thing I would do for struggling students would be assign objects to them instead of having them choose. Some students might have trouble narrowing it down to six items in a classroom full of tons of stuff. This would help them to stay a little more focused because they would have a task in mind and know exactly what to do. If the students still struggle I might even give them a sheet with an object and what to measure it with. This way I could just focus on the estimating part of the lesson with them instead of having so many components. If the student struggles with the content, the step before standard units of measure is using non-standard units of measure. I would go back to using non-standard units for them because it is easier for them to understand than using standard units. I would encourage them to use things such as paper clips, shoes, pencils etc. An example would be that I would just have them say how many paperclips an object is instead of how many inches. Then once they grasped this concept I would move forward with them to the standard units.
· For advanced students: I would have these students complete the worksheet and then I would assign them a length. They would then go around the room on a measure hunt finding as many objects as they could that were that length or very close to that length. They could write the objects down on the back of their sheet. Another way to get these students thinking more would be to have them measure each of their items using centimeters and inches (and even yards for large objects).
3rd Grade: Polygon Perimeter and Area
By: Brittany Armon
![Picture](/uploads/9/2/4/5/9245768/8030680.jpg?1)
Objectives:
· The student will be able to use pieces from the Blokus game to find the area and perimeter of each piece in the game (Areas of 1, 2 3, 4, and 5).
· The student will be able to compare shapes that have the same area and/or perimeter and discuss their findings with others.
· The student will be able to find the perimeter and area of household objects using multiplication and addition.
Common Core Standards Addressed:
·3.MD (6) Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)
·3.Md (7b) Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems and represent whole number products as rectangular areas in mathematical reasoning.
·3.MD (8): Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or within the same area and different perimeters.
Materials:
-Blokus game
-Household objects brought in by the teacher: Notecard, CD case, Math textbook, small and large post-its
-Rulers
-Chart for students to fill in areas and perimeters + answer key for teacher (See below)
-Calculators
Procedure:
1.Begin by reviewing what the definitions of area and perimeter are.
2. Have students hold up rectangle pieces from Blokus game and ask students what the perimeter and area of each one is. Then teacher will hold up an irregular polygon. Ask students how they might find the area and perimeter of shapes like these. (Response should be “count the squares for area and edges for perimeter”
3.Give each student, or pair if there are enough students, a set of pieces from the Blokus game. Tell students to find and write down the perimeter and area in centimeters of all of their pieces. When students finish, teacher checks to see if they are right. Then have them compare with each other what they discovered/ patterns they found: Which ones had the same perimeter? Same area? Same area but different perimeter? Vice versa? Share as a whole group. Regroup and share with teacher. Why did all but one of the 4cm areas have the same perimeter0what makes that shape special? Same for the 5cm pieces.
4.Teacher holds up Blokus game board. Ask students how we could find the area and perimeter of it. If no one suggests adding and multiplying the side lengths to get the perimeter and area respectively, ask students if they could think of a way without counting every single square. As a class, find the area and perimeter of the board and remind students to use addition and multiplication to find areas and perimeters.
5. Distribute household objects and have the students first find the length and width of each object in inches to the nearest inch and record their findings in the table. Then using these measurements, find the perimeter and area in inches. Write them down in the given chart and share their findings with the teacher to check for correct answers. When they have finished this, have students walk around the room and find other objects. See if they can find objects with the same area and/or perimeter.
6.Have students show an example of a number sentence used to find the area and perimeter of one of the objects below their chart.
7.Bring the class back together to wrap up the lesson. Ask students to share their findings, i.e. which object had the biggest area, biggest perimeter, smallest area, smallest perimeter, etc. Have students show an example on the board of a number sentence they wrote to find the area and perimeter. Ask students why we use addition and multiplication to find the area and perimeter of shapes rather than counting each individual unit.
Assessment:
·The teacher will check the student’s work to see if they found the correct area and perimeter of each polygon in the Blokus game.
·The teacher will walk around during the lesson to check to see the students correctly counting the unit centimeters of the Blokus game to find the area and perimeters.
· The teacher will be sure to remind students how they measure precisely: lining the ruler up at the “0 mark” with the edge of the object they are using and then recording to the nearest inch.
·The teacher will check the student’s measurements of the household objects with her own findings to be sure they are correct and to the nearest inch.
·The teacher will ask the students how they found the area and perimeter using multiplication and addition, and check their answers with the answer key to ensure they did so correctly.
