Measurement and Data

Students explore measurement and data by describing, sorting, classifying, and comparing familiar objects. They collect, represent, and interpret meaningful classroom data while comparing measurable attributes such as length, height, weight, and capacity.

Math

Unit 3

Kindergarten

Unit Summary

In Unit 3, students expand their understanding of mathematics by exploring measurement and data through describing, sorting, classifying, comparing, and representing the attributes of objects in their world. The math community continues to foster curiosity through playful inquiry, discussion, and hands-on exploration as students investigate similarities and differences, organize information, and make meaningful comparisons.

In Unit 2, students developed strong number sense within 10 by counting, representing, comparing, and reasoning about quantities. They learned to identify similarities and differences between sets, communicate their mathematical thinking, and use counting to answer questions. These foundational skills now support students as they classify objects, organize data, and compare measurable attributes.

In this unit, students notice and use familiar observable attributes such as color, shape, size, and texture to describe and sort objects in multiple ways. They collect, represent, and interpret data to answer questions about their classroom and world. Students also investigate measurable attributes including length, height, weight, and capacity through direct comparison and ordering. Through these experiences, students recognize that objects can be described, organized, and compared in systematic ways.

Throughout the unit, students model with mathematics as they sort, classify, represent, and compare objects and data MP.4 Model with mathematics. . They look for and make use of structure as they identify attributes and organize collections MP.7 Look for and make use of structure. , and look for and express regularity in repeated reasoning as they develop generalizations about measurement and data MP.8 Look for and express regularity in repeated reasoning. . This work establishes a conceptual basis for future learning in measurement, data analysis, and mathematical reasoning as students make sense of the world through mathematics.

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Assessment

The following assessments accompany Unit 3.

Student Observational Spreadsheet

Print the Student Observational Spreadsheet to use as a formative tool to monitor the progress of students throughout the unit.

Student Observational Spreadsheet

Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Post-Unit Assessment

Unit Prep

Intellectual Prep

Suggestions for how to prepare to teach this unit

Intellectual Prep for All Units

Read and annotate the "Unit Summary" and "Essential Understandings" portions of the unit plan.
Do all the Target Tasks and annotate them with the "Unit Summary" and "Essential Understandings" in mind.
Take the Post-Unit Assessment.

Unit-Specific Intellectual Prep

Read pp. 72-75 on Measurement and Data in The Progressions for the Common Core State Standards in Mathematics.
Read pp. 86-91 on Geometric Measurement in The Progressions for the Common Core State Standards in Mathematics.
Read pp. 6-8 on Standards for Mathematical Practice in the Common Core State Standards for Mathematics.

Essential Understandings

The central mathematical concepts that students will come to understand in this unit

Describe objects using observable and measurable attributes.
Sort and classify objects into categories based on shared attributes and recognize that the same collection can be sorted in different ways.
Collect, organize, and represent data to answer questions and make comparisons about categories.
Count and compare quantities within categories using mathematical language such as “more,” “fewer,” and “same”.
Compare and order objects by measurable attributes through direct comparison.

Materials

The materials, representations, and tools teachers and students will need for this unit

