Students generate and represent length measurement data in halves and fourths of an inch on line plots. They learn about and estimate relative units of measure, including weight, liquid volume, and time, and use the four operations to solve problems involving measurement.
Unit Narrative
In this unit, students measure length, weight, liquid volume, and time. They begin with a study of length measurement, building on their recent work with fractions.
In grade 2, students measured lengths using informal and formal units to the nearest whole number. They also plotted such length data on line plots. Here, students explore length measurements in halves and fourths of an inch. They use a ruler to collect measurements and then display the data on line plots, learning about mixed numbers and revisiting equivalent fractions along the way.
Kiran says that the worm is inches long.
Jada says that the worm is inches long.
Use the ruler to explain how both of their measurements are correct.
Next, students learn about standard units for measuring weight (kilograms and grams) and liquid volume (liters). To build a sense of the weight of 1 gram or 1 kilogram, students hold common objects, such as paper clips and bottles of water.
To gain familiarity with liters, students measure the volume of a container by filling it with water by the liter and estimate the volume of everyday containers, such as pots, tubs, and buckets. They then use the scale on measurement tools to measure and represent the volume of liquids.
From there, students move on to measure time. In grade 2, they told and wrote time to the nearest 5 minutes. Now, they tell time to the minute, using the relationship between the hour hand and the minute hand to make sense of times such as 3:57 p.m.
In the final section of the unit, students make sense of and solve problems related to all three measurements. The work here allows students to continue to develop their fluency with addition and subtraction within 1,000 and understanding of properties of operations. It also prompts them to use the relationship between multiplication and division to solve problems.
Measure and estimate weights and liquid volumes of objects.
Section Narrative
In earlier grades, students learned that weight is a measurable attribute, and they directly compared the weights of two objects. In this section, students learn that weight is a measure of how heavy something is and that grams and kilograms are units for measuring weight. Since the distinction between mass and weight is beyond what students need to learn in this grade, the term “weight” is used throughout the unit.
To establish some benchmarks for weights, students hold objects of different numbers of grams and kilograms. Then they estimate the weight of other objects relative to those benchmarks.
Next, students learn that the volume of a liquid is the amount of space a liquid takes up and the volume of a container is the amount of liquid it takes to completely fill it. Students first use informal units, such as plastic cups or spoons to compare the volume of two containers before learning about liters as a unit for measurement.
Students gain concrete experience with this new unit by filling a large container in 1-liter increments. They also estimate the volume of everyday objects, such a sink, a bucket, and a bathtub.
Later, students make sense of fractional units of liquid volume, learn to read the scale on liquid measurement tools (such as beakers), and compare the scales to the marks on rulers.
Measure lengths using rulers marked with halves and fourths of an inch to generate data for making a line plot.
Section Narrative
In this section, students learn to measure lengths in fractions of an inch—first in halves of an inch and then in fourths of an inch. Students partition rulers with whole-number inch marks into equal intervals and then use them to measure lengths of objects in the classroom.
Students learn that measurements that are greater than 1 can be expressed with mixed numbers, which combine a whole number and a fraction less than 1.
As they measure with greater levels of precision, students revisit the idea of equivalent fractions. They see that the half-inch marks are also two-fourths of an inch, and that each whole number of inches can also be expressed as some number of halves or fourths.
Students then use their understanding of the number line and rulers to interpret and create line plots that represent lengths measured in half inches and quarter inches. Students see that all three representations—number lines, rulers, and line plots—have the same structure, which shows whole-number intervals being partitioned into equal parts.
Solve problems involving the four operations and measurement contexts.
Section Narrative
In this section, students solve problems that involve measurements of weight, liquid volume, and time in the context of a state or county fair. The problems prompt students to use all four operations: addition and subtraction within 1,000 and multiplication and division within 100. The problems also prompt students to make sense of the situations and the questions being asked.
In two Information Gap routines, students also have to consider information that might be needed to answer questions. They explain to a partner why they need that information, and they may need to ask different questions if their partner does not have the information requested (MP1). In each situation, students make sense of quantities and their relationships (MP2).
A fair is holding a pumpkin weigh-off. The farmer who grew the winning pumpkin says during some days in August, his pumpkin gained a lot of weight each day. How much did the weight of the pumpkin increase during this time? Missing Information: How much did it gain each day? For how many days?
An optional lesson at the end of the section gives students a chance to examine carnival games and design a game that incorporates concepts of measurement and operations.
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Ways to Represent Measurement Situations
Let’s make sense of and represent measurement situations at the fair.
Solve problems involving addition and subtraction of time intervals in minutes.
Tell time to the minute.
Section Narrative
In this section, students learn to tell and write time to the nearest minute and to show a given time on an analog clock. They also solve elapsed time problems with an unknown start time, unknown duration, or unknown end time.
Han got on the bus:
Han got off the bus:
For how many minutes was Han on the bus?
To reason about the problems, students can use any representation that makes sense to them, such as tables, words, equations, or marks on a clock. Students also examine a variety of reasoning strategies and adjust their approach depending on the problem at hand.
Elena arrived at the bus stop at 3:45 p.m.
She waited 24 minutes for her bus to arrive.
What time did the bus arrive?
Show your thinking. Organize it so it can be followed by others.
As they solve problems, students continue to build their fluency with addition, subtraction, and multiplication (especially multiples of 5, 10, and 15).
