General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to relate odd and even numbers to factors and multiples. In Grade 2, students learn to represent an even number using two equal groups or two equal addends and as odd number as two equal groups or two equal addends with one left over (MA.2.AR.3.1). In Grade 3, instruction extends to use patterns to generalize whether any number is odd or even (MTR.2.1, MTR.5.1).- Instruction should connect multiples of 2 to the patterns that the ones digit in any even number is 0, 2, 4, 6, or 8. By teaching this benchmark with MA.3.AR.3.2, students can see that multiples of 2 can form any even number. If a number is not a multiple of 2, then the number is odd (MTR.5.1).
- These beginning understandings about multiples will help students explore factors and divisibility with prime and composite numbers in Grade 4.
Common Misconceptions or Errors
- Students may confuse that in an even number, the ones digit indicates whether it is a multiple of 2. For example, students may look at the number 883 as even because the digit 8 in the hundreds and tens places is even.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to practice identifying if multi-digit numbers are even or odd by using a place-value chart. The teacher explains that even numbers can be represented by two equal groups or two equal addends and that odd numbers can be represented by two equal groups or two equal addends with one left over while modeling using visual representations with several examples (e.g., drawings, tally marks).
- For example, the teacher uses visual representations to identify whether numbers are even or odd by sorting them into two equal groups using drawings or tally marks and entering numbers into a place value chart while asking “What do you notice about the digits in the ones place?” Students should explain that even numbers all have digits in the ones place that are multiples of 2 (0, 2, 4, 6, or 8). Additional examples are used in the place-value chart to practice identifying if numbers are even or odd by looking at the digits in ones place.
- For example, students use counters to identify if numbers are even or odd by sorting into two equal groups and enter numbers into a place value chart.
- As in the previous example, the students use counters by sorting into two equal groups. The teacher asks, “How many total counters are there, and what is the digit in the ones place?” Students should explain that even numbers all have digits in the ones place that are multiples of 2 (0, 2, 4, 6, or 8). Additional examples are used in the place-value chart to practice identifying if numbers are even or odd by looking at the digits in ones place.
Instructional Tasks
Instructional Task 1
Is the number 461 even or odd? Explain how you know.
Instructional Items
Instructional Item 1
Determine whether the numbers are even or odd in the table below.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.