3rd Grade Mathematics
Instructional Week 21
Estimating and measuring objects and solving real-world problems involving
measurement
Paced Standards:
3.M.1: Estimate and measure the mass of objects in grams (g) and kilograms (kg) and the volume of
objects in quarts (qt), gallons (gal), and liters (l). Add, subtract, multiply, or divide to solve one-step
real-world problems involving masses or volumes that are given in the same units (e.g., by using
drawings, such as a beaker with a measurement scale, to represent the problem). +
3.M.2: Choose and use appropriate units and tools to estimate and measure length, weight, and
temperature. Estimate and measure length to a quarter-inch, weight in pounds, and temperature in
degrees Celsius and Fahrenheit. 
(Note: Estimating and measuring length to the nearest quarter-inch will be taught and assessed
after fractions are introduced in February.)
Connections to other 3rd Grade Standards:
3.NS.3: Understand a fraction, 1/b, as the quantity formed by 1 part when a whole is partitioned into
b equal parts; understand a fraction, a/b, as the quantity formed by a parts of size 1/b.
3.NS.4: Represent a fraction, 1/b, on a number line by defining the interval from 0 to 1 as the whole,
and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of
the part based at 0 locates the number 1/b on the number line.
3.NS.5: Represent a fraction, a/b, on a number line by marking off lengths 1/b from 0. Recognize that
the resulting interval has size a/b, and that its endpoint locates the number a/b on the number line.
3.AT.1: Solve real-world problems involving addition and subtraction of whole numbers within 1000
(e.g., by using drawings and equations with a symbol for the unknown number to represent the
problem).
Prerequisite/Foundational Standards:
2.M.1: Describe the relationships among inch, foot, and yard. Describe the relationship between
centimeter and meter.
2.M.2: Estimate and measure the length of an object by selecting and using appropriate tools, such as
rulers, yardsticks, meter sticks, and measuring tapes to the nearest inch, foot, yard, centimeter and
meter.
2.M.3: Understand that the length of an object does not change regardless of the units used.
Measure the length of an object twice using length units of different lengths for the two
measurements. Describe how the two measurements relate to the size of the unit chosen.
2.M.4: Estimate and measure volume (capacity) using cups and pints.
1.M.1: Use direct comparison or a nonstandard unit to compare and order objects according to
length, area, capacity, weight, and temperature.
3rd Grade ISTEP+ Toolkit
Indianapolis Public Schools
Curriculum and Instruction
3.M.1
3.M.1: Estimate and measure the mass of objects in grams (g) and kilograms (kg) and the volume of objects in quarts
(qt), gallons (gal), and liters (l). Add, subtract, multiply, or divide to solve one-step real-world problems involving
masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement
scale, to represent the problem).
Teacher Background Information:
Measurement involves a comparison of an attribute of an item or situation with a unit that has the same
attribute. Lengths are compared to units of length, areas to units of area, time to units of time, etc.
Estimation of measures and the development of benchmarks for frequently used units of measures help
students increase their familiarity with units, preventing errors and aiding in the meaningful use of
measurement.
Teaching standard units of measure can be organized around three broad goals:
1) Familiarity with the unit. Students should have the basic idea of the size of commonly used units and
what they measure. Knowing approximately how much 1 liter of water is or being able to estimate a
shelf as 5 feet long is as important as measuring either of these accurately.
2) Ability to select an appropriate unit. Students should know both what is a reasonable unit of
measure in a given situation and the precision that is required. (Would you measure your lawn to
purchase grass seed with the same precision as you would use in measuring a window to buy a pane
of glass?) Students need practice in selecting appropriate units and judging the level of precision.
3) Knowledge of relationship between units. Students should know the relationships that are commonly
used such as grams and kilograms.
This standard asks for students to reason about the units of mass and volume using units g, kg, and L.
Students need multiple opportunities weighing classroom objects and filling containers to help them develop
a basic understanding of the size and weight of a liter, a gram, and a kilogram. Milliliters may also be used to
show amounts that are less than a liter emphasizing the relationship between smaller units to larger units in
the same system. Word problems should only be one-step and include the same units.
Students are not expected to do conversions between units, but reason as they estimate, using benchmarks
to measure weight and capacity.
Example:
Students identify 5 things that weigh about one gram. They record their findings with words and pictures.
(Students can repeat this for 5 grams and 10 grams.) This activity helps develop gram benchmarks. One large
paperclip weighs about one gram.
Example:
A paper clip weighs about a) 1 gram, b) 10 grams, c) 100 grams. Explain why.
Indianapolis Public Schools
Curriculum and Instruction
3.M.1
3.M.1: Estimate and measure the mass of objects in grams (g) and kilograms (kg) and the volume of objects in quarts
(qt), gallons (gal), and liters (l). Add, subtract, multiply, or divide to solve one-step real-world problems involving
masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement
scale, to represent the problem).
Teacher Background Information:
Foundational understandings to help with measurement concepts:
 Understand that larger units can be subdivided into equivalent units
(partition).
 Understand that the same unit can be repeated to determine the
measure (iteration).
 Understand the relationship between the size of a unit and the number of units needed
(compensatory principal).
Before learning to measure attributes, children need to recognize them, distinguishing them from other
attributes. That is, the attribute to be measured has to “stand out” for the student and be discriminated from
the undifferentiated sense of amount that young children often have, labeling greater lengths, areas,
volumes, and so forth, as “big” or “bigger.”
These standards do not differentiate between weight and mass. Technically, mass is the amount of matter in
an object. Weight is the force exerted on the body by gravity. On the earth’s surface, the distinction is not
important (on the moon, an object would have the same mass, would weigh less due to the lower gravity).
Process Standards to Emphasize with Instruction of 3.M.1:
3.PS.1: Make sense of problems and persevere in solving them.
3.PS.2: Reason abstractly and quantitatively.
3.PS.4: Model with mathematics.
3.PS.5: Use appropriate tools strategically.
3.PS.6: Attend to precision.
3.PS.7: Look for and make use of structure.
Indianapolis Public Schools
Curriculum and Instruction
3.M.2
3.M.2: Choose and use appropriate units and tools to estimate and measure length, weight, and temperature.
Estimate and measure length to a quarter-inch, weight in pounds, and temperature in degrees Celsius and
Fahrenheit. (Note: Estimating and measuring length to the nearest quarter-inch will be taught and assessed after
fractions are introduced in February.)
Teacher Background Information:

