Volume, Capacity and Mass - 3P Learningstatic.3plearning.com/...volume_student_AUS_Jan11.pdf ·...

Student BookSERIES

GN

ame

____

____

____

____

____

____

____

____

____

_

Volume, Capacity and Mass

Series G – Volume, Capacity and Mass

Contents

Topic 1 – Volume and capacity• millilitres and litres_ ____________________________________

• cubic centimetres and cubic metres________________________

• displacement__________________________________________

• linking mass, capacity and volume_ ________________________

• measuring mud – investigate_ ____________________________

• water, water, everywhere – investigate_ ____________________

Topic 2 – Mass• grams________________________________________________

• grams and kilograms____________________________________

• tonnes_ ______________________________________________

• mass and capacity______________________________________

• the chocolate challenge – solve____________________________

• cupcake creation – solve_________________________________

Date_completed

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

Copyright ©

Series Authors:

Rachel Flenley

Nicola Herringer

Contents

Topic 1 – Volume and capacity (pp. 1–8)• millilitres and litres_ ____________________________________

• cubic centimetres and cubic metres________________________

• displacement__________________________________________

• linking mass, capacity and volume _________________________

• measuring mud – investigate _____________________________

• water, water, everywhere – investigate _____________________

Topic 2 – Mass (pp. 9–16)• grams________________________________________________

• grams and kilograms____________________________________

• tonnes_ ______________________________________________

• mass and capacity______________________________________

• the chocolate challenge – solve____________________________

• cupcake creation – solve_________________________________

Date_completed

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

/ /

SERIES TOPIC

1G 1Copyright © 3P Learning


Capacity refers to the amount a container can hold and is usually associated with liquid.Common capacity measurements are millilitres and litres. 1000 millilitres = 1 litre 1000 mL = 1 L

Volume and capacity – millilitres and litres

1 When_we_convert:

a millilitres to litres, we by 1000

b litres to millilitres, we by

Convert_these_amounts_to_litres:

a 3 452 mL = b 7 895 mL =

c 10 000 mL = d 12 674 mL =

e 56 780 mL = f 235 mL =

2

3

Solve_these_word_problems._They_all_involve_conversion.

a Omar was filling up a 3 L container with cordial. He only had a small 300 mL jug. How many times did he have to fill the jug to totally fill the container?

____________________________________________________________________________________

b I poured 375 mL out of a 2 L milk container. How much was left? I then poured out another 375 mL. How much is left now?

____________________________________________________________________________________

c How many 315 mL glasses can be filled from a 1.7 L jug? How much is left over?

____________________________________________________________________________________

d Paula is making a punch for her party. She uses 1.5 L of orange juice, 750 mL pineapple juice, 1.25 L of lemonade and 1.25 L of ginger ale. How much punch does she have altogether? How many 250 mL cups will she be able to fill?

____________________________________________________________________________________

4

Convert_these_amounts_to_millilitres:

a 2.568 L = b 3.999 L =

c 10.566 L = d 1.78 L =

e 7.305 L = f 0.35 L =

SERIES TOPIC

G 12Copyright © 3P Learning


Volume and capacity – millilitres and litres

5

6

7

8

How_much_liquid_is_in_each_jug?_Answer_in_both_litres_and_millilitres._The_first_one_has_been_done_for_you.

Fill_the_jugs_below_to_the_amount_shown:

Below_is_a_recipe_for_the_delicious_summer_drink,_Lava_Flow._The_capacity__measurements_are_expressed_in_cups_or_teaspoons._Express_them_in_millilitres:

Lava_FlowIngredients_(for one drink)

• 12 cup of pineapple juice _______ mL

• 12 cup of cream _______ mL

• 12 a banana

• 3 teaspoons of coconut cream _______ mL

• 4 strawberries

• 1 cup ice _______ mL

If_you_were_going_to_make_this_drink_for_your_entire_class,_what_amounts_of_each_ingredient_would_you_need__to_purchase?_Use_a_calculator_if_you_wish._What_is_the_most_effective_unit_in_which_to_express_the_amounts?

a ________ L

________ mL

b ________ L

________ mL

c ________ L

________ mL

d ________ L

_________ mL

e ________ L

________ mL

a 600 mL b 0.4 L c 1800 mL d 1.6 L e 500 mL

1 L

1 L 1 L2 L

1 L

2 L

1 L

1 L

1 L 1 L1 L 1 L

These capacity measurements are useful to know: 1 teaspoon = 5 mL 1 cup = 250 mL

0.5

500

MethodBlend all ingredients (except strawberries) until smooth. Put the strawberries in the bottom of a tall glass and add the blended mixture. Decorate with a drizzle of strawberry topping.

