Place Value to 100
The focus of these three specific outcomes is the development of number sense through experiences with numbers to 100. "Number sense" can be described as a "good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms" (Howden 1989, p. 11). Lessons designed for students in meeting these specific learner outcomes develop an understanding of place value, relationships between quantities represented by numerals to 100 and the concept of estimation. Students become more adept at comparing and estimating quantities as they accumulate benchmarks or referents and use groupings to efficiently compare and calculate. Parallel to the development of place value concepts is the development of their communication skills with the language of math in words, symbols and illustrations.
This sample targets the following changes to the curriculum:
- The General Outcome focuses on number sense; whereas the previous mathematics curriculum divided the "Number" strand under the subheadings of "Number Concepts" and "Number Operations." The underlying change is in the greater emphasis now given to making sense of the number system as a way of describing the environment and solving problems. In recognition of the need for students to each construct his or her mathematical concepts, more emphasis is given to students' learning experiences, metacognition and sharing strategies to solve problems or represent mathematically things in their environment. Flexibility and proficiency are expected while allowing for personal preferences. More emphasis is on students actively participating in mathematics to develop understanding, then explaining their thinking to demonstrate their level of development. Correct answers and procedures are recognized as an insufficient foundation for numeracy. This informs the instruction that follows. Assessment is through observation during lessons, student work, and interviews and from performance tasks more often than in the past. Less emphasis is on what marks to assign the student for their performance. More emphasis is on what can we be sure students understand and how this informs our decisions about what instruction should follow for each student or group of students. Are our students through their experiences learning that the number system and mathematics make sense?
Place Value to 100 addresses the following outcomes from the Program of Studies:
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:
See Bibliography for reference information.