Measure and Calculate Mass and Volume - 3rd Grade Math

1. Keisha has 6 kg of rice and shares it equally into 2 bags. How many kilograms of rice go in each bag?
   Answer: 3 kg Keisha divides 6 kg of rice equally into 2 bags, so each bag gets 6 divided by 2, or 3 kg, making Choice C correct. Choice A (2 kg) would result from dividing by 3 bags instead of 2. Choice B (4 kg) does not match dividing 6 kg by any whole number of bags in this problem. Choice D (12 kg) comes from multiplying 6 by 2 instead of dividing.
2. A sandwich has a mass of 200 g and an apple has a mass of 150 g. How much more mass does the sandwich have?
   Answer: 50 g 50 g is correct because 200 g minus 150 g equals 50 g. 150 g is incorrect because it repeats the apple's mass instead of the difference. 50 kg is incorrect because it uses the wrong unit; the problem is measured in grams. 350 g is incorrect because it adds the two masses instead of subtracting them.
3. Keisha has 6 kg of dog food and shares it equally into 2 bags. How many kilograms are in each bag?
   Answer: 3 kg 6 kg divided equally into 2 bags means 6 divided by 2, which equals 3 kg in each bag, so D is correct. Choice A (12 kg) doubles the amount instead of dividing. Choice B (4 kg) does not match dividing 6 by 2. Choice C (2 kg) confuses the number of bags with the amount in each bag.
4. Which is a reasonable estimate for the mass of a pencil?
   Answer: 10 g 10 g is correct because a pencil is light, and grams are used to measure small masses. 10 kg is incorrect because that is far too heavy for a pencil. 100 kg is incorrect because it is an unreasonably large mass for a pencil. 1 kg is incorrect because it is still much heavier than a real pencil.
5. Based on the measuring cup shown, if Alex pours the liquid into $4$ equal glasses, how many milliliters will be in each glass?
   Answer: $175$ milliliters per glass The measuring cup shows 700 mL of liquid. Dividing equally into 4 glasses: 700 ÷ 4 = 175 mL per glass. Choice B results from misreading the cup as 800 mL. Choice C comes from reading 900 mL. Choice D assumes 1000 mL (1 liter).
6. Three packages have masses of 1.5 kg, 800 g, and 1200 g. What is the total mass of all three packages in kilograms?
   Answer: 3.5 kilograms total mass Converting 800 g to 0.8 kg and 1200 g to 1.2 kg, the total mass is 1.5 + 0.8 + 1.2 = 3.5 kilograms, so Choice D is correct. Choice A (2.3 kilograms) comes from adding only the first two packages and forgetting the third. Choice B (4.7 kilograms) comes from an addition error when combining the three masses. Choice C (3500 kilograms) comes from not converting grams to kilograms at all before adding.
7. Sofia bought 3 apples, and each apple has a mass of 200 g. What is the total mass of the apples?
   Answer: 600 g Three apples at 200 g each means 3 times 200, which equals 600 g. Choice B comes from multiplying by 2 apples instead of 3. Choice C comes from an addition error. Choice D comes from multiplying by 4 apples instead of 3.
8. Maya has a water bottle that holds 850 milliliters when full. She drinks 300 milliliters and then adds 150 milliliters back to the bottle. How many milliliters of water are now in Maya's bottle?
   Answer: 700 milliliters Starting with 850 milliliters, subtracting the 300 milliliters Maya drinks gives 550 milliliters, and adding back 150 milliliters gives 700 milliliters, matching choice A. Choice B is just the bottle's full capacity with no change applied. Choice C only accounts for the milliliters Maya drank and forgets she added some back. Choice D adds all three amounts instead of subtracting and then adding.
9. Marcus has a backpack that weighs 5 kg and adds a 2 kg lunch bag. What is the total mass?
   Answer: 7 kg Adding 5 kg and 2 kg gives a total mass of 7 kg. Choice B comes from a multiplication error instead of addition. Choice C comes from subtracting instead of adding. Choice D comes from an addition error.
10. Sofia bought 3 apples that each have a mass of 200 g. What is the total mass?
    Answer: 600 g 600 g is correct because 3 times 200 g equals 600 g. 400 g is incorrect because it does not match multiplying 3 by 200. 800 g is incorrect because it does not match the correct product. 600 kg is incorrect because it uses the wrong unit; the apples are measured in grams, not kilograms.
11. Keisha has 6 kg of rice. She keeps none for herself and divides all of it equally between 2 friends. How many kilograms does each friend get?
    Answer: 3 kg Each friend gets 3 kg, since Keisha divides the 6 kg equally between her 2 friends: 6 divided by 2 equals 3. Choice A (2 kg) would result from splitting the rice three ways instead of two. Choice C (4 kg) doesn't match dividing 6 by 2. Choice D (3 g) has the right number but the wrong unit; the rice is measured in kilograms, not grams.
12. Emma has 3000 milliliters of juice. She pours it equally into 5 glasses, then drinks the juice from 2 of the glasses. How many milliliters of juice are left?
    Answer: 1800 milliliters 1800 milliliters is correct because pouring 3000 mL into 5 equal glasses gives 600 mL per glass; drinking 2 glasses removes $2 \times 600 = 1200$ mL, leaving $3000 - 1200 = 1800$ mL. 600 milliliters is incorrect; that's the amount in just one glass, not what remains overall. 1200 milliliters is incorrect because that's the amount Emma drank, not what's left. 2400 milliliters is incorrect; it doesn't match subtracting the amount drunk from the total.