1 L

SERIES TOPIC



Use_the_formula_L_×_W_×_H_=_V_to_find_the_volume_of_these_prisms._You_may_use_a_calculator.

a_ b_ c

d_ e_ f

Volume and capacity – cubic centimetres and cubic metres

1

2

Find_the_volume_of_these_shapes_by_counting_the_cubes._Each_cube_is_1_cm³.

a Volume =______________cm3 b Volume =______________cm3 c Volume =______________cm3

Shape a b c d e f

Volume

15 cm

6.5 cm

8 cm

5 cm4 cm

2 cm

11 cm3.5 cm

7 cm

6 cm 1 cm

2 cm

5 cm4.5 cm

6 cm

4 cm2 cm

2 cm

Remember that volume refers to the amount of space occupied by an object or substance.Commonly used volume measurements are the cubic centimetre and the cubic metre.

One cubic centimetre is 1 cm long, 1 cm wide and 1 cm high. The symbol we use for cubic cm is cm3.1 cm × 1 cm × 1 cm = 1 cm3

One cubic metre is 1 m long, 1 m wide and 1 m high. The symbol we use is m3.1 m × 1 m × 1 m = 1 m3

We can find out the volume of a rectangular prism or cube without counting each block. We just multiply the length by the width by the height.

Length

Height

Width

L × W × H = V5 × 2 × 2 = 20 cm3

SERIES TOPIC



3

4

5

Use_the_formula_L_×_W_×_H_=_V_to_find_the_volume_of_these_prisms._You_may_use_a_calculator.

a_ b_ c_ d

Boxes_of_tissues_are_packed_in_cubic_metre_containers_to_be_shipped_to_supermarkets._Use_a_calculator_to_work_out_how_many_of_these_boxes_will_fit_into_each_container._You_will_first_need_to_work_out_how_many_cubic_centimetres_are_in_a_cubic_metre.

Work_with_a_friend_on_this_activity._You_may_either_physically_build_the_towers_or_choose_to_talk_through_the_problem_together._You_are_building_towers_using_centicubes._One_of_you_makes_your_first_level_with_4_rows_of_3_blocks._The_other_person_starts_with_5_rows_of_4_blocks._The_first_one_has_been_done_for_you.

a Fill in the table to show how the volume of the towers would increase as they grow.

b Your teacher says you can only have 200 cubes between you. You build the towers to the same height. How many levels could you each build?

_____________________________________

_____________________________________

_____________________________________

Person_1 Person_2

1st_level 12 cm3 20 cm3

2nd_level cm3 cm3

3rd_level cm3 cm3

4th_level cm3 cm3

5th_level cm3 cm3

6th_level cm3 cm3

7th_level cm3 cm3

8th_level cm3 cm3

Shape a b c d

Volume

a

________________ boxes

b

________________ boxes

c

________________ boxes

10 cm

20 cm 10 cm

10 cm

10 cm10 cm 10 cm25 cm

10 cm

7.5 m

4 m

4 m

3.25 m3 m

4 m

4 m

3.5 m

5 m

4 m

3.5 m

10 m

Volume and capacity – cubic centimetres and cubic metres

SERIES TOPIC



Now_use_the_objects_below_(or_something_equivalent)._Using_displacement,_find_the_volume_and_capacity_of_each_object.

Objecta b c d e f g

Volume

Capacity

Volume and capacity – displacement

Remember that volume is the amount of space occupied by an object or substance and capacity is the amount an object will hold.Displacement is the amount of fluid that is pushed away when an object is placed in the fluid. We can use displacement to calculate both volume and capacity.

