Measurement



Math 10 Essentials - Measurement

Key Elements:

➢ Benchmarks for estimating.

➢ Units of measure: Metric and Imperial

➢ Conversion within each system i.e. km to m

➢ Situations that require metric to imperial conversion i.e. American tourists and temperature conversions, km to miles, construction industry.

➢ Measurement of length, capacity, and mass

➢ Developmental Framework

Note:

The following lesson plans are laid out according to topic, not according to a single class. The duration of each lesson plan is dependent on the amount of background knowledge required and the ability of your class. The amount of practice required once the lesson is completed should also be adjusted on a class-by-class basis.

Lesson 1

➢ Topic: Measuring Length: Metric Units

➢ Outcomes

D1, D2, D3

➢ Worthwhile Activities

#1 – Measuring and Estimating Using Non-Standard Units of Measurement

This activity will begin with students measuring arm length, hand span, etc. in metric units and using these as their non-standard benchmarks to estimate length of objects around the classroom. For example a student may measure their stride in metres and then walk around the classroom and count how many strides long the room is. They may then use their stride measurement times the number of strides to estimate the dimensions of the room. You may wish to choose ten or so objects for the students to estimate metric length using different benchmarks.

#2 – Measuring and Estimating Using Standard Metric Units

Once students are comfortable with estimating length using their benchmarks, you will have them actually measure length using standard metric units (centimetre, metre). Give each student a metre stick and a thirty centimetre ruler, have them actually measure a several objects around the classroom. Having students measure everyday objects will allow them to form mental benchmarks that they can use when estimating.

➢ Assessment

Estimating and Measurement Journal

See enclosed journal

Students will now measure the same objects they estimated and calculate their error. This will allow students to study and critique their estimates.

➢ Communication

When introducing this section you may wish to have students first guess the measurements of certain objects around the classroom before they have measured their non-standard benchmarks and discuss their predictions and how they arrived at them. Another opportunity for communication may arise when students measure their hand span, stride, etc. This is a good time to discuss which benchmark is appropriate when estimating different lengths and why. This conversation can serve as an introduction and conclusion to worthwhile activity #2 and the journal.

➢ Technology and Materials

- Metre Sticks, 30cm Rulers and Calculators.

- See included worthwhile activity and journal sheets.

Lesson 2

➢ Topic: Measuring Length: Metric Conversions

In this lesson student will develop the skills to complete metric conversions of length by revisiting operations with ten. The amount of time you spend on this lesson will be determined by the ability of your class. It is vital that these conversions happen without the aid of a calculator and with the knowledge of the base ten number system.

➢ Outcomes

C2

➢ Mental Math

You may wish to focus the mental math portion of your class on operations with the number ten. Refer to p.147-148, # 5 and 6 for extra practice.

➢ Assessment

Text book: p. 147-148, #’s 7 - 13

➢ Communication

In addition to having students convert metric measurement you could also discuss the appropriateness of their solutions. Meaning, if you are converting from centimetres to metres will you have more or less metres than you had centimetres? It is hoped that this ability to arrive at logical solutions will help to build students confidence.

➢ Technology and Materials

- Metric Conversion Practice Sheets (See enclosed)

- Text Book

Lesson 3

➢ Topic: Introduction to Units of Imperial Measurement

The purpose of this lesson is to introduce students to the units of the imperial system and become comfortable manipulating the common fractions used in measurement. It is because of this connection to the imperial system that we limit our activities on fractions to halves, fourths, eights and sixteenths.

➢ Outcomes

A7, A8, A9, C3

➢ Mental Math

Students should practise doubling and halving.

➢ Worthwhile Activities

Fraction Referral Sheet

Instruct students to select one of the five strips of paper and label it 1. Then have students select another strip and fold it once. Draw a line on the fold and label each piece the appropriate fraction as it pertains to the whole (students should have the fold in the center of the strip). Now have students fold another strip of paper twice and repeat the same procedure. Students should now have three strips of paper labelled as one, halves and fourths. Repeat this step twice folding one strip of paper in half three times and another strip in half four times. This will create eights and sixteenths. Once students have all five strips labelled, have them glue the strips to a sheet of paper so that the folds are aligned and equivalent fractions are easily read.

One Inch Rulers

Included in this package is a page of blank one inch rulers that can be used as templates. One suggestion is to have students label the rulers in different intervals and fill in the increments. This is reinforcing the halving and doubling strategies reviewed in the mental math portion of the lesson.

➢ Assessment

- In-Class Activity: Using the fraction referral sheet, list 12 pairs of equivalent fractions.

- Adding Fractions #1 and #2 (See enclosed)

➢ Communication

This lesson has many opportunities for communication. The concept of a whole and the process of dividing it into pieces is an important concept.

➢ Technology and Materials

- Coloured paper cut into strips

- Glue and Scissors

- One Inch Rulers

Lesson 4

➢ Topic: Measuring Length: Imperial Units

In this lesson, students will continue to work with the Imperial system. Students will estimate and measure in the imperial system by completing the worthwhile tasks listed below. It is recommended that you also have students convert within the Imperial system, meaning feet to inches and vice versa. The practice of converting between Imperial and Metric Systems is not covered in this unit.

