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November 1, 2015

NS/N: Place Value


This week we will be shifting our focus away from patterning to place value. Over the course of the next few weeks, here are the "Big Ideas" we will be focusing on.

NS/N: Place Value and Decimals

BIG IDEAS

(taken from “Big Ideas by Dr. Small”):
1. The place value system we use is built on patterns to make our work with numbers more efficient.
2. Students gain a sense of the size of numbers by comparing them to meaningful benchmark numbers.
3. Decimals are an alternative representation to fractions, but one that allows for modeling, comparisons, 
and calculations that are consistent with whole numbers; because decimals extend the pattern of the 
base ten place value system.
4. A decimal can be read and interpreted in different ways; sometimes one representation is more useful 
than another in interpreting or comparing decimals or for performing and explaining a computation.

STUDENT LEARNING GOALS

GOAL: I can demonstrate and explain equivalent representations using powers of ten
GOAL: I can identify and explain patterns within our place value system (including decimals)
GOAL: I can use these patterns to represent whole and decimals numbers in standard form, 
expanded form, in pictures, and in words
GOAL: I can compare and order whole and decimals numbers and plot them on a number line
GOAL: I can round whole and decimals numbers to meaningful benchmarks

CURRICULUM EXPECTATIONS:

  • represent, compare, and order whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools (e.g., number lines with appropriate increments, base ten materials for decimals);
  • demonstrate an understanding of place value in whole numbers and decimal numbers from 0.01 to 100 000, using a variety of tools and strategies (e.g., use numbers to represent 23 011 as 20 000 + 3000 + 0 + 10 + 1; use base ten materials to represent the relationship between 1, 0.1, and 0.01) (Sample problem: How many thousands cubes would be needed to make a base ten block for 100 000?);
  • read and print in words whole numbers to ten thousand, using meaningful contexts (e.g., newspapers, magazines);
  • round decimal numbers to the nearest tenth, in problems arising from real-life situations;
  • demonstrate and explain equivalent representations of a decimal number, using concrete materials and drawings (e.g., use base ten materials to show that three tenths [0.3] is equal to thirty hundredths [0.30]);
  • read and write money amounts to $1000 (e.g., $455.35 is 455 dollars and 35 cents, or four hundred fifty-five dollars and thirty-five cents);
  • solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 100 000 (Sample problem: How many boxes hold 100 000 sheets of paper, if one box holds 8 packages of paper, and one package of paper contains 500 sheets of paper?).
  • count forward by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines (e.g., use base ten materials to represent 2.96 and count forward by hundredths: 2.97, 2.98, 2.99, 3.00, 3.01, …; “Two and ninety-six hundredths, two and ninety-seven hundredths, two and ninety-eight hundredths, two and ninety-nine hundredths, three, three and one hundredth, …”) (Sample problem: What connections can you make between counting by hundredths and measuring lengths in centimetres and metres?).
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