1

2

3

Try_this_experiment_to_find_out_about_displacement._You_will_need_a_jug,_a_lunchbox,_a_tray_and_a__model_made_from_100_centicubes._Work_with_a_friend_or_in_a_small_group.

1_ _Stand the lunchbox in the tray.

2__ _Fill the box to the top with water.

3__ _Carefully submerge the model in the water in the box.

4_ _Pour the water that overflowed into the tray into the measuring jug. How many mL equals 100 cm³?

___________________________________________

_ _Check your answer with that of two other groups. Do they agree with you?

___________________________________________

Using_what_you_now_know_about_volume_and_displacement,_how_many_millilitres_of_water_would_be_displaced_by_objects_with_these_volumes?

a 100 cm3 = __________ mL b 250 cm3 = __________ mL c 500 cm3 = __________ mL

d 8 cm3 = __________ mL e 1000 cm3 = __________ mL f 56 cm3 = __________ mL

g 86 cm3 = __________ mL h 4300 cm3 = __________ mL i 1.9 cm3 = __________ mL

SERIES TOPIC



a

Volume = _____________ cm3

Capacity = _____________ mL

Mass = _____________ g

d

Volume = _____________ cm3

Capacity = _____________ mL

Mass = _____________ g

b

Volume = _____________ cm3

Capacity = _____________ mL

Mass = _____________ g

e

Volume = _____________ cm3

Capacity = _____________ mL

Mass = _____________ g

c

Volume = _____________ cm3

Capacity = _____________ mL

Mass = _____________ g

f

Volume = _____________ cm3

Capacity = _____________ mL

Mass = _____________ g

Do you remember the relationship between volume, mass and capacity?

1 cm³ = 1 mL = 1 g

Volume and capacity – linking mass, capacity and volume

1

2

3

Calculate_the_volume,_mass_and_capacity_of_these_shapes_by_counting_the_cubes._Each_cube_is_1_cm³.

Seven_tenths_of_the_human_body_is_water._Weigh_yourself_in_kg_then_use__a_calculator_to_help_you_work_out_the_answers_to_the_following:

a_ How much of your mass is water? ____________________________

b_ What is the capacity of this water? ____________________________

c_ What is the volume of this water? ____________________________

If_you_could_drain_yourself_of_all_the_water_(not_a_good_idea),_what_kind_and_size_of_container_would_be_suitable_and_why?

____________________________________________________________

____________________________________________________________

____________________________________________________________

SERIES TOPIC



Measuring mud investigate

In this activity you are going to use what you know about the relationship between mass and volume to calculate the volume of the water in mud. You will need a cup, some newspaper and a scale.

Work with a partner. This experiment may take a day or so to complete and is probably best done outside.

Collect a cupful of mud or damp soil. Make sure the mud is not too sloppy. Find its mass by weighing it. How will you do this? Perhaps you could weigh the empty cup and then subtract the weight of the cup.

Now spread out your mud onto sheets of newspaper and leave it to dry in the sun. It may help to place weights on the paper or tape it down. You may also need to label your experiment so it doesn’t get accidentally cleaned up!

Once your mud has dried, carefully collect it and measure its mass. Remember to use the same cup. Why do you need to do this?

What was the volume of water in the mud?

How do you know?

Find a rock that has the same volume as the lost water. How will you do this? How will you know that it has the same volume?

What_to_do

What_to_do_next

Getting_ready

SERIES TOPIC



Water, water, everywhere … investigate

This activity could come in handy should you ever be stranded in the bush somewhere! You will need a garbage bag, some string and a measuring jug. Work in a small group.

You are going to predict, collect and measure the amount of water a tree branch loses through transpiration (evaporation) over the period of a day. It is best to begin the experiment as early in the day as possible and to collect the water as late in the day as you can. Choose a nice sunny day for your experiment. A bit of a breeze will help too.

Choose a nice leafy tree branch. How much water do you think you will be able to collect from it? Write down your predictions.

Put your bag over your selected branch and tie it off. Now, make a pouch at the bottom of the bag and tie that off too.

Leave the bag over the day and come back to collect the water as late as you can.

Cut the pouch and carefully drain the water into a measuring jug. What is the capacity of the water you have collected?

