Unit 1 — Place Value & Operations with Whole Numbers
Description
Unit 1 establishes foundational understanding of place value and whole number operations. Students extend their knowledge of the base ten system to one million and learn to recognize place value relationships. They develop familiarity with factors and multiples, including identifying prime and composite numbers. Students generate and analyze number and shape patterns that follow given rules. Measurement understanding is extended as students learn relative sizes of units within systems and express larger units in terms of smaller units. Multiplicative comparison is introduced through interpreting and representing multiplication equations. Students apply these concepts to solve word problems using the four operations.
Essential Questions
- How does our base ten number system work?
- How does understanding the base-ten number system help us add and subtract?
- What is a sensible answer to a real problem?
- How can estimation help us understand large numbers?
- What information is needed in order to round a whole number to any place?
Learning Objectives
- Find all factor pairs for whole numbers 1-100 and determine if a number is prime, composite, or a multiple.
- Generate number or shape patterns following a given rule and identify implicit features in the pattern.
- Understand relative sizes of measurement units and express measurements in a larger unit as a smaller unit.
- Interpret multiplication equations as comparisons and solve multiplicative comparison problems.
- Recognize that a digit in one place represents ten times the digit in the place to its right.
- Read, write, and compare multi-digit whole numbers using base-ten numerals, number names, and expanded form.
- Round multi-digit whole numbers to any place.
Supplemental Resources
- Index cards for sorting factors and multiples
- Chart paper for displaying patterns and place value relationships
- Sticky notes for identifying prime and composite numbers
- Printed word lists of mathematical vocabulary
- Graphic organizers for comparing numbers
Measurement
Number and Operations in Base Ten
Operations and Algebraic Thinking
Students use reading comprehension skills to decode words, study vocabulary, and solve word problems. Students identify important information and write explanations of their mathematical thinking using mathematical terms. Students connect everyday vocabulary to strengthen understanding of mathematical terms.
Students represent data, discover patterns, and read information to analyze observations. Students use measuring tools to create models and measure results of experiments. Students analyze data to form conclusions and use data to prove theories across life science, physical science, and earth science modules.
Students understand how to read dates properly and interpret historical information.
Formative Assessments
- Exit tickets assessing understanding of place value relationships and factor identification
- Task cards for pattern recognition and multiplication comparison
- Classwork involving measurement conversions recorded in two-column tables
- Whiteboards for quick checks on rounding and number comparisons
- Individual and group work on multi-step word problems
Summative Assessment
Unit benchmark assessment covering place value, factors/multiples, patterns, measurement conversion, and multiplicative comparison; chapter tests; performance tasks involving real-world applications
Benchmark Assessment
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Alternative Assessment
Students may demonstrate understanding of place value, factors, and patterns through manipulatives, base ten blocks, or number lines with teacher guidance, rather than written responses. Sentence frames, partially completed graphic organizers, and reduced problem sets may be provided to scaffold access to concepts while maintaining grade-level rigor.
IEP (Individualized Education Program)
Students with IEPs may benefit from having place value charts, number lines, and multiplication reference tables available during instruction and practice to reduce cognitive load while building conceptual understanding. Word problems involving multiplicative comparison or multi-step operations should be broken into smaller, sequenced steps with visual models such as tape diagrams or base-ten representations to support processing. Output flexibility—such as allowing oral explanations of reasoning, use of a calculator for computation when the focus is conceptual understanding, or reduced problem sets targeting key skills—ensures students can demonstrate mastery without being impeded by volume or format. Frequent check-ins during independent work, especially during factor identification and pattern tasks, will help teachers catch and address misconceptions early.
Section 504
Students with 504 plans should be provided extended time on benchmark assessments and chapter tests covering place value, rounding, and operations. Preferential seating near the board and access to a printed copy of any place value charts or conversion tables displayed in the room will support focus and reduce barriers during instruction. Minimizing distractions during multi-step problem solving tasks—such as providing a quieter workspace or limiting visual clutter on worksheets—helps students maintain attention across the longer reasoning demands of this unit.
ELL / MLL
Multilingual learners should have access to a visual word wall that includes unit-specific vocabulary—such as 'factor,' 'multiple,' 'prime,' 'composite,' 'round,' and 'multiplicative comparison'—accompanied by illustrations, examples, and translations in students' home languages where possible. Directions for tasks involving measurement conversions, pattern rules, or multi-step word problems should be simplified and paired with visual models or worked examples so that language demands do not obscure mathematical reasoning. Allowing students to discuss their thinking with a partner who shares their home language, or to annotate work in their first language before translating, supports deeper engagement with the unit's concepts.
At Risk (RTI)
Students who need additional support should begin place value and factor work with concrete or visual representations—such as base-ten blocks, hundreds charts, or factor rainbows—before moving to abstract notation, ensuring a solid entry point into the unit. Rounding and comparison tasks can be scaffolded by anchoring numbers on a number line so students can reason spatially before applying rules symbolically. Connecting new concepts, such as multiplicative comparison, to students' existing understanding of repeated addition or equal groups helps build confidence and reduces the novelty of unfamiliar problem types. Monitoring progress on foundational skills like factor identification and place value relationships early in the unit allows for timely, targeted small-group support.
Gifted & Talented
Students who demonstrate early mastery of place value and whole number operations should be encouraged to explore number theory concepts in greater depth—for example, investigating patterns among prime numbers, examining why certain numbers have more factor pairs than others, or exploring the relationship between factors and area models. Extension opportunities might involve applying multiplicative comparison and measurement conversion concepts to authentic, multi-layered problems that require students to construct their own solution pathways and justify their reasoning. Encouraging students to generate their own pattern rules, test conjectures about composite and prime numbers, or connect place value structure to number systems beyond base ten promotes the kind of abstract, in-depth thinking appropriate for advanced learners in this unit.