The focus of this week’s instruction is to deepen students’ understanding of:
- Multiply unit fractions by non-unit fractions.
- Relate decimal and fraction multiplication.
- Divide a whole number by a unit fraction.
- Divide a unit fraction by a whole number.
- Explore volume by building with and counting unit cubes.
- Find the volume of a right rectangular prism by packing with cubic units and counting.
- Student Print Packets for each day
- End of Week Assessment
- Personal white boards
- Millions through thousandths place value chart
- 4” x 2” rectangular paper (several pieces per student)
- 50 centimeter cubes per student and teacher
- Centimeter grid paper (print free here: Free Printable Graph Paper)
- Isometric dot paper (print free here: Free printable isometric dot paper)
- Net template
- 27 centimeter cubes per student and teacher
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.
- Interpret the product a/b x q as a x (q ÷ b) (partition the quantity q into b equal parts and then multiply by a). Interpret the product a/b x q as (a x q ) ÷ b (multiply a times the quantity q then partition the product into b equal parts). For example, use a visual fraction model or write a story context to show that 2/3 x 6 can be interpreted as 2 x (6 ÷ 3) or (2 x 6) ÷ 3. Do the same with 2/3 x 4/5 = 8/ 15. (In general, a/b x c/d = ac/bd.)
- Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations; assess the reasonableness of answers using estimation strategies. (Limit division problems so that either the dividend or the divisor is a whole number.)
5.NF.B.6 Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.
5.MD.A.1 Convert customary and metric measurement units within a single system by expressing measurements of a larger unit in terms of a smaller unit. Use these conversions to solve multi-step real-world problems involving distances, intervals of time, liquid volumes, masses of objects, and money (including problems involving simple fractions or decimals). For example, 3.6 liters and 4.1 liters can be combined as 7.7 liters or 7700 milliliters.
5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
- Interpret division of a unit fraction by a non-zero whole number and compute such quotients. For example, use visual models and the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.
- b. Interpret division of a whole number by a unit fraction and compute such quotients. For example, use visual models and the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4.
- Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins?
5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
- Understand that a cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume and can be used to measure volume.
- Understand that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.C.4 Measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units.
- 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?
- 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)
- Base (one face of a three-dimensional solid—often thought of as the surface on which the solid rests)
- Bisect (divide into two equal parts)
- Cubic units (cubes of the same size used for measuring volume)
- Height (adjacent layers of the base that form a rectangular prism)
- Unit cube (cube whose sides all measure 1 unit; cubes of the same size used for measuring volume)
- Volume of a solid (measurement of space or capacity)
- Area (the number of square units that covers a two-dimensional shape)
- Cube (three-dimensional figure with six square sides)
- Face (any flat surface of a three-dimensional figure)
- Rectangle (parallelogram with four 90° angles)
- Rectangular prism (three-dimensional figure with six rectangular sides)
- Solid figure (three-dimensional figure)
- Square units (squares of the same size—used for measuring)
- Three-dimensional figures (solid figures)
- Two-dimensional figures (figures on a plane)