13. Carlos has a backpack that weighs 5 kg and a bicycle that weighs 8 kg. What is the total mass of both?
    Answer: 13 kg This question tests 3rd grade measurement: measuring and calculating with mass (grams, kilograms) and volume (liters), and solving one-step word problems (CCSS.3.MD.2). Mass measures how heavy something is. We use grams for lighter objects and kilograms for heavier objects (1 kg = 1000 g). Volume measures how much liquid something holds, using liters. To solve measurement word problems, identify the operation (add, subtract, multiply, divide) and make sure units are the same. The problem gives a backpack with 5 kg and a bicycle with 8 kg, and asks us to find the total mass of both. Choice B is correct because 5 kg + 8 kg = 13 kg. This shows understanding of adding masses in kilograms. Choice D represents unit confusion: 13 g, which typically happens because students might confuse heavy items like bicycles with light units. To help students: Provide hands-on measurement experiences using scales (balance and digital) and measuring cups/beakers. Have students hold objects and estimate mass before measuring. Create reference points ('A pencil is about 10 grams, a textbook is about 500 grams, I weigh about 35 kilograms'). Use real containers to understand liters (water bottle = 1 liter, juice box = smaller). Practice with manipulatives and real measurements. Watch for: Students who don't include units in answers, students who use unrealistic measurements (person weighing 5 g), students who confuse grams and kilograms, and students who don't convert units when needed (adding 2 kg + 500 g without converting to same unit).
14. A recipe calls for $2$ kilograms of flour. Sam has three bags of flour with masses of $750$ grams, $600$ grams, and $500$ grams. How many more grams of flour does Sam need for the recipe?
    Answer: $150$ grams more flour is needed Recipe needs 2 kg = 2000 g. Sam has 750 + 600 + 500 = 1850 g. He needs 2000 - 1850 = 150 g more. Choice B subtracts only the largest bag from 2000 g. Choice C adds all bags instead of finding the difference. Choice D makes an arithmetic error in addition.
15. Jamal's pencil case has a mass of 150 g and his notebook is 300 g. What is the total mass?
    Answer: 450 g Adding 150 g and 300 g gives 150 plus 300, which is 450 g. Choice B, 500 g, comes from a rounding error in the addition. Choice C, 350 g, does not match the sum of the two masses. Choice D, 150 g, is only the mass of the pencil case and leaves out the notebook.
16. A soccer ball has a mass of 450 g and a basketball is 600 g. What is the difference in mass?
    Answer: 150 g This question tests 3rd grade measurement: measuring and calculating with mass (grams, kilograms) and volume (liters), and solving one-step word problems (CCSS.3.MD.2). Mass measures how heavy something is. We use grams for lighter objects and kilograms for heavier objects ($1 \, \text{kg} = 1000 \, \text{g}$). Volume measures how much liquid something holds, using liters. To solve measurement word problems, identify the operation (add, subtract, multiply, divide) and make sure units are the same. The problem gives a soccer ball mass of 450 g and a basketball of 600 g, and asks for the difference in mass. Choice A is correct because $600 \, \text{g} - 450 \, \text{g} = 150 \, \text{g}$, showing subtraction in the same unit, like comparing the weight of sports balls where a basketball is typically heavier. Choice D represents a unit confusion error by using kilograms instead of grams; this typically happens because students ignore the unit scale, as 150 kg would be like a person's mass. To help students: Provide hands-on measurement experiences using scales (balance and digital) and measuring cups/beakers. Have students hold objects and estimate mass before measuring. Create reference points ('A pencil is about 10 grams, a textbook is about 500 grams, I weigh about 35 kilograms'). Use real containers to understand liters (water bottle = 1 liter, juice box = smaller). Practice with manipulatives and real measurements. Watch for: Students who don't include units in answers, students who use unrealistic measurements (person weighing 5 g), students who confuse grams and kilograms, and students who don't convert units when needed (adding $2 \, \text{kg} + 500 \, \text{g}$ without converting to same unit).
17. Jamal's pencil case has a mass of 150 g. His notebook has a mass of 300 g. What is the total mass?
    Answer: 450 g 150 g plus 300 g equals 450 g, so B is correct. Choice A (500 g) does not match adding the two given masses. Choice C (350 g) is too low for the sum of 150 g and 300 g. Choice D (150 g) repeats the mass of the pencil case alone, not the total.
18. A backpack has a mass of 3,200 grams. A lunchbox has a mass of 800 grams. What is the difference in mass between the backpack and the lunchbox?
    Answer: 2,400 grams Since 3,200 minus 800 equals 2,400, the difference in mass is 2,400 grams. Choice A (400 grams) comes from a subtraction error rather than the actual difference. Choice C (4,000 grams) comes from adding the two masses instead of subtracting them. Choice D (240 grams) drops a zero from the correct difference by mistake.
19. Which is a reasonable estimate for the mass of a backpack?
    Answer: 5 kg A backpack's mass is best estimated as D) 5 kg, about the weight of a few textbooks. Choice A (50 kg) is ten times too heavy, closer to an adult's body weight. Choice B (0.5 kg) is too light, closer to a small book. Choice C (5 g) confuses grams with kilograms; 5 grams is lighter than a paperclip.
20. Emma has 5 kg of rice and uses 2 kg for dinner. How many kilograms of rice are left?
    Answer: 3 kg Subtracting 2 kg from 5 kg leaves 3 kg. Choice A comes from a subtraction error. Choice B has the right number but the wrong unit, grams instead of kilograms. Choice C comes from adding instead of subtracting.

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