➢ Outcomes

A7, A8, A9, C3, D1, D2, D3

➢ Mental Math

- Students should practice working with multiplying and dividing by twelve.

- It may be useful to have students record the multiples of twelve on the back of their Fraction Referral Sheet.

➢ Worthwhile Activities

#1 – Measuring and Estimating Using Non-Standard Units of Measurement

This activity will begin with students measuring arm length, hand span, etc. in imperial units and using these as their non-standard benchmarks to estimate objects around the classroom. For example a student may measure their stride and then walk around the class room and count how many strides long the class is. They may then use their stride measurement times the number of strides to estimate the dimensions of the room. You may wish to choose ten or so objects for the students to estimate using different benchmarks.

#2 – Measuring and Estimating Using Standard Imperial Units

Once students are comfortable with estimating length using their benchmarks you may wish to have them measure actual length using standard Imperial units of measure( inches, feet). Give each student a yard stick and a 12-inch ruler and have them actually measure several objects around the classroom. Having students measure common objects in Imperial measure will allow them to form additional mental benchmarks that they can use when estimating length in Imperial units.

➢ Assessment

- Text p. 149 -150 Review examples with class, p. 151 #’s 1, 2, 5, 6, p. 153, #’s 5, 6

- You may wish to expand #7 on page 151 into another form of assessment. One suggestion would be to have students study flyers from local hardware stores and identify products and industries that are measured using the imperial system. Another possibility would be to have students research which countries work predominantly in the imperial versus metric system.

- Feet ( Inches Practice Sheet (See enclosed)

➢ Communication

The activities outlined above will spark discussion similar to when the metric unit started. You may also discuss the practice of converting from metric to imperial and the necessity for preciseness.

➢

➢ Technology and Materials

- Rulers, Metre Sticks, Fraction Referral Sheet

➢

Practise Imperial conversions

Mental Math: Multiplying and dividing by 10

Textbook: Imperial conversion p 147-148 (Length only)

Blackline Masters: Imperial Conversion practise

➢

Which countries still use Imperial measure? Which industries

Lesson 5

➢ Topic: Fraction use in Imperial measureMeasuring Capacity : Metric Units

This lesson focuses on estimating capacity and conversion among metric units for measuring capacity.

➢ Outcomes

C2, D4

➢ Mental Math

You may wish to focus the mental math portion of your class on operations with the number ten.

Refer to p.147-148, # 5 and 6 for extra practice.

➢ Worthwhile Activities

One suggestion for this lesson is to collect common containers (500 ml, 1L, 2L, etc.) and use these as benchmarks to estimate capacity.

➢ Assessment

- p. 154 – 155, #’s 3 – 9

- Estimating Capacity Activity (See enclosed)

➢ Communication

Prior to estimating capacity you may choose to discuss the concept of more or less with respect to certain containers. Meaning, obtain one container and have students estimate whether or not other objects will hold more or less volume. This activity will allow students to discuss their methods of estimating and explain their reasoning. Allow students to see that different containers with different shapes hay have the same capacity

➢ Technology and

➢ Materials

- Tim Horton’s large coffee, water bottle, milk bottle, juice box, water dispenser bottle or other possible common containers to using when estimating. Containers with different shape, same capacity

Fraction strip activity

Make their own ruler. (Up to sixteenths)

Practise sheets: adding and subtracting fractions and mixed numbers

Textbook: p. 153 #5,6,

Lesson 6 (Optional)

➢ Topic: Estimating Mass in Metric Units

This topic is listed as optional and teachers may explore it as much as there time or audience allows. It is suggested that the mass portion of this unit focus on converting between common metric units such as millilitres to litres. You may also wish to use this time to review and incorporate discussion on unit price and better buys.

➢ Assessment

- Metric Conversion Practice Sheet (See enclosed)

Lesson 7

➢ Topic: Estimating Large Numbers

The ability to estimate large numbers is a valuable skill which is explored in this lesson

➢ Outcomes

D5

➢ Worthwhile Activity

- Have students estimate the number of Jelly beans in a container and discuss how they arrived at their solution.

- Examine pictures with large numbers of people, cars, buildings, etc. Have students come develop methods to estimate the total number of objects in the pictures. For example, some students may place a coin over a small portion of the photo, count how many objects are under the coin and use this information along with how many coins it takes to cover the photo to estimate the total.

- Another possible activity is to place a measured grid on a small portion of a lawn and count the blades of grass in this grid. You could then measure the lawn and use your estimate to determine the number of blades of grass in the lawn.

➢ Assessment

- p. 157, #’s 1 - 3

➢ Communication

Again, this is another opportunity to discuss methods and strategies for estimating and how these strategies can be applied to practical situations.

Lesson 8: (Optional)

➢ Topic: Applications of Measurement

This topic is more of an extension that an actual lesson. Teachers may wish to end the measurement unit by having students complete a project that could extend their measurement knowledge to a practical assignment or study. Some possibilities may be to have students examine recipes and discuss how to half or double a recipe, determine how much paint is needed to paint a room, or examine building plans. [pic][pic]

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