Compare your results with the results of other groups. Do they differ? Why?

Repeat your experiment on another day using the same branch. Are your results different to those of the original experiment? What was different about the two days?

What_to_do

What_to_do_next

Getting_ready

SERIES TOPIC

9GCopyright © 3P Learning

Volume, Capacity and Mass 2

Mass measures how much matter is in an object. We usually measure this by finding out what the object weighs. Mass and weight are slightly different but we often use weight terms when we are talking about day to day mass measurements.Common measurements are grams (g), kilograms (kg) and tonnes (t).There are 1000 g in each kilogram and 1000 kg in a tonne.

Mass – grams

1

2

3

4

This_activity_will_help_you_get_a_feel_for_different_masses._You̕ ll_need_the_objects_in_the_table,_a_calibrated_scale_or_a_balance_scale_and_some_small_masses_(10_g,_50_g,_or_100_g)._Estimate,_then_measure_the_mass:

Item Estimate Mass

scissors

glue stick

calculator

lunch box (full)

lunch box (empty)

pencil case (full)

pencil case (empty)

Estimate_and_then_measure_how_many_of_each_of_these_objects_are_needed_to_balance_10_grams._

Centicubes 5¢_Coins Drawing_pins

Estimate

Measure

Use_your_answers_in_question_1_to_place_the_7_items_on_the_line_in_order_of_their_individual_mass.

Write_each_mass_in_grams,_kilograms_and_grams,_and_as_a_decimal.

Grams 1000 g 350 g

Kilograms_and_grams 2 kg 700 g 5 kg 50 g

Decimal_notation 7.125 kg 3.2 kg

Lightest Heaviest

Weight_measures_the_force_of_gravity_on_an_object_and_mass_measures_its_inertia_or_the_amount_of_matter_that_can_‘push_back’._A_brick_weighs_less_in_outer_space_where_there_is_no_gravity_but_its_mass_stays_the_same._

SERIES TOPIC

G10Copyright © 3P Learning

Volume, Capacity and Mass2

Mass – grams and kilograms

There_are_28_students_in_Mr_Brown’s_class._Being_the_dedicated_and_hardworking_teacher_that_he_is,_he_lugs_their_books_home_to_mark_each_week._

a Each maths book has a mass of 550 g. He puts them all in a tote tray which has a mass of 345 g. What is the total mass he will carry to his car?

_____________________________________________________________

b Last week he took home the spelling books in the same tote tray. The total mass was 9.445 kg. What was the mass of each spelling book?

_____________________________________________________________

c Next week, the football starts again. There goes the marking. Mr Brown will now be sitting in the grandstand munching chips and cheering on the Mighty Blues. If he consumes four 375 g bags of chips in a particularly tense game, how much does he eat?

_____________________________________________________________

1

2

3

Five_children_measured_their_mass.__

a Use decimal notation to write the masses in kilograms as shown on the scales:

A_regular_packet_of_cereal_has_a_mass_of_540_g._An_average_serving_is_45_g.__Answer_these_questions_without_a_calculator.

a How many average servings are there in one packet? ___________________

b There are four people in Michaela’s family. Each has an average serve per day. How many days will the box last? ___________________

c The largest sized box has a mass of 720 g. How long will this box last her family? ___________________

d Michaela’s family is going camping for 2 weeks. They need to take all their food with them. They want to take exactly the right amount of cereal. How many boxes of each size will they need to take? ___________________

Minh

kg

Ben

kg

Heba

kg

Sara

kg

Yasmin

kg

b Now order the children from lightest to heaviest.

15 20 45 50 25 30 35 40 35

40

Lightest Heaviest

SERIES TOPIC



Mass – tonnes

Tonnes are used to measure the mass of heavier objects.An average car has a mass of approximately 2 tonnes. An elephant can have a mass of up to 6 tonnes.

