Unit 3 — Place Value, Measurement and Shapes
Description
Students extend place value understanding to 90 through composing and decomposing tens and ones. They add within 100 using concrete models and place value strategies, working with two-digit and one-digit numbers and two-digit numbers with multiples of 10. Students mentally find 10 more or 10 less than a given number and subtract multiples of 10 from multiples of 10. Measurement work focuses on ordering objects by length, comparing lengths using a third object (indirect comparison), and expressing length using multiple copies of equal-sized units (iteration). Students measure to the nearest whole unit without gaps or overlaps. Time is introduced through telling and writing time in hours and half-hours on both analog and digital clocks. Students add and subtract within 20 as it relates to measurement contexts.
Essential Questions
- How can words be used to illustrate the comparison of numbers?
- How can benchmark numbers build our understanding of numbers?
- How can we measure the length of an object?
- What can we use to measure objects?
- How can we tell which of two objects is longer than the other?
- How can we order a group of objects by their length?
- Why is telling time important?
- How do you use time in your daily life?
- What does the hour hand on a clock tell us?
Learning Objectives
- Compose and decompose numbers to 90 into tens, identifying the value of the number in the tens and ones place.
- Add a 2-digit and a 1-digit number using concrete models and drawings with a place value strategy or properties of operations; explain or show how the model relates to the strategy (sums within 100).
- Add a 2-digit number and a multiple of 10, using concrete models and drawings with a place value strategy or properties of operations; explain or show how the model relates to the strategy (sums within 100).
- Explain, given a two-digit number, how to find 10 more or ten less than the number without having to count.
- Subtract a multiple of 10 from a multiple of 10 (both within the range 10-90) using concrete models and drawings with a place value strategy or properties of operations; explain or show how the model relates to the strategy.
- Order three objects by length and compare the lengths of two objects by using the third object as a measuring tool.
- 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.
- Tell and write time to the half-hour using the term o'clock and using digital notation (include both analog and digital clocks).
- Add and subtract whole numbers within 20 using various strategies.
Supplemental Resources
- Base-ten blocks and bundles of tens for place value activities
- Rulers and measuring tapes (marked or unmarked) for length measurement
- Non-standard measurement units (paper clips, blocks, straws, string)
- Analog clocks (one per pair or small group) for time-telling practice
- Digital clock images and printed clock templates for practice
- Chart paper for recording measurement discoveries and place value patterns
Measurement
Number and Operations in Base Ten
Operations and Algebraic Thinking
Standards for Mathematical Practice
Students connect everyday vocabulary to mathematical terms, utilize reading comprehension skills by acting out or drawing the order of important events in story problems, and create mathematical stories using numbers, pictures, and words through interactive student notebooks and read-alouds.
Students work with data and make calculations involving measurements and other data across all mathematical modules, engaging in investigations and observations related to patterns and phenomena.
Students connect money as a means for helping people buy things they need or want and complete independent or partner projects to plan and market a good or service, exploring economic concepts and community responsibilities.
Formative Assessments
- Place value decomposition activities using base-ten blocks and tens/ones representations
- Exit tickets assessing mental math skills for finding 10 more or 10 less
- Measurement activities comparing object lengths using indirect methods
- Hands-on measurement tasks with non-standard units (paper clips, blocks, string)
- Clock reading and time-telling activities on analog and digital clocks
- Math journals documenting measurement processes and time concepts
Summative Assessment
Unit 3 chapter tests assessing place value understanding within 90, two-digit addition strategies, measurement and length comparison skills, and time-telling abilities.
Benchmark Assessment
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Alternative Assessment
Students may demonstrate place value understanding and addition strategies through manipulating base-ten blocks, drawings, or other concrete materials while explaining their thinking aloud to a teacher or peer. Visual supports such as tens-and-ones mats, number lines, or partially completed models may be provided to reduce cognitive load.
IEP (Individualized Education Program)
Students benefit from using concrete manipulatives such as base-ten blocks, linking cubes, and visual place value mats to support understanding of tens and ones throughout this unit. For measurement and time tasks, physical objects and real analog clocks help connect abstract concepts to tangible experience. Teachers should allow oral explanations in place of written responses when assessing strategies for adding, finding 10 more or less, or describing measurement reasoning. Breaking multi-step tasks into smaller numbered steps and providing a reference card with place value frames and clock models can reduce cognitive load and support independent work.
Section 504
Students should be provided with extended time during place value, measurement, and clock-reading tasks, particularly when recording work in math journals or on assessments. A number line, hundred chart, or place value reference card taped to the desk supports access without removing the mathematical thinking required. Preferential seating near instruction during hands-on measurement or clock-reading demonstrations helps ensure students can clearly observe models and teacher examples.
ELL / MLL
Teachers should use visual supports throughout the unit, including labeled diagrams of base-ten blocks, picture-supported vocabulary cards for terms such as 'tens,' 'ones,' 'length,' 'compare,' 'hour,' and 'half-hour,' and physical demonstrations before asking students to work independently. Directions for measurement and addition tasks should be given in short, simple steps and accompanied by a visual example of the process. Connecting unit vocabulary to students' home language where possible helps build conceptual bridges for new mathematical ideas.
At Risk (RTI)
Students who need additional support should begin place value work with numbers within 50 before extending to 90, using concrete materials to build confidence with tens and ones before moving to drawings or written strategies. For measurement tasks, starting with direct comparison of objects before moving to indirect comparison gives students a concrete entry point. Connecting time-telling to familiar daily routines helps make abstract clock concepts meaningful and accessible.
Gifted & Talented
Students who have demonstrated readiness can extend place value thinking beyond 90, exploring three-digit numbers and investigating how patterns of tens and ones continue into the hundreds. In measurement contexts, these students can be challenged to design their own measurement investigations, consider why using equal-sized units matters, or explore what happens when different-sized units are used for the same object. For time, students may explore elapsed time or connect half-hour intervals to the concept of fractions, deepening their understanding of both time and number relationships.