Mathematics
Grade 5: Number Sense and Numeration |
Planning: Term # Tracking: Ach. Level |
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Overall Expectations |
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read, represent, compare, and order whole numbers to 100 000, decimal numbers
to hundredths, proper and improper fractions, and mixed numbers; |
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demonstrate an understanding of magnitude by counting forward and backwards by
0.01; |
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solve problems involving the multiplication and division of multi-digit whole
numbers, and involving the addition and subtraction of decimal numbers to
hundredths, using a variety of strategies; |
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demonstrate an understanding of proportional reasoning by investigating
whole-number rates. |
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Specific Expectations |
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Quantity Relationships |
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– 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); |
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– 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?); |
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read and print in words whole numbers to ten thousand, using meaningful
contexts (e.g., newspapers, magazines); |
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round decimal numbers to the nearest tenth, in problems arising from
real-life situations; |
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represent, compare, and order fractional amounts with like denominators, including
proper and improper fractions and mixed numbers, using a variety of tools
(e.g., fraction circles, Cuisenaire rods, number lines) and using standard
fractional notation; |
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– demonstrate
and explain the concept of equivalent fractions, using concrete materials
(e.g., use fraction strips to show that 3/4 is equal to 9/12) |
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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]); |
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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); |
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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?). |
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Counting |
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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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Operational Sense |
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– solve
problems involving the addition, subtraction, and multiplication of whole
numbers, using a variety of mental strategies (e.g., use the commutative
property: 5 x 18 x 2 = 5 x 2 x 18, which gives 10 x 18 = 180); |
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– add
and subtract decimal numbers to hundredths, including money amounts, using
concrete materials, estimation, and algorithms (e.g., use 10 x 10 grids to
add 2.45 and 3.25); |
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multiply two-digit whole numbers by two-digit whole numbers, using
estimation, student-generated algorithms, and standard algorithms; |
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divide three-digit whole numbers by one-digit whole numbers, using concrete
materials, estimation, student-generated algorithms, and standard algorithms; |
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multiply decimal numbers by 10, 100, 1000, and 10 000, and divide decimal
numbers by 10 and 100, using mental strategies (e.g., use a calculator to
look for patterns and generalize
to develop a rule); |
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– use
estimation when solving problems involving the addition, subtraction,
multiplication, and division of whole numbers, to help judge the
reasonableness of a solution (Sample problem: Mori used a calculator to add
7.45 and 2.39. The calculator display showed 31.35. Explain why this result
is not reasonable, and suggest where you think Mori made his mistake.). |
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Proportional Relationships |
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describe multiplicative relationships between quantities by using simple fractions
and decimals (e.g.,“If you have 4 plums and I have 6 plums, I can say that I
have 1 1/2 or 1.5 times as many plums as you have.”); |
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determine and explain, through investigation using concrete materials,
drawings, and calculators, the relationship between fractions (i.e., with
denominators of 2, 4, 5, 10, 20, 25, 50, and 100) and their equivalent
decimal forms (e.g., use a 10 x 10 grid to show that 2/5 = 40/100 , which can
also be represented as 0.4); |
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– demonstrate
an understanding of simple multiplicative relationships involving
whole-number rates, through investigation using concrete materials and
drawings (Sample problem: If 2 books cost $6, how would you calculate the
cost of 8 books?). |
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Student Name: |
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Expectations: Copyright The Queen's Printer for Ontario, 2005. Format: Copyright B.Phillips, 1998.