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Description:
Students use models, manipulatives, or
number lines to add fractions with unlike denominators. Students find like
denominators to add fractions. Students
solve problems involving addition and subtraction of fractions with unlike
denominators. Students also use
benchmarks, comparisons and mental math to justify their thinking and to
determine whether their answer is reasonable.
Students learn to express the remainder of a division problem as a
fraction as they solve real-life problems.
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Standards:
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NBT - Number and
Operation in Base Ten
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Use
equivalent fractions as a strategy to add and subtract fractions.
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5.NF.A.1
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Add and subtract fractions with unlike
denominators (including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent sum or
difference of fractions with like denominators.
For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.
(in general, a/b + c/d = (ab + bc)/bd.)
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5.NF.A.2
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Solve
word problems involving addition and subtraction of fractions.
- Solve word problems involving addition and
subtraction of fractions referring to the same whole, including cases
of unlike denominators, e.g., by using visual fraction models or
equations to represent the problem.
- Use benchmark fractions and number sense of
fractions to estimate mentally and justify the reasonableness of
answers. For example, recognize an incorrect result 2/5 + 1/2 =
3/7, by observing that 3/7 < 1/2.
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Apply
and extend previous understandings of multiplication and division to
multiply and divide fractions.
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5.NF.B.3
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Interpret
a fraction as division of the numerator by the denominator (a/b = a ÷
b). Solve word problems involving
division of whole numbers leading to answers in the form of fractions or
mixed numbers, e.g., by using visual fraction models or equations to
represent the problem. For example, interpret 3/4 as the result
of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when
3 wholes are shared equally among 4 people each person has a share of size
3/4. If 9 people want to share a 50‐pound sack of rice
equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your
answer lie?
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Enduring Understandings:
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Landmark/benchmark numbers should be used when
making decisions about other numbers.
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Models
can be used to compute fractions with like and unlike denominators.
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A
fraction describes the division of a whole into equal parts, and it can be
interpreted in more than one way depending on the whole to be divided.
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Multiplying
a whole number by a fraction involves division as well as
multiplication. The product is a
fraction of the whole number.
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Rounding
and compatible numbers can be used to estimate the product of fractions or
mixed numbers.
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The
relative size of the factors can be used to determine the relative size of
the product.
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Essential Questions:
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Why
would I need to use landmark/benchmark numbers when making decisions about
other numbers?
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How
can models (line plots, etc.) be used to compute fractions with like and
unlike denominators?
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What
strategies can be used to determine if answers are reasonable?
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How
can I tell if a fraction is greater than, less than, or equal to one whole?
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How
can fractions with different denominators be added together? Subtracted?
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How are fractions related to
division?
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How can I multiply fractions and
whole numbers?
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How does multiplying by a fraction
change the other factor?
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