All the resources on this page come from the GADOE Framework 3rd Grade Unit 6 Overview. Reviewing this information before or during planning can help ensure your instruction is aligned with the standards and is at the depth expected.

Unit 6 Overview

In this unit students will:

● Tell and write time to the nearest minute and measure time intervals in minutes.

● Solve elapsed time, including word problems, by using a number line diagram.

● Reason about the units of mass and liquid volume. ○ 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 principle).

● Graph data that is relevant to their lives. While exploring data concepts, students should Pose a question, Collect data, Analyze data, and Interpret data (PCAI).

STANDARDS FOR MATHEMATICAL PRACTICE (SMP)

This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. The statements provided offer a few examples of connections between the Standards for Mathematical Practice and the Content Standards of this unit. The list is not exhaustive and will hopefully prompt further reflection and discussion.

1. Make sense of problems and persevere in solving them. Students make sense of problems involving intervals of time, measuring and estimating liquid volume and masses, and interpreting scaled picture graphs and scaled bar graphs.

2. Reason abstractly and quantitatively. Students demonstrate abstract reasoning by connecting quantity of data and representing the data using a scaled picture graph or scaled bar graph.

3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding their solutions for word problems involving addition and subtraction of time intervals in minutes.

4. Model with mathematics. Students represent data in multiple ways using a scaled picture graph, scaled bar graph and line plot. Additionally, they record their thinking using words, pictures, and numbers to further explain their reasoning in problems throughout many of the tasks in this unit.

5. Use appropriate tools strategically. Students utilize a number line to assist with determining time intervals to the nearest minute. Students also use estimation when determining liquid volume and masses.

6. Attend to precision. Students attend to the language of real-world situations to determine appropriate ways to organize data.

7. Look for and make use of structure. Students make sense of structure when looking at multiplicative patterns in word problems.

8. Look for and express regularity in repeated reasoning. Students continually evaluate their work by asking themselves “Does this make sense?”

*Mathematical Practices 1 and 6 should be evident in EVERY lesson!

CONTENT STANDARDS ADDRESED

Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

MGSE3.MD.1 Tell and write time to the nearest minute and measure elapsed time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram, drawing a pictorial representation on a clock face, etc.

MGSE3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word 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.

Represent and interpret data.

MGSE3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

MGSE3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units – whole numbers, halves, or quarters.

For more detailed information about unpacking the content standards, unpacking a task, math routines and rituals, maintenance activities and more, please refer to the Grade Level Overview.

BIG IDEAS

Time…

● The duration of an event is called elapsed time and it can be measured. Mass and Liquid Volume…

● Mass and liquid volume are important parts of everyday life and can determined a variety of ways.

● Larger units can be subdivided into equivalent units (partition).

● The same unit can be repeated to determine the measure (iteration).

● There is a relationship between the size of a unit and the number of units needed (compensatory principle).

Data and Graphing…

● Charts, tables, line plot graphs, pictographs, Venn diagrams, and bar graphs may be used to display data.

● One way to compare data is through the use of graphs.

● The scale increments used when making a bar graph is determined by the scale intervals being graphed.

ESSENTIAL QUESTIONS

Telling Time…

● What strategies can I use to help me tell and write time to the nearest minute and measure time intervals in minutes?

● How can I use what I know about number lines to help me figure out how much time has passed between two events?

Liquid Volume and Mass…

● What happens when your units of measure change?

● Why is it important to know the mass of an object?

● In what ways can we determine the mass of an object?

● What units are appropriate to measure mass?

● How are units in the same system of measurement related?

● What strategies could you use to figure out the mass of multiple objects?

● What are some ways I can measure the liquid volume?

Graphing and Data…

● · How are tables, bar graphs, and line plot graphs useful ways to display data?

● · How can you use graphs to answer a question?

● · How can surveys be used to collect data?

● · How can surveys be used to gather information?

● · How can graphs be used to display data gathered from a survey?

CONCEPTS AND SKILLS TO MAINTAIN

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

● Fluency with basic addition and subtraction

● Conceptual understanding of multiplication

● Duration and sequence of events

● Telling time

● Comparison/Estimation/Ordering of measurements (length, weight, liquid volume)

● Use straight edge and pencil to draw straight lines

● Measurement to the nearest inch

● Collecting and representing data

● Interpreting line plot and bar graphs

● Organizing and recording data using objects, pictures, pictographs, bar graphs, and simple charts/tables

● Relate addition and subtraction to length

● Using and understanding number lines

Fluency: Procedural fluency is defined as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. Fluent problem solving does not necessarily mean solving problems within a certain time limit, though there are reasonable limits on how long computation should take. Fluency is based on a deep understanding of quantity and number.

