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Place Value

Strand: Number
Outcome: 5

Curriculum Focus

This sample targets the following changes to the curriculum:

• The general outcome for the number strand in the revised program of studies states simply that the goal of this entire strand is to "develop number sense." The number strand is no longer divided into "number concepts" and "number operations." Number sense includes, for example, the ability to partition numbers and the ability to reason multiplicatively. These abilities apply to both numbers and operations.
• In the previous program of studies, general outcomes at each grade level specified magnitudes of numbers and particular operations, implying that number sense develops in a linear fashion. A more current understanding of student's mathematical development is that number sense broadens and deepens over time. Student's understanding of even 1-digit numbers is not fully developed until they are able to think of numbers abstractly (as quantities that do not necessarily refer to specific objects or as progressions on a scale).
• The wording of Specific Outcome 5 is somewhat different from the equivalent outcome in the previous program of studies; however, the intention of this outcome is virtually the same as previously. What is different is our understanding of how students show their understanding of the meaning of place value. Students can, and frequently do, learn or invent procedures for using expanded notation or base ten blocks that are utterly devoid of any understanding of place value. It is essential that students construct their own understanding of place value as it applies to real magnitudes of numbers and relevant contexts for counting and calculating quantities, rather than simply learning to use notations or manipulatives in a purely procedural way.

Place Value addresses the following outcomes from the Program of Studies:

Strand:	Number
Specific Outcome:	5. Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000.

What is a Planning Guide?

Planning Guides are a tool for teachers to use in designing instruction and assessment that focuses on developing and deepening students' understanding of mathematical concepts. This tool is based on the process outlined in Understanding by Design, by Grant Wiggins and Jay McTighe.

The following steps will help you through the Planning Guide:

• Step 1: Identify Outcomes to Address
• Step 2: Determine Evidence of Student Learning
• Step 3: Plan for Instruction
• Step 4: Assess Student Learning
• Step 5: Follow-up on Assessment

See Bibliography for reference information.