The focus of this week’s instruction is to deepen students’ understanding of:
- Add fractions with unlike units using the strategy of creating equivalent fractions.
- Add fractions with sums between 1 and 2.
- Subtract fractions with unlike units using the strategy of creating equivalent fractions.
- Subtract fractions from numbers between 1 and 2.
- Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.
- Add and subtract fractions making like units numerically.
- Subtract fractions greater than or equal to 1.
- Interpret a fraction as division
- Use tape diagrams to model fractions as division
- Multiply any whole number by a fraction using tape diagrams
- Student Print Packets for each day
- End of Week Assessment
- Empty number line template or lined paper
- Two-sided counters
- Drinking straws (5 per student)
5.NF.A.1 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 = (ad + bc)/bd.)
5.NF.A.2 Solve contextual problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
5.NF.B.3 Interpret a fraction as division of the Numerator by the denominator (a/b = a ÷ b). For example, 3/4 = 3 ÷ 4 so when 3 wholes are shared equally among 4 people, each person has a share of size 3/4. Solve contextual problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. For example, if 8 people want to share 49 sheets of construction paper equally, how many sheets will each person receive? Between what two whole numbers does your answer lie?
5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction by a fraction.
- Tape Diagrams: Tape diagrams are also called “bar models” and consist of a simple bar drawing that students make and adjust to fit a word or computation problem. They then use the drawing to discuss and solve the problem.
Example: A goat produces 5,212 gallons of milk a year. A cow produces 17,279 gallons of milk a year. How much more milk does a goat need to produce to make the same amount of milk as a cow?
- Standards Algorithm: A standard algorithm or method is a specific method of computation which is conventionally taught for solving mathematical problems.
- Rectangular Fraction Models: A rectangular fraction model is an insightful way to represent a fraction. The rectangle represents the whole and is divided into equal parts. Each part is a unit fraction.
Additional Terms and Symbols
- Benchmark fraction (e.g., 1/2 is a benchmark fraction when comparing 1/3 and 3/5 )
- Like denominators (e.g., 1/8 and 5/8 )
- Unlike denominators (e.g., 1/8 and 1/7 )
- Between (e.g., 1/2 is between 1/3 and 3/5 )
- Denominator (denotes the fractional unit: fifths in 3 fifths, which is abbreviated as the 5 in 3/5 )
- Equivalent fraction (e.g., 3/ 5 = 6 /10)
- Fraction (e.g., 3 fifths or 3 /5 )
- Fraction greater than or equal to 1 (e.g., 7/ 3 , 3 1 /2 , an abbreviation for 3 + 1/ 2 )
- Fraction written in the largest possible unit (e.g., 3 /6 = 1 × 3/ 2 × 3 = 1 /2 or 1 three out of 2 threes = 1/ 2 )
- Fractional unit (e.g., the fifth unit in 3 fifths denoted by the denominator 5 in 3/ 5 )
- Hundredth ( 1/ 100 or 0.01)
- Kilometer, meter, centimeter, liter, milliliter, kilogram, gram, mile, yard, foot, inch, gallon, quart, pint, cup, pound, ounce, hour, minute, second
- More than halfway and less than halfway
- Number sentence (e.g., Three plus seven equals ten. Usually written as 3 + 7 = 10.)
- Numerator (denotes the count of fractional units: 3 in 3 fifths or 3 in 3/ 5 )
- One tenth of (e.g., 1 /10 × 250)
- Tenth ( 1/ 10 or 0.1)
- Whole unit (e.g., any unit that is partitioned into smaller, equally sized fractional units)