Bags of objects (1 per pair of students with a maximum of 8-10 classroom objects in each)
Sort It! Mats (1 mat per pair of students) – These may be laminated and cut apart for individual use
Sort It! Cards (1 set per pair of students) – These may be laminated and cut apart ahead of time
Dry erase marker (1 per pair of students and 1 for teacher)
Data Four Corners Cards (1 set per class) – Choose the 4 transportation cards that make the most sense for your class
Sorting Animals (1 per pair of students)
Scissors (1 pair per pair of students)
Glue stick (1 per pair of students)
Data Picture Cards (1 per student) –These can be printed and cut out ahead of time based on data from Lesson 5 Anchor Task 1
Chart Paper (1 per class) – Or large pocket chart or magnetic board
Pet Picture Mat (1 per group of 4-5 students) – These should be prepared ahead of time by taping/pasting together along the dotted lines
Bins of objects (4-6 bins per class and 6-10 classroom objects per bin) – These these should include objects that vary in length, height, weight, and capacity
Find someone who... Checklist (1 per student)
Pencil (1 per student) –May substitute crayon, marker, or other writing utensil
Optional: Paper plate (1 per student) – Or circular piece of construction paper. Print or write comparison sentence frames on these ahead of time
Sticky notes (1 pad per group of students) – Depending on the lengths of names in your class, you may use standard 3 x 3 sticky notes, or smaller size if a large number of students have names longer than 8 letters
Markers (1 per student) – Could substitute crayons or other writing utensil
Sentence strips (at least 1 per student) – Depending on the length of students’ names and size of the sticky notes
Boxes (1 set of 3 per group and 1 set of 3 for teacher) – These can be tissue boxes, shoe boxes, or other small boxes that are the same size and shape
Classroom objects (1 per box) – These should be noticeably different weights across each set of 3
Bin (6-8 per class) – Or tray to be used at exploration stations around the classroom for overflow
Containers (6-8 sets of 2 per class) – To be compared at exploration stations around the classroom
Pompoms (6-8 small bins per class) – To be used at exploration stations around the classroom, could alternately use cotton balls or other filling material
Sorting Containers Mat (1 per pair of students)
Sorting Containers Cards (1 per pair of students)

Vocabulary and Models

Unit Vocabulary

capacity

height

length

sort

weight

To see all the vocabulary for Unit 3, view our Kindergarten Vocabulary Glossary.

Lesson Map

Topic A: Describe, Sort, and Classify Objects

Lesson

Describe objects using observable attributes such as color, shape, size, or texture.

Standards

K.MD.A.1MP.7

Lesson

Compare objects by describing similarities and differences.

Standards

K.MD.B.3MP.8

Lesson

Sort objects or images using one observable attribute and count to tell how many in each group.

Standards

K.CC.B.5K.MD.B.3MP.4

Lesson

Sort the same collection of objects in different ways and count to tell how many in each group.

Standards

K.CC.B.5K.MD.B.3MP.7MP.8

Topic B: Sort, Classify, and Represent Data

Lesson

Collect and classify data into categories based on a given attribute.

Standards

K.CC.B.5K.MD.B.3MP.4

Lesson

Represent data using objects or drawings.

Standards

K.CC.B.5K.MD.B.3MP.4

Lesson

Interpret data by counting and comparing categories.

Standards

K.CC.C.6K.MD.B.3MP.8

Topic C: Compare and Order Measurable Attributes

Lesson

Describe measurable attributes such as length/height, weight, or capacity.

Standards

K.MD.A.1MP.7

Lesson

Compare height through movement and discussion.

Standards

K.MD.A.2MP.8

Lesson

Compare and order objects by length and height.

Standards

K.MD.A.2MP.4MP.8

Lesson

Compare objects by weight.

Standards

K.MD.A.2MP.4MP.8

Lesson

Compare objects by capacity.

Standards

K.MD.A.2MP.4

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

Counting and Cardinality

Counting and Cardinality

K.CC.B.5 — Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1—20, count out that many objects.
Counting and Cardinality

K.CC.C.6 — Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Include groups with up to ten objects.

Measurement and Data

Measurement and Data

K.MD.A.1 — Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
Measurement and Data

K.MD.A.2 — Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
Measurement and Data

K.MD.B.3 — Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Limit category counts to be less than or equal to 10.

Standards for Mathematical Practice

Standards for Mathematical Practice

MP.4 — Model 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.
Standards for Mathematical Practice

MP.7 — Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
Standards for Mathematical Practice

MP.8 — Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Future Standards

Standards in future grades or units that connect to the content in this unit

Measurement and Data

Measurement and Data

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

Operations and Algebraic Thinking

Operations and Algebraic Thinking

1.OA.C.5 — Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

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