1 tonne (t) = 1 000 kg

1

2

When_we_convert:

a tonnes to kilograms we by 1000

b kilograms to tonnes we by

Convert_these_measurements_from_tonnes_to_kilograms:

a_ 5 t = kg b_ 16 t = kg

c_ 56.25 t = kg d_ 4.125 t = kg

e_ 0.5 t = kg f_ 13.05 t = kg

3 Use_decimal_notation_to_convert_these_kilograms_into_tonnes:

a_ 5 000 kg = t b_ 12 245 kg = t

c_ 44 567 kg = t d_ 6 009 kg = t

e_ 450 kg = t f_ 677 kg = t

5 Complete:

a_ 500 kg + = 1 t b_ 125 kg + = 1 t c_ 456 kg + = 1 t

2 tonnes 6 tonnes

4 1.5 _ 2.5 _ 120 _ 440 _

4 Choose_the_correct_unit_of_measurement_(g,_kg,_t)_for_these_objects:

Now_order_their_masses_from_least_to_greatest:

Least Greatest

When_converting_between__tonnes_and_kilograms_we__often_have_to_move_in_and__out_of_decimal_numbers.___Drawing_the_jumps_can_help.

6___7___8_kg__=__0.678_t

SERIES TOPIC



Mass – tonnes

6

7

8

9

Write_each_mass_in_kilograms,_tonnes_and_kilograms,_and_as_a_decimal.__

Kilograms 1000 kg 350 kg

Tonnes_and_kilograms 2 t 700 kg 5 t 50 kg

Decimal_notation 7.125 t 3.2 t

The_weighbridge_on_the_expressway_measures_the_mass_of_heavy_vehicles.

a Calculate the mass of each load by subtracting the tare (mass without a load) from the total mass measured on the weighbridge. The first one is done for you.

Vehicle Total_mass Tare Mass_of_load

Coach 17 t 200 kg 13.1 t 4 t 100 kg

Tow truck 3 t 878 kg 2.75 t

Campervan 4 t 250 kg 2.569 t

Cement mixer 20 t 456 kg 12.842 t

Semi-trailer 11 t 300 kg 8.675 t

b Which vehicle has the heaviest load? ____________________________

Louisa’s_family_did_a_big_clean_up_at_home_and_took_the_rubbish_to_the_tip._The_total_mass_of_the_car_and_the_trailer_was_measured_each_time.__

a The car’s mass was 1.78 t. Complete the chart to show the total mass measured each time

b What is the total amount of rubbish taken to the tipaltogether? Answer in tonnes.

___________________________________________

A_32_seater_aeroplane_was_filled_to_capacity._The_passengers_had__an_average_mass_of_74_kg._The_average_mass_of_the_luggage_was_15_kg__per_person.

a What is the total mass of passengers in tonnes? __________________

b What is the total mass of the luggage? __________________

c The aeroplane is licensed to carry 4 t. How much extra cargo can they now take? __________________

Load Mass_of_load Total_mass

1 675 kg

2 935 kg

3 798 kg

The_average_was_found_by__dividing_the_total_mass_by_the__number_of_people._So_you_can__‘undo’_this_by_multiplying._

SERIES TOPIC



What is the mass of 1 millilitre of water?

Mass – mass and capacity

1

2

3

Try_this_experiment_to_find_out_about_the_mass_of_water._You_will_need__a_measuring_cup_or_jug,_some_balance_scales_and_some_weights.

1 Measure the mass of the measuring cup.

2 Pour 50 mL of water into the cup.

3 Measure the mass of the cup and water.

4 Calculate the mass of the water by subtracting the mass of the cup.

5 Repeat for 100 mL, 250 mL, 500 mL and 1 L and record your results.

Amount_of_water 50 mL 100 mL 250 mL 500 mL 1 L

Mass

a What have you discovered? 1 mL of water = gram.

b Why did you need to subtract the mass of the cup? ________________________________________

Without_measuring,_can_you_now_calculate_the_mass_of_these_amounts_of_water?

a_ 150 mL = ____________ g b_ 467 mL = ____________ g_ c_ 1.5 L = __________ kg

d_ 980 mL = ____________ kg_ e_ 2.75 L = ____________ kg_ f_ 8.45 L = __________ g

Ben_poured_the_same_amount_of_water_into_five_different_containers._He_then_measured_the_mass_of_each_of_them._If_you_can_work_out_the_mass_of_each_of_the_containers,_Ben_says_your_teacher_will_give_you_5_early_minutes._All_the_clues_you_need_are_in_the_table.

