Place Value
Strand: Number
Outcome: 5
Step 3: Plan for Instruction
Guiding Questions
- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?
A. Assessing Prior Knowledge and Skills
Before introducing new material, consider ways to assess and build on students' knowledge and skills related to place value. For example:
- Make sure students can count by tens and identify place value patterns in the hundreds chart.
- See if students can count by hundreds.
- Check to see if students start counting at 90 and count past 100 to 120.
- Check to see if students can read and name 2-digit and 3-digit numbers.
- Check to see if students can subitize up to 10 by flashing ten frames with different numbers of squares filled in. Alternatively, string five beads or cubes of one colour and five of another colour on a slightly longer string, and push different numbers of beads to one side. Show briefly to see if students can subitize the amount.
- To see if students can unitize (i.e., think of a group as a countable unit in itself, as well as being made up of single units), have them make 3 ten bars by snapping cubes together and take 4 single cubes as well. Ask, "How many cubes?" and then observe whether students count by tens and ones or count each cube in each of the ten bars.
- To determine if students understand that a set contains the same amount of items whether you count by ones or by tens and ones, after completing the above exercise, ask students to break their ten bars apart to create a pile of single cubes, and ask "How many?" Students should be able to answer without counting all the cubes again.
- Check to see if students can make 2-digit numbers using small ten frames. Students should have a set of ten frame cards from 0–9 and several tens. Call out a 2-digit number and have the students make it using their cards. See if you have any students who can use these cards to make a number between 100 and 200.
If a student appears to have difficulty with these tasks, consider further individual assessment, such as a structured interview, to determine the student's level of skill and understanding. See Sample Structured Interview: Assessing Prior Knowledge and Skills 
.
B. Choosing Instructional Strategies
Consider the following guidelines for teaching about place value:
- Use an "Assessment for Learning" approach to ensure that students understand the learning intentions for all activities, understand what distinguishes quality work, receive descriptive feedback about their progress and have opportunities for self and peer assessment. For example, use the "Traffic Lights for Place Value" masters found at the end of this document. Students can use this tool for self-assessment before and after learning about place value.
- Immediately after presenting a task, have students discuss the task with a partner and make predictions as to the outcome of the task.
- Have students work in partners or groups of three or four to complete tasks.
- Invite students to reflect on their predictions after a task has been completed.
- Plan a significant amount of time for students to compare strategies and outcomes as a whole class after a task has been completed. During this time, ask questions about the efficiency and mathematical thinking of particular responses in order to encourage greater abstraction and mathematical elegance.
- As much as possible, use real quantities and hands-on activities to teach about place value so that an understanding of place value number patterns and conventions is tied into an experience of the magnitude and meaning of numbers.
- Ensure that tasks are differentiated. Have students who are struggling do the same tasks using lower numbers, including 2-digit numbers. Students who have mastered 3-digit numbers can be introduced to the terminology and conventions for numbers into the millions. It is a good idea to post a chart showing how the number naming system works – progressing from units, tens and hundreds to units, tens and hundreds of thousands, then to units, tens and hundreds of millions. Some students are already beginning to form understandings and misconceptions about these large numbers in Grade 3.
- Make sure you include problems and activities that use numbers with zero in the tens place and the ones place.
- Rather than treating place value as a discrete unit, teach about place value as students need the concepts in order to solve problems and complete other number-related tasks.
- Reinforce place value concepts throughout the year, through solving problems involving
3-digit numbers in meaningful contexts and through games involving 3-digit numbers, cumulative scoring or bundling into tens and hundreds.
C. Choosing Learning Activities
Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.
Grade 3