For most attributes measured in school, we can say that to measure means that the attribute measured is
“filled” or “covered” or “matched” with a unit of measure with the same attribute.

Teaching standard units of measure can be organized around three goals:
1. Familiarity with the unit. Students should have a basic idea of the size of commonly used units and
what they measure.
2. Ability to select an appropriate unit. Students should know both what is a reasonable unit of
measure in a given situation and the precision that is required.
3. Knowledge of relationships between units. Students should know the relationships that are
commonly used, such as those between inches, feet, and yards or milliliters and liters.

Developing Unit Familiarity:
o Two types of activities develop familiarity with standard units: (1) comparisons that focus on a single unit and
(2) activities that develop personal referents or benchmarks for single units or easy multiples of units.
o Measurement sense demands that students be familiar with standard measurement units, be able to make
estimates in terms of these units, and meaningfully interpret measures depicted with standard units. As you
teach the standard units, review necessary words and symbols and include these on your math word wall.
Perhaps the biggest error in measurement instruction is the failure to recognize and separate two types of
objectives: (1) understanding the meaning and technique of measuring a particular attribute and (2) learning
about the standard units commonly used to measure that attribute.
Indianapolis Public Schools
Curriculum and Instruction
3.M.2
3.M.2: Choose and use appropriate units and tools to estimate and measure length, weight, and temperature.
Estimate and measure length to a quarter-inch, weight in pounds, and temperature in degrees Celsius and
Fahrenheit. (Note: Estimating and measuring length to the nearest quarter-inch will be taught and assessed after
fractions are introduced in February.)
Teacher Background Information:
Students also need to be able to measure temperature in degrees Celsius and Fahrenheit.
Process Standards to Emphasize with Instruction of 3.M.2:
3.PS.1: Make sense of problems and persevere in solving them.
3.PS.2: Reason abstractly and quantitatively.
3.PS.4: Model with mathematics.
3.PS.5: Use appropriate tools strategically.
3.PS.6: Attend to precision.
3.PS.7: Look for and make use of structure.
Indianapolis Public Schools
Curriculum and Instruction
Instructional Week 21
3rd Grade Mathematics Assessment
Name: _____________________________
1.
Jorge is filling a large fish tank. Which of the following containers should Jorge use to fill his fish tank
most quickly?
A) one gram
B) one quart
C) one liter
D) one gallon
2.
The total weight, in grams, of an apple, lemon, and banana is shown below. If the apple and lemon
together weigh 316 grams, what is the weight of the banana?
A) 194 grams
B) 200 grams
C) 284 grams
D) 916 grams
Indianapolis Public Schools
Curriculum and Instruction
3.
Julius put a lime on the scale and found that it weighed 60 grams. He used the same scale to weigh an
orange. About how much did the orange weigh?
A) 75 grams
B) 90 grams
C) 63 grams
D) 85 grams
4.
Keisha is dressed to go outside as shown in the picture below.
Which of the following is the best estimate of the outside temperature if Keisha is dressed perfectly for
the weather?
A) 82°F
B) 82°C
C) 28°F
D) 28°C
Indianapolis Public Schools
Curriculum and Instruction
5.
Lonnie and Mason have a leaky faucet in their backyard. They want to find out how much water is
wasted by that faucet in one hour. At 2:15 p.m., they put a container under the faucet to catch the
water. At 2:30 p.m., they checked to see how much water was in the container. The picture below
shows how much water they had collected.
If the faucet continues to leak at this rate, how much water will they collect in one hour?
Show all work.
Answer _________________________
If Lonnie and Mason leave the container under the faucet and don’t pour any water out, will the
container overflow before 4:00 p.m.? Explain how you know.
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Indianapolis Public Schools
Curriculum and Instruction
Instructional Week 21
3 Grade Assessment Answer Key
Correct Answer
D
C
B
C
4 liters
Yes, it looks like a little less than
6 liters will fit in the container. 6
liters of water will leak from the
faucet by 3:45, so the container
will overflow before 4:00.
rd
Question
1
2
3
4
5a
5b
2
1
0
Standard(s)
3.M.1
3.M.1
3.M.1
3.M.2
3.M.1
3.M.1
Content Rubric
A score of two indicates a thorough understanding of the mathematical concepts embodied in the
task. The response
 shows content related work executed correctly and completely.
A score of one indicates a partial understanding of the mathematical concepts embodied in the
task. The response
 contains errors in the content related work
A score of zero indicates limited or no understanding of the mathematical concepts embodied in
the task.
Indianapolis Public Schools
Curriculum and Instruction