Grade 5 Practice Problems: Geometry
Examples from Standards Revision and GLEs
5G-15) Answer: 35 cubes
The tower below is made up of five horizontal layers of cubes with no gaps. How many individual cubes are in the tower? Write to help explain your best thinking using words, numbers, or pictures.
5G-14) Answer: 22 Squares
Each of the boxes in the figure below is a square. Using the lines of the figure, how many different squares can be traced?
5G-13) Answer: $6
Mrs. Smith is taking a log to the lumberyard. The log is 12 feet long, and she wants to have it cut into four pieces that are each 3 feet long. If the lumber-yard charges $2 per cut, how much will she spend? Write to help explain your best thinking using words, numbers, or pictures.
