Measurement
90 Degree Angles
Practice Measuring with a Ruler!!!
Finding Perimeter
Here is another website for you to see it
www.mathsisfun.com/geometry/perimeter.html
www.mathsisfun.com/geometry/perimeter.html
How to Find Shapes With The Same Perimeter!
John has 14m of landscaping ties (wood) and he would like to make a flowerbed frame using it. Find all the dimensions John could make for his flower bed.
Step 1. Write the formula ( P= L + L + W + W ) Perimeter = Length + Length + Width + Width Step 2. Write what do you know. We know the question is about perimeter because he would like to find all of the frames not the space inside the frame. We also know that the perimeter is 14m. Step 3. Draw the chart and start with 1. |
Step 3. Draw the chart and start with 1.
Step 4. Subtract the two lengths from the perimeter. This will give you the sum of both widths.
14 - (1 +1) = 12
Step 5. Take the sum of both widths and divide it by 2. This will make 2 width dimensions which is what you will need for a rectangle.
12 divided by 2 = 6.
Step 6. Check! Does 6 + 6 + 1 + 1 = 14? Yes!
Step 6. We next try the length as 2.
14 = 2 + 2 + W + W
Step 7. Same thing! 14 subtract the two lengths.
14 - ( 2+2) = 10
10 is the sum of both widths.
Step 8. Divide the sum of both widths by two.
10 divided by 2 = 5
Step 9. Check! Does 2 + 2 + 5 + 5 = 14? Yes!
14 = 2 + 2 + W + W
Step 7. Same thing! 14 subtract the two lengths.
14 - ( 2+2) = 10
10 is the sum of both widths.
Step 8. Divide the sum of both widths by two.
10 divided by 2 = 5
Step 9. Check! Does 2 + 2 + 5 + 5 = 14? Yes!
Do you notice a patterns forming? As the length increases by one, the width decreases by one.
Step 10. Try 3. 14 = 3 + 3 + W + W Step 11. Same thing! 14 subtract the two lengths. 14 - ( 3+3) = 8 8 is the sum of both widths. Step 12. Divide the sum of both widths by two. 8 divided by 2 = 4 Step 13. Check! Does 3 + 3 + 4 + 4 = 14? Yes! |
Finding Area
Here is another way explanation for area
www.mathsisfun.com/geometry/area.html
www.mathsisfun.com/geometry/area.html
How to Find Shapes with The Same Area
Sarah would like to make a fairy garden with an area of 24 cm square.
Find all of the potential dimension for Sarah's garden.
Find all of the potential dimension for Sarah's garden.
Step 8. STOP! We already know that 4 x 6 = 24. We stop when we start to repeat ourselves.
Finding a Given Area and Perimeter
Mike would like to make his garden 32 m square, but he only have 24 m of fence to keep the deer out. What dimensions does Mike have to make his garden.
Step 1. Write the formulas.
A = L X W P = L + L + W + W Step 2. What do we know? A = 32 m square P = 24 m Step 3. We start by following the steps to solve for area. This is because there will be WAY more dimensions for perimeter than their will be for area. Step 4. Start with 1. 1 X ___ = 32 Step 5. 2 X ___ = 32 |
Step 6. Continue to find all of the dimensions for area until you start to repeat.
Step 7. Once you have found all the dimensions for area the rest is easy! Simply fill in the formula for perimeter using the numbers from area! P = L + L + W + W P = 1 + 1 + 32 + 32 = 66m P = 2 + 2 + 16 + 16 = 36m Can't do 3. P = 4 + 4 + 8 + 8 = 24m Here is our answer! Mike can make his garded 8m X 4 m so that he can use his 24m of word and have a 32 m square garden! |
Volume
When looking for volume, start by finding area. L X W. The only difference is we are also adding height. This makes a 3D object.
L X W X H
10 X 10 X 10 = 1000 cm cubed
L X W X H
10 X 10 X 10 = 1000 cm cubed
Find all the Dimensions for a Given Volume
Christy has 24 centimeter cube blocks. She wants to make the perfect tower so she would like to find all of the dimensions she can make using 24 blocks.
Step 1. Write the formula. V = L X W X H
Step 2. Write out all the multiplication facts for 24.
Step 3. Start with 1.
1 X 24 = 24 2 X 12 = 24 3 X 8 = 24 4 X 6 = 24 Stop (repeating)
Step 4. Find all of the factors for each individual number.
Work up from 1.
1 X 24 = 24 2 X 12 = 24 3 X 8 = 24 4 X 6 = 24
1 X(24x1) (2x1) x 12 (have it) (3x1) x 8 (have it) (4x1) x 6 (have it)
1 X(2x12 2 x (1x12)(have it) 3 x (1x8) (have it) (2x2) x 6 (have it)
1 X(3x8) 2 x (2x6) 3 x (2x4) (have it) 4 x (1x6) (have it)
1 X(4X6) 2 x (3 x4) 4 x (2x3) (have it)
Please work through and find all of the factors of each number. Yes it is a lot of work, but if you miss factors earlier, you will catch any that you miss by doing this.