·The teacher will check the student’s number sentences used to find the area and perimeter of one object to make sure it is correct.
Differentiation:
Gearing up: Tell students the area or perimeter of one of the household objects, and have them come up with as many different side lengths possible for each area/perimeter.
Gearing down: For household objects, tell students the length of each side so they only have to add/multiply to find the perimeter/area.
· The student will be able to use pieces from the Blokus game to find the area and perimeter of each piece in the game (Areas of 1, 2 3, 4, and 5).
· The student will be able to compare shapes that have the same area and/or perimeter and discuss their findings with others.
· The student will be able to find the perimeter and area of household objects using multiplication and addition.
Common Core Standards Addressed:
·3.MD (6) Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)
·3.Md (7b) Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems and represent whole number products as rectangular areas in mathematical reasoning.
·3.MD (8): Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or within the same area and different perimeters.
Materials:
-Blokus game
-Household objects brought in by the teacher: Notecard, CD case, Math textbook, small and large post-its
-Rulers
-Chart for students to fill in areas and perimeters + answer key for teacher (See below)
-Calculators
Procedure:
1.Begin by reviewing what the definitions of area and perimeter are.
2. Have students hold up rectangle pieces from Blokus game and ask students what the perimeter and area of each one is. Then teacher will hold up an irregular polygon. Ask students how they might find the area and perimeter of shapes like these. (Response should be “count the squares for area and edges for perimeter”
3.Give each student, or pair if there are enough students, a set of pieces from the Blokus game. Tell students to find and write down the perimeter and area in centimeters of all of their pieces. When students finish, teacher checks to see if they are right. Then have them compare with each other what they discovered/ patterns they found: Which ones had the same perimeter? Same area? Same area but different perimeter? Vice versa? Share as a whole group. Regroup and share with teacher. Why did all but one of the 4cm areas have the same perimeter0what makes that shape special? Same for the 5cm pieces.
4.Teacher holds up Blokus game board. Ask students how we could find the area and perimeter of it. If no one suggests adding and multiplying the side lengths to get the perimeter and area respectively, ask students if they could think of a way without counting every single square. As a class, find the area and perimeter of the board and remind students to use addition and multiplication to find areas and perimeters.
5. Distribute household objects and have the students first find the length and width of each object in inches to the nearest inch and record their findings in the table. Then using these measurements, find the perimeter and area in inches. Write them down in the given chart and share their findings with the teacher to check for correct answers. When they have finished this, have students walk around the room and find other objects. See if they can find objects with the same area and/or perimeter.
6.Have students show an example of a number sentence used to find the area and perimeter of one of the objects below their chart.
7.Bring the class back together to wrap up the lesson. Ask students to share their findings, i.e. which object had the biggest area, biggest perimeter, smallest area, smallest perimeter, etc. Have students show an example on the board of a number sentence they wrote to find the area and perimeter. Ask students why we use addition and multiplication to find the area and perimeter of shapes rather than counting each individual unit.
Assessment:
·The teacher will check the student’s work to see if they found the correct area and perimeter of each polygon in the Blokus game.
·The teacher will walk around during the lesson to check to see the students correctly counting the unit centimeters of the Blokus game to find the area and perimeters.
· The teacher will be sure to remind students how they measure precisely: lining the ruler up at the “0 mark” with the edge of the object they are using and then recording to the nearest inch.
·The teacher will check the student’s measurements of the household objects with her own findings to be sure they are correct and to the nearest inch.
·The teacher will ask the students how they found the area and perimeter using multiplication and addition, and check their answers with the answer key to ensure they did so correctly.
·The teacher will check the student’s number sentences used to find the area and perimeter of one object to make sure it is correct.
Differentiation:
Gearing up: Tell students the area or perimeter of one of the household objects, and have them come up with as many different side lengths possible for each area/perimeter.
Gearing down: For household objects, tell students the length of each side so they only have to add/multiply to find the perimeter/area.
4th Grade: Flooring Our Rooms
Objective:
Common Core Standards Addressed: 4.MD.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
Materials:
Procedure:
o Students will work individually on this task and then move to small groups
o We will wrap up with whole group discussion about the various solutions.
o Also ask students to share and justify why they chose those flooring options.
Assessment:
Differentiation:
- The students will be able to use the area formula to calculate the area of four rooms.
- Students will also be able to explain and justify the flooring option they chose orally in small or whole group discussion.
