Dear Family,
Your student is finding areas of rectangles that have fraction side lengths. Through an exploration with unit squares, students discover they can use the same method they used in earlier grades when multiplying whole-number side lengths. Your student is also finding the area of composite figures with fraction side lengths, which builds on their skills with finding area of composite figures with whole-number side lengths. These skills support students in later grades when they find the surface area of solids.
NEW KEY TERMS
base: The base of a prism is one of the faces of the prism, often thought of as the surface on which the prism rests. (Lesson 16)
composite figure: A composite figure is a geometric figure composed of two or more smaller figures. (Lesson 13)
cubic centimeter: Cubic centimeters are a unit for measuring volume. 1 cubic centimeter of volume is defined as the volume of a cube with side lengths of 1 centimeter. (Lesson 17)
cubic inch: Cubic inches are a unit for measuring volume. 1 cubic inch of volume is defined as the volume of a cube with side lengths of 1 inch. (Lesson 17)
cubic unit: Cubic units are a unit for measuring volume. 1 cubic unit of volume is defined as the volume of a cube with side lengths of 1 unit. (Lesson 17)
right rectangular prism: A right rectangular prism is a solid where all the faces are rectangles. (Lesson 16)
unit cube: A unit cube is a cube with edges that each measure 1 unit. (Lesson 17)
volume: The volume of a solid is the amount of three-dimensional space it takes up. (Lesson 17)
acute angle, acute triangle, attribute, capacity, cube, diagonal, edge, equilateral triangle, face, figure, formula, height, intersect, isosceles triangle, line of symmetry, liquid volume, obtuse angle, obtuse , triangle, parallel, parallelogram, perpendicular, quadrilateral, rectangle, rhombus, right angle, right triangle, square, square unit, straight angle, supplementary angles, three-dimensional figure, trapezoid, two-dimensional figure, unit square, vertex
AT HOME ACTIVITY
Square Masterpiece
Provide your student with a pad of square sticky notes or about 30 same-size square pieces
of paper. Explain that each square represents an area of 1/8 square unit. (Do not use a specific
measurement such as inches or centimeters.) Invite your student to arrange the squares into
an artistic design that does not include gaps or overlaps. When the design is complete, ask
them to calculate the total area of the squares. One method to find the area is to count all
the squares and multiply by 1/8 . Another method is to repeatedly add 1/8 for the squares in each
section of the design and then add the totals for each section together. For an additional
challenge, ask your student to make a design that uses more than one color of squares and
find the area of each color.
Compare Squares
Gather a few items in your home that are square such as napkins, washcloths, drink coasters,
or crackers. Choose one of the squares to use as a unit square. The unit square can be larger or
smaller than the other objects. Use paper to trace and cut out a few squares of the item you
chose as the unit square. Then use those paper squares to estimate how many it will take to
cover one of the other square items you found. Check your estimate by tiling the unit squares
without gaps or overlaps. You will notice that the unit square does not fit perfectly in most
cases. When this occurs, encourage your student to mark one of the paper squares to show
what part of it is used to cover the item. Then find the fraction of the paper square that is used.
Repeat this activity by using both larger and smaller unit squares.
Find a sample of our lessons below to help support MATH TALK at home.
Students also have these in their APPLY workbook.
Lesson 8 Find areas of square tiles with fraction side lengths by relating the tile to a unit square.
I can tile a unit square with squares that have unit-fraction side lengths. The area of each tile is 1 out of the total number of tiles it takes to cover the unit square.
Lesson 9 Organize, count, and represent a collection of square tiles.
I can tile a rectangle with square tiles that have fraction side lengths. The area of the rectangle is the product of the area of each square tile and the number of square tiles.
Lesson 10 Find the area of a rectangle with fraction side lengths by relating the rectangle to a unit square.
I can tile a unit square with rectangular tiles that have unit-fraction side lengths. I can use the area of the rectangular tiles to determine the area of a rectangle with side lengths that are fractions less than 1 and side lengths that are fractions greater than 1.
Lesson 11 Find areas of rectangles with fraction side lengths by using multiplication.
I can determine the area of any rectangle, whether it has whole-number side lengths or fraction side lengths, by multiplying the rectangle’s length and its width.
Lesson 12 Multiply mixed numbers.
Rectangles can have side lengths that are mixed numbers. I can multiply mixed numbers by using an area model and the break apart and distribute strategy or by converting mixed numbers to fractions greater than one.
Lesson 13 Solve mathematical problems involving areas of composite figures with mixed-number side lengths.
I can use a variety of methods to find the areas of rectangles and composite figures with mixed-number side lengths and of shaded and unshaded regions of figures.
Lesson 14 Solve real-world problems involving areas of composite figures with mixed-number side lengths.
I can use a variety of strategies to solve real-world problems that involve area of composite figures with mixed-number side lengths.
Lesson 15 Solve multi-step word problems involving multiplication of mixed numbers.
I can solve multi-step word problems involving area and multiplication with mixed numbers. I can use estimation to determine whether my answers are reasonable.