Step 2. Write out all the multiplication facts for 24.
Step 3. Start with 1.
1 X 24 = 24 2 X 12 = 24 3 X 8 = 24 4 X 6 = 24 Stop (repeating)
Step 4. Find all of the factors for each individual number.
Work up from 1.
1 X 24 = 24 2 X 12 = 24 3 X 8 = 24 4 X 6 = 24
1 X(24x1) (2x1) x 12 (have it) (3x1) x 8 (have it) (4x1) x 6 (have it)
1 X(2x12 2 x (1x12)(have it) 3 x (1x8) (have it) (2x2) x 6 (have it)
1 X(3x8) 2 x (2x6) 3 x (2x4) (have it) 4 x (1x6) (have it)
1 X(4X6) 2 x (3 x4) 4 x (2x3) (have it)
Please work through and find all of the factors of each number. Yes it is a lot of work, but if you miss factors earlier, you will catch any that you miss by doing this.
Capacity
When you fill a container with liquid to find out how much it holds, you measure its capacity.
We measure capacity in liters and millilitres.
We measure capacity in liters and millilitres.
Converting mL and L
1 L = 1000mL
This makes converting mL and L easy! When converting L to mL you times the number by 1000. Move the decimal 3 jumps to the left (because of the three zeroes in 1000 and the number is getting smaller) When converting mL to L you divide the number by 1000. Move the decimal 3 jumps to the right. |
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Displacement
Capacity can be used to solve for volume of shapes that are not square, such as marbles, change, dice, etc.
1 mL of displaced (moved) water is equivalent to 1cm cubed volume. When solving for displacement add water to a graduated cylinder then take a measurement. (25mL) Add the object to the graduated cylinder then take another measurement (36mL) |
Take the measurement after you added the dice (36mL) and subtract from it, the measurement before (25mL).
36 - 25 = 11mL
If 1mL is equivalent to 1cm cubed then,
11mL = 11cm cubed
If 3 dice are 11 cm cubed then we can easily find out what the volume of one di is.
Divide the volume by the number of objects to find out the single volume.
11 divided by 3 equals 3.66 repeating.
We can also use this process to find out the volume for more than three dice.
Find the volume of 10 dice.
3.66 repeating time 10 = 36.66 repeating.
36 - 25 = 11mL
If 1mL is equivalent to 1cm cubed then,
11mL = 11cm cubed
If 3 dice are 11 cm cubed then we can easily find out what the volume of one di is.
Divide the volume by the number of objects to find out the single volume.
11 divided by 3 equals 3.66 repeating.
We can also use this process to find out the volume for more than three dice.
Find the volume of 10 dice.
3.66 repeating time 10 = 36.66 repeating.
Show What You Know - Extra practice
show_what_you_know.docx | |
File Size: | 143 kb |
File Type: | docx |
show_what_you_know_solutions.docx | |
File Size: | 221 kb |
File Type: | docx |
extra_practice_questions_for_measurement__can_be_study_guide_.docx | |
File Size: | 242 kb |
File Type: | docx |
extra_practice_questions_measurement_answer_key__1_.pdf | |
File Size: | 156 kb |
File Type: |
Program of Study
Measurement: Attributes such as length, area, volume, and angle are quantified by measurement.
In what ways can area be communicated?
Students estimate and calculate area using standard units.
Knowledge
Area is expressed in the following standard units, derived from standard units of length: square centimetres square metres square kilometres
A square centimetre (cm2 ) is an area equivalent to the area of a square measuring 1 centimetre by 1 centimetre. A square metre (m2 ) is an area equivalent to the area of a square measuring 1 metre by 1 metre. A square kilometre (km2 ) is an area equivalent to the area of a square measuring 1 kilometre by 1 kilometre. Among all rectangles with the same area, the square has the least perimeter. |
Understanding
Area can be expressed in various units according to context and desired precision.
Rectangles with the same area can have different perimeters. |
Skills and Procedures
Relate a centimetre to a square centimetre.
Relate a metre to a square metre. Relate a square centimetre to a square metre. Express the relationship between square centimetres, square metres, and square kilometres. Justify the choice of square centimetres, square metres, or square kilometres as appropriate units to express various areas. Estimate an area by comparing to a benchmark of a square centimetre or square metre. Express the area of a rectangle using standard units given the lengths of its sides. Compare the perimeters of various rectangles with the same area. Describe the rectangle with the least perimeter for a given area. Solve problems involving perimeter and area of rectangles. |