Grade 1: Number Sense and Numeration Template

Mathematics

Grade 4: Number Sense and Numeration

Planning: Term #

Tracking: Ach. Level

Overall Expectations

1

2

3

4

• read, represent, compare, and order whole numbers to 10 000, decimal numbers to tenths, and simple fractions, and represent money amounts to \$100;

• demonstrate an understanding of magnitude by counting forward and backwards by 0.1 and by fractional amounts;

• solve problems involving the addition, subtraction, multiplication, and division of single- and multi-digit whole numbers, and involving the addition and subtraction of decimal numbers to tenths and money amounts, using a variety of strategies;

• demonstrate an understanding of proportional reasoning by investigating whole-number unit rates.

Specific Expectations

Quantity Relationships

– represent, compare, and order whole numbers to 10 000, using a variety of tools (e.g., drawings of base ten materials, number lines with increments of 100 or other appropriate amounts);

– demonstrate an understanding of place value in whole numbers and decimal numbers from 0.1 to 10 000, using a variety of tools and strategies (e.g., use base ten materials to represent 9307 as 9000 + 300 + 0 + 7) (Sample problem: Use the digits 1, 9, 5, 4 to create the greatest number and the least number possible, and explain your thinking.);

– read and print in words whole numbers to one thousand, using meaningful contexts (e.g., books, highway distance signs);

– round four-digit whole numbers to the nearest ten, hundred, and thousand, in problems arising from real-life situations;

– represent, compare, and order decimal numbers to tenths, using a variety of tools (e.g., concrete materials such as paper strips divided into tenths and base ten materials, number lines, drawings) and using standard decimal notation (Sample problem: Draw a partial number line that extends from 4.2 to 6.7, and mark the location of 5.6.);

– represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of fractional parts being considered;

– compare and order fractions (i.e., halves, thirds, fourths, fifths, tenths) by considering the size and the number of fractional parts (e.g., 4/5 us greater than 3/5 because there are more parts in 4/5; 1/4 is greater than 1/5 because the size of the part is larger in 1/4)

- compare fractions to the benchmarks of 0, 1/2, and 1 (e.g., 1/8 is closer to 0 than 1/2; 3/5 more than 1/2); demonstrate and explain the relationship between equivalent fractions, using concrete materials (e.g., fraction circles, fraction strips, pattern blocks) and drawings (e.g., “I can say that 3/6 of my cubes are white, or half of the cubes are white. This means that 3/6 and 1/2 are equal.”);

– read and represent money amounts to \$100 (e.g., five dollars, two quarters, one nickel, and four cents is \$5.59);

– solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 10 000 (Sample problem: How high would a stack of 10 000 pennies be? Justify your answer.).

Counting

– count forward by halves, thirds, fourths, and tenths to beyond one whole, using concrete materials and number lines (e.g., use fraction circles to count fourths: “One fourth, two fourths, three fourths, four fourths, five fourths, six fourths, …”);

– count forward by tenths from any decimal number expressed to one decimal place, using concrete materials and number lines (e.g., use base ten materials to represent 3.7 and count forward: 3.8, 3.9, 4.0, 4.1, …; “Three and seven tenths, three and eight tenths, three and nine tenths, four, four and one tenth, …”) (Sample problem: What connections can you make between counting by tenths and measuring lengths in millimetres and in centimetres?).

Operational Sense

– add and subtract two-digit numbers, using a variety of mental strategies (e.g., one way to calculate 73 - 39 is to subtract 40 from 73 to get 33, and then add 1 back to get 34);

– solve problems involving the addition and subtraction of four-digit numbers, using student-generated algorithms and standard algorithms (e.g., “I added 4217 + 1914 using 5000 + 1100 + 20 + 11.”);

– add and subtract decimal numbers to tenths, using concrete materials (e.g., paper strips divided into tenths, base ten materials) and student-generated algorithms (e.g., “When I added 6.5 and 5.6, I took five tenths in fraction circles and added six tenths in fraction circles to give me one whole and one tenth. Then I added 6 + 5 + 1.1, which equals 12.1.”);

– add and subtract money amounts by making simulated purchases and providing change for amounts up to \$100, using a variety of tools (e.g., currency manipulatives, drawings);

– multiply to 9 x 9 and divide to 81 ÷ 9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting);

– solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x 8);

– multiply whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule);

– multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., base ten materials or drawings of them, arrays), student-generated algorithms, and standard algorithms;

– divide two-digit whole numbers by one digit whole numbers, using a variety of tools (e.g., concrete materials, drawings) and student-generated algorithms;

– use estimation when solving problems involving the addition, subtraction, and multiplication of whole numbers, to help judge the reasonableness of a solution (Sample problem: A school is ordering pencils that come in boxes of 100. If there are 9 classes and each class needs about 110 pencils, estimate how many boxes the school should buy.).

# Proportional Relationships

– describe relationships that involve simple whole-number multiplication (e.g.,“If you have 2 marbles and I have 6 marbles, I can say that I have three times the number of marbles you have.”);

– determine and explain, through investigation, the relationship between fractions (i.e., halves, fifths, tenths) and decimals to tenths, using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., decompose 2/5 into 4/10 by dividing each fifth into two equal parts to show that 2/5 can be represented as 0.4);

– demonstrate an understanding of simple multiplicative relationships involving unit rates, through investigation using concrete materials and drawings (e.g., scale drawings in which 1 cm represents 2 m) (Sample problem: If 1 book costs \$4, how do you determine the cost of 2 books?… 3 books?…4 books?).

Student Name:

Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.