Common Core Standards Addressed: 4.MD.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
Materials:
- Rectangles with measurement lengths
- Floor plan with measurements
- Pencils
- Flooring type chart
- Task sheet
Procedure:
- Start with a warm up activity to review finding the area of a square. Provide students with a rectangle that he/she must calculate the area of. There will be three different size rectangles distributed amongst the students. Students will work in groups of three (one size rectangle in each group).
- Discuss the strategies used for finding the area. If no student provides the area formula use one of the strategies and show how it can be formed into the area formula.
- Show the picture of the room layout. Point out the dimensions labeled on it. (See attached sheet)
- Describe to students that we need to put flooring into each of the rooms.
- Talk about what type of flooring they have in those rooms in their houses (ex: bathroom tile, hallway hardwood, bedroom carpet…)
- Students will then be given the task of choosing which flooring options they want, and deciding how much of it they will need, and what the cost will be.
o Students will work individually on this task and then move to small groups
o We will wrap up with whole group discussion about the various solutions.
- Students will then share what type of flooring they chose and how much they spent.
o Also ask students to share and justify why they chose those flooring options.
- Collect the students’ task sheets
Assessment:
- Visually assess student progress while calculating the area.
- Ask questions for understanding
- What do the numbers represent, what strategy are you using to solve this problem?
- Collect the sheet where students write which flooring option they chose and how much they spent on the floor.
- Assess students based on the use of the area formula
- Ask students to justify their answers to a partner
Differentiation:
- For more advance students I would give them a spending budget and challenge those students to find the type of flooring for each room that was most cost effective.
- For struggling students I would have them use the flooring that was a friendly multiplier, like the five-dollar carpet.
![](http://www.weebly.com/weebly/images/file_icons/rtf.png)
math_task.docx | |
File Size: | 90 kb |
File Type: | docx |
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math_task2.docx | |
File Size: | 47 kb |
File Type: | docx |
5th Grade: Conversion
Grade level:Fifth Grade
Objectives:
· The student will be able to convert units of measurement: centimeters to meters and meters to centimeters.
Common Core Standards Addressed:
· 5.MD Convert like measurement units within a given measurement system.
o Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi- step, real world problems.
o Ex. Convert 5 cm to 0.05m
Materials:
· Meter sticks
· Lined Paper
· Pencils
· White boards
· Dry erase markers
· Worksheet
Procedures:
1. Give each student a meter stick and a blank sheet of lined paper.
2. The student will have roughly five minutes to find three to five things in the classroom that are the same length as the meter stick.
3. Ask students to show the things that they found that were the same length as the meter stick.
4. Tell the students that they will be talking about two units of measurement: centimeters, and meters.
5. Ask students to tell you what system of measurement these units belong to.
6. Tell the students that by the end of the lesson they will be able to convert centimeters to meters and meters to centimeters.
7. Have the students go back to three of their items they measure previously and measure them in centimeters this time. They should write the number of centimeters next where the item is written on their paper.
8. Ask the students what is common among all the items that they measured? (They all are 1 meter and 100 centimeters.)
9. Show the students the meter stick again and tell them that it is the same stick they used during the opening activity. Ask the students how many centimeters are on a meter stick. If they do not know tell them there are 100 cm on a meter stick.
10. Write on the board that 1 m = 100 cm. Explain to the students that these numbers are equivalent with each other.
11. Ask the students how many centimeters would be in two meters. Show them two meter sticks next to each other for a visual. Write this answer on the board as well.
12. Ask the students how they decided that 2 meters was equal to 200 centimeters?
13. Draw the length of a meter on the board and next to it draw a centimeter. Ask the students which is smaller. Ask the students which is bigger. Explain to the students that when they are talking about centimeters and meters the centimeter is smaller.
14. Ask the students if I want to go from centimeters to meters which operation should I use since centimeters are smaller? (multiplication)
15. And if I want to go from meters to centimeters which operation should I use since meters are bigger? (division)
16. The teacher will write
the formula on the board for converting both ways. (Centimeter/100 = Meter. and Meter x 100 = Centimeter) Ask the students if they can guess why there is a 100 in each formula.
17. Write a few problems on the board and have the students solve them on their white boards and then raise their hand when they have the answer.
18. Wait for a majority of the students to have an answer and then take an answer.
19. The class will work on these problems together. The teacher will guide the students in this activity and everyone will figure out the answers together.
20. Have counters available and blocks for concrete learners.
21. Pass out a worksheet and have the students work on it individually. The teacher will circulate the room during this time to help students with any questions they may have.
