The focus of this week’s instruction is to deepen students’ understanding of:
- Compose and decompose right rectangular prisms using layers.
- Use multiplication to calculate volume.
- Find the total volume of solid figures composed of two non-overlapping rectangular prisms.
- Find the area of rectangles with whole-by-mixed and whole-by-fractional number side lengths by tiling, record by drawing, and relate to fraction multiplication.
- Measure to find the area of rectangles with fractional side lengths.
- Multiply mixed number factors, and relate to the distributive property and area model.
- Solve real-world problems involving area of figures with fractional side lengths using visual models and/or equations.
- Student Print Packets for each day
- End of Week Assessment
- Personal white boards
- 50 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.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)