Container A B C D E

Mass_of_container_filled_with_water

365 g 678 g 458 g 1 kg 1.3 g

Mass_of_container 15 g

How_did_you_go?_Did_your_teacher_get_the_memo_about_the_early_minutes?

_______________________________________________________________________________________

_______________________________________________________________________________________

4

1 L

SERIES TOPIC



Try_this_experiment._You’ll_need_10_centicubes,_plasticine,_a_measuring_cup_and_a_tap._Push_the_centicubes_gently_but_fully_into_the_plasticine,_then_carefully_remove_them._Now,_fill_the_holes_with_water._Finally,_measure_the_amount_of_water._

a How much water was used? _____________________________________________________________

b Was it the amount you expected? If not, why do you think it is different?

____________________________________________________________________________________

Mass – mass and capacity

5

6

Sean’s_teacher_asked_him_to_conduct_an_experiment_to_find_out_more_about_the_mass_of_water.__

a He started to draw this graph and table. Complete both for him:

b Sean then decided to see what would happen when he submerged centicubes in the water. This graph shows how much water was displaced as he did this. Use the graph to complete the table:

c Use the information Sean discovered to complete the following table:

Volume_(cm³) 500 cm³ 7 cm³

Capacity_(mL) 25 mL 1 200 mL

Mass_(g) 350 g 1 kg

Cubic_centimetres Water_displaced

10 cm3

20 cm3

5 mL

14 mL

50 cm3

100 mL

850 cm3

Mass_of_water

05 10 15 20

5

10

15

20

Cubic centimetres (cm3)

Mill

ilitr

es (m

L)

Water_displaced

Volume_of_water Mass_of_water

100 mL 100 g

200 mL 200 g

300 mL 300 g

500 mL

600 mL

800 mL

1000 mL0

200

400

600

800

1000

100

100

Volume of water in mL

Mas

s in

g

200 300 400 500 600 700 800 900 1000

300

500

700

900

SERIES TOPIC



The chocolate challenge solve

This word problem requires you to calculate the weight of two identical chocolate bars.

Work with a friend to solve it. You only need a pencil, paper and your brains.

You have two identical chocolate bars. You also have a set of balance scales and two weights, one measuring 100 g and the other measuring 50 g.

If you place one of the chocolate bars on one side of the balance scales, it is balanced by both weights and 13 of the other chocolate bar.

How heavy is each chocolate bar?

Could you write a similar problem for a friend? Use a 200 g weight, a 100 g weight and 2 identical objects in your problem.

What_to_do

What_to_do_next

100g

50g

100g

50g

Getting_ready

Hmmm_…_I_think_algebra__could_be_used_here.

SERIES TOPIC



Cupcake creation solve

This word problem requires you to work out how many cupcakes you could make if you had a specifed amount of ingredients.

You can work alone or with a friend.

Here is the method. Maybe you could make these at home.

Method

1. Preheattheovento200°Candgreasea12cupmuffinpan.

2. Sifttheflourandaddthecastersugar.

3. Makeaholeinthecentreofthemixandaddmilk,butter,vanillaandeggs.

4. Mixgentlyandwhencombined,spoonintothemuffinpan.

5. Bakefor12–15minutes.Letcakescoolinthepanfor5minutesbeforetransferringtoawireracktocool.

6. Oncecold,iceusing112 cupsoficingsugarmixedwith1tablespoonhotwaterandfoodcolouring.

7. Decoratewithsprinkles.

What_to_do

What_to_do_next

Read the recipe (on the right) for cupcakes:

This recipe makes 12 cupcakes.

How many cupcakes could you make if you had:

Ingredients3 kg self-raising flour720 g caster sugar1 L milk600 g butter5 teaspoons vanilla essence

Getting_ready

Volume, Capacity and Mass - 3P Learningstatic.3plearning.com/...volume_student_AUS_Jan11.pdf ·...

Documents

Transcript of Volume, Capacity and Mass - 3P Learningstatic.3plearning.com/...volume_student_AUS_Jan11.pdf ·...