Deep Understanding: Teachers teach more than simply “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives. Therefore, students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of foundational mathematics concepts by applying them to new situations, as well as writing and speaking about their understanding.

Memorization: The rapid recall of arithmetic facts or mathematical procedures. Memorization is often confused with fluency. Fluency implies a much richer kind of mathematical knowledge and experience.

Number Sense: Students consider the context of a problem, look at the numbers in a problem, make a decision about which strategy would be most efficient in each particular problem. Number sense is not a deep understanding of a single strategy, but rather the ability to think flexibly between a variety of strategies in context.

Fluent students:

• flexibly use a combination of deep understanding, number sense, and memorization.

• are fluent in the necessary baseline functions in mathematics so that they are able to spend their thinking and processing time unpacking problems and making meaning from them.

• are able to articulate their reasoning.

• find solutions through a number of different paths.

For more about fluency, see: http://www.youcubed.org/wpcontent/uploads/2015/03/FluencyWithoutFear-2015.pdf and https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/nctm-timedtests.pdf

STRATEGIES FOR TEACHING AND LEARNING

Taken from: http://www.education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?Page=3&TopicRel ationID=1704&Content=118060

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

MGSE3.MD.1 Tell and write time to the nearest minute and measure elapsed time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram, drawing a pictorial representation on a clock face, etc.

MGSE3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word 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.

Time…

● A clock is a common instrument for measuring time. Learning to tell time has much to do with learning to read a dial-type instrument and little to do with time measurement.

● Students have experience in telling and writing time from analog and digital clocks to the hour and half hour in Grade 1 and to the nearest five minutes, using a.m. and p.m. in Grade 2. Now students will tell and write time to the nearest minute and measure time intervals in minutes.

● Provide analog clocks that allow students to move the minute hand.

● Students need experience representing time from a digital clock to an analog clock and vice versa.

● Provide word problems involving addition and subtraction of time intervals in minutes. Have students represent the problem on a number line. Student should relate using the number line with computation from Grade 2.

Liquid Volume and Mass…

● Provide opportunities for students to use appropriate tools to measure and estimate liquid volumes in liters only and masses of objects in grams and kilograms. Students need practice in reading the scales on measuring tools since the markings may not always be in intervals of one. The scales may be marked in intervals of two, five or ten.

● Allow students to hold gram and kilogram weights in their hand to use as a benchmark. Use water colored with food coloring so that the water can be seen in a beaker.

● Students should estimate liquid volumes and masses before actually finding the measuring. Show students a group containing the same kind of objects. Then, show them one of the objects and tell them its weight. Fill a container with more objects and ask students to estimate the weight of the objects.

● Use similar strategies with liquid measures. Be sure that students have opportunities to pour liquids into different size containers to see how much liquid will be in certain whole liters. Show students containers and ask, “How many liters do you think will fill the container?”

Represent and interpret data.

MGSE3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

MGSE3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units – whole numbers, halves, or quarters.

Data and Graphing…

● Representation of a data set is extended from picture graphs and bar graphs with singleunit scales to scaled picture graphs and scaled bar graphs. Intervals for the graphs should relate to multiplication and division with 100 (product is 100 or less and numbers used in division are 100 or less). In picture graphs, use values for the icons in which students are having difficulty with multiplication facts. For example, an icon represents 7 people. If there are three icons, students should use known facts to determine that the three icons represents 21 people. The intervals on the vertical scale in bar graphs should not exceed 100.

● Students are to draw picture graphs in which a symbol or picture represents more than one object. Bar graphs are drawn with intervals greater than one. Ask questions that require students to compare quantities and use mathematical concepts and skills. Use symbols on picture graphs that student can easily represent half of, or know how many half of the symbol represents.

● Students are to measure lengths using rulers marked with halves and fourths of an inch and record the data on a line plot. The horizontal scale of the line plot is marked off in whole numbers, halves or fourths. Students can create rulers with appropriate markings and use the ruler to create the line plots. **For additional assistance see the Unit Webinar at Georgiastandards.org.

SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, teachers should pay particular attention to them and how their students are able to explain and apply them. The terms below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers. Mathematics Glossary ● decompose ● elapsed time ● estimate ● gap ● gram (g) ● hour ● kilogram (kg) ● liquid volume ● liter (l) ● mass ● measure ● metric ● minute ● nonstandard units ● standard units ● time ● time intervals