Grade 1 Mathematics, Quarter 2, Unit 2.2Interpret Data, Measure Length, and
Tell and Write Time to the Hour(10 days)

Grade 1 Mathematics, Quarter 2, Unit 2.2

Interpret Data, Measure Length, and Tell and Write Time to the Hour

Overview
Number of Instructional Days: / 10 / (1 day = 45–60 minutes)

Content to be Learned

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Mathematical Practices to Be Integrated

  • Compare the lengths of two objects indirectly by using a third object (if ab and bc then
    ac; transitivity).
  • Express the length of an object as a whole number of length units (by laying multiple copies of a shorter object end to end).
  • Understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
  • Tell and write time in hours using analog and digital clocks.
  • Looking at data sets, tell how many more or less are in one category than another (up to three categories).
/ 4 – Model with mathematics
  • Model indirect measurements
  • Identify important quantities in a practical situation
5 - Use appropriate tools strategically.
  • Consider available tools when solving a mathematical problem.
  • Detect possible errors by strategically using estimation and other mathematical knowledge.
6 - Attend to precision.
  • Communicate precisely, using clear definitions in discussions with others.
  • Carefully specify units of measure and calculate accurately and efficiently.

Essential Questions

  • How could you put these objects in order? Explain your thinking.
  • Is the third object (longer, shorter) than the first? How do you know?
  • How could you use this (non-standard) tool to measure the length of this object?
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  • What time does this (analog) clock show? Write this time as you would see it on a digital clock.
  • Look at this data. What is the total number of data points? How many (data points) are in each category? How many more or less are in one category than another? What else can you tell me about this data?

Written Curriculum

Common Core State Standards for Mathematical Content

Measurement and Data 1.MD

Measure lengths indirectly and by iterating length units.

1.MD.1.Order three objects by length; compare the lengths of two objects indirectly by using a third object.

1.MD.2.Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Tell and write time.

1.MD.3.Tell and write time in hours and half-hours using analog and digital clocks.

Represent and interpret data.

1.MD.4.Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Common Core Standards for Mathematical Practice

4Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

(Practices continued on the next page)

5Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

Clarifying the Standards

Prior Learning

In kindergarten, students did direct comparisons by comparing two objects with a measureable attribute in common (taller/shorter). They classified objects into given categories, counted the numbers in each category (up to 10) and sorted the categories by count.

Current Learning

In Unit 1.2, students order three objects by length. Also, students interpret data up to three categories and ask and answer questions about how many data points in each category. In this unit, these concepts are taught at the reinforcement level.

In this unit, students compare the lengths of two objects indirectly by using a third object (see Additional Findings below on transitivity).Refer to CCSS (p. 90), Table 4 for further information on the transitive property of equality (if a= b and b= c then a= c) and Table 5 for the properties of inequality (if ab and bc then ac). Students express the length as a whole number of length units. These skills are taught at the developmental level.

Students tell and write time in hours using digital and analog clocks. These skills are taught at the developmental level.

Students will use data to tell how many in each category and how many more or less are in one category than in another. Interpreting data in this way is taught at the developmental level.

Later in grade 1, students tell and write time to the half hour. They also organize and represent data with up to three categories.

Teachers may want to reference Table 1 on page 4 of the K–3 Categorical Data Learning Progressions to see connection between 1. MD.4 and Operations and Algebraic thinking standards in grade 1.

Future Learning

In grade 2, students will select and use appropriate tools to measure objects. They will be measuring to determine how much longer one object is than another, expressing the difference in terms of a standard length unit. Students will also estimate lengths using inches, feet, centimeters, and meters. Students will measure the same object using different units of measure.

In grade 3, students tell time to the minute (3.MD.1), solve word problems that involve adding and subtracting time intervals in minutes (3.MD.1) and measure areas by “unit squares” (3.MD.5&6).

Additional Findings

According to the K–3 Categorical Data Learning Progressions, “there is no single correct way to represent categorical data—the standards do not require grade 1 students to use any specific format” (p. 5).

“Students should be supported as they learn to construct picture graphs, bar graphs, and line plots” (p. 3).

“In students work with data, context is important … students should work with data in the context of science, social studies, health, and other subjects, always interpreting data plots in terms of the data they represent” (p. 3).

To represent data, grade 1 students may find it useful to use a picture graph in which one picture represents one object. Students’ data work in grade 1 has important connections to addition and subtraction. For example, a student might ask how many specimens there are altogether representing this problem by writing an equation … students should be familiar with mark schemes” and “students devise different ways to represent the same data set” (p. 5).

A Research Companion to Principles and Standards for School Mathematics states, “Children’s first understandings of length measure often involve direct comparisons of objects” (Lindquist, 1989; Piaget et al, 1960) (p. 182).

Southern Rhode Island Regional Collaborative with process support from The Charles A. Dana Center at the University of Texas at Austin Revised 2013-2014