Assessment:
· Were the students able to convert the units of measurement from centimeters to meters and from meters to centimeters? This will be evaluated based on how well they did on the individual practice worksheet. Were the students able to correctly fill out the worksheet and show their work?
Differentiation:
· For struggling students: Work on more guided practice with these students. Allow students to work with counters if they need the concrete style of learning. Also allow students to work in pairs if they need to so that they can learn from each other.
· For advanced students: Have them mentor the students who might struggle a little more. This will help them learn because they might have to explain some things in their own words to the student they are helping.
6th Grade: Right Triangles
By: Brittany Armon
![Picture](/uploads/9/2/4/5/9245768/9047012.jpg?1)
Objectives:
1. The student will be able to name the formula for the area of a right triangle.
2. The student will be able to find the hypotenuses of triangles using the Pythagorean Theorem.
3. The student will be able to find the area of right triangles using the lengths of the triangles they found.
4. The student will use proper units when finding the areas of triangles.
5. The student will be able to write their own problem for finding the area of right triangles.
Common Core Standards Addressed:
1. 6.G (1): Solve the area of right triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Materials:
-Sticky notes
-Calculators
-Neighborhood sheet + answer key
-Tables to write answers
Procedure:
1. When students come in, hand them a sticky note to write their name and how we find the area of a right triangle. (1/2(b*h)) Post them on the board. Read over them together and correct any that need correcting, discuss any that are written differently (i.e b*h/2) and discuss why they work/don’t work.
2. Ask students how we find the area of a right triangle if we do not know one of the side lengths. (Pythagorean Theorem)
3. Together, Practice finding the area of the following triangle: base=6in, height=? hypotenuse=12in. How do we find the height? (√122-62)
4. Ask students where they have seen right triangles in the real world? At home, outside, in restaurants, stores, etc. Ask students to share with a partner and then with the class
5. Pass out the neighborhood sheet to students. Read intro. Sarah lives in her dad’s house Spring Street, not far from one of her friends. Her mom lives on the other side of the block on Main Street. The school she goes to is on 1st street, and the grocery store her family goes to is on 3rd street. Sarah loves finding math in her environment. She noticed that the street corners and buildings make right triangles. Sarah is in 6th grade and is currently learning about how to find the area of right triangles. She wonders what the areas are of the following:”
6. Working with a partner, students will need to find the areas of the following right triangles:
a. School and her friend’s house using the top, right corner of school, and both bottom corners of friend’s house.
b. Dad’s house and the Grocery store using the top left of store, and both bottom corners of dad’s house.
c.Mom’s house and the Grocery store using the left, bottom corner of store and both top corners of mom’s house.
d.Between the school, her friend’s house, and her dad’s house using the right corners of each.
e.Any other combination the students have time for.
7. Students will record their findings in a table, including the hypotenuses they calculated. Note: Each square represents a square yard.
8. Come back together as a group and discuss findings. What was the smallest area you found for a right triangle? What was the biggest area? Were any areas the same? Did anyone find the area from one corner of a street to another (i.e. half of the grid)?
9. After students have found at least 5 areas, including the 4 required, students can create their own problems by drawing in extra buildings and having their partner find the areas of their new right triangles.
Assessment:
1. The teacher will check for understanding of the proper formula for the area of a triangle through the post-its they will fill out with their name.
2. The teacher will check the student’s tables and findings to see if they have the correct areas.
3. The teacher will check to see that the student’s found the hypotenuses correctly using the Pythagorean Theorem.
4. The teacher will check for the correct units of cm2 on the student’s work.
5. The teacher will check the problems students made up for correct units, formulas, and answers.
Differentiation:
Gearing up: Give the students the same paper with map, but without the grid. Give them some of the lengths of the streets and other helpful lengths, but not all.
Gearing down: Give the students the hypotenuses so they only need to do the computations.
1. The student will be able to name the formula for the area of a right triangle.
2. The student will be able to find the hypotenuses of triangles using the Pythagorean Theorem.
3. The student will be able to find the area of right triangles using the lengths of the triangles they found.
4. The student will use proper units when finding the areas of triangles.
5. The student will be able to write their own problem for finding the area of right triangles.
Common Core Standards Addressed:
1. 6.G (1): Solve the area of right triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Materials:
-Sticky notes
-Calculators
-Neighborhood sheet + answer key
-Tables to write answers
Procedure:
1. When students come in, hand them a sticky note to write their name and how we find the area of a right triangle. (1/2(b*h)) Post them on the board. Read over them together and correct any that need correcting, discuss any that are written differently (i.e b*h/2) and discuss why they work/don’t work.
2. Ask students how we find the area of a right triangle if we do not know one of the side lengths. (Pythagorean Theorem)
3. Together, Practice finding the area of the following triangle: base=6in, height=? hypotenuse=12in. How do we find the height? (√122-62)
4. Ask students where they have seen right triangles in the real world? At home, outside, in restaurants, stores, etc. Ask students to share with a partner and then with the class
5. Pass out the neighborhood sheet to students. Read intro. Sarah lives in her dad’s house Spring Street, not far from one of her friends. Her mom lives on the other side of the block on Main Street. The school she goes to is on 1st street, and the grocery store her family goes to is on 3rd street. Sarah loves finding math in her environment. She noticed that the street corners and buildings make right triangles. Sarah is in 6th grade and is currently learning about how to find the area of right triangles. She wonders what the areas are of the following:”
6. Working with a partner, students will need to find the areas of the following right triangles:
a. School and her friend’s house using the top, right corner of school, and both bottom corners of friend’s house.
b. Dad’s house and the Grocery store using the top left of store, and both bottom corners of dad’s house.
c.Mom’s house and the Grocery store using the left, bottom corner of store and both top corners of mom’s house.
d.Between the school, her friend’s house, and her dad’s house using the right corners of each.
e.Any other combination the students have time for.
7. Students will record their findings in a table, including the hypotenuses they calculated. Note: Each square represents a square yard.
8. Come back together as a group and discuss findings. What was the smallest area you found for a right triangle? What was the biggest area? Were any areas the same? Did anyone find the area from one corner of a street to another (i.e. half of the grid)?
9. After students have found at least 5 areas, including the 4 required, students can create their own problems by drawing in extra buildings and having their partner find the areas of their new right triangles.
Assessment:
1. The teacher will check for understanding of the proper formula for the area of a triangle through the post-its they will fill out with their name.
2. The teacher will check the student’s tables and findings to see if they have the correct areas.
3. The teacher will check to see that the student’s found the hypotenuses correctly using the Pythagorean Theorem.
4. The teacher will check for the correct units of cm2 on the student’s work.
5. The teacher will check the problems students made up for correct units, formulas, and answers.
Differentiation:
Gearing up: Give the students the same paper with map, but without the grid. Give them some of the lengths of the streets and other helpful lengths, but not all.
Gearing down: Give the students the hypotenuses so they only need to do the computations.
7th Grade: Calculating Pizza Crusts
Objectives: After the lesson the students will be able to calculate the area and perimeter of squares and rectangles and find circumference and area of a circle pizza.
Materials:
Procedure:
Assessment:
Differentiation:
Gear Down:
Gearing up:
Materials:
- Pizza task work sheet
- Pencils & paper
- Manipulatives (blocks, cubes, paper)
Procedure:
- Introduce the lesson by giving a warm-up activity where students find the area of a rectangle on the board with given lengths of 5cm by 8 cm.
- Then introduce the task of pizza crusts.
- Students will work in groups of three while solving these problems.
- While students are working make sure they are writing all their work down, this will help in the assessment process.
- Provide the students with the sheet and let them start solving the problems. If needed provide the student with manipulatives to help them solve the areas and perimeters.
- For the back problem where they create their own pizza allow students to use paper and other supplies to create their own pizza. (Square cubes, blocks, ect.)
- When students are finished collect their sheets.
Assessment:
- After collecting the students sheets look over them to see what strategies students are using to solve for area and perimeter. They should be using the formulas, but if they are not make a note of it and the next day show that student the steps he/she can take to get to the abstract formula use.
- While they are working ask students questions like how will you calculate the area?
- What made you decide that the area of this pizza would be 36inches?
Differentiation:
Gear Down:
- I would change some of the numbers on the pizza measurements.
- Instead of the circle being 9 inches I would have it be 5inches. I would also allow the student to use a calculator for the areas. Since they are already working with other students I think that would be helpful to clear up some confusion as well while the students are working.
Gearing up:
- Provide students with the worksheet without the formulas on it.
- Have the students create a pizza example where the area of the pizza must be between 63 and 71 inches. This would allow them to have to think of multiples that equaled a product in this range and provide them with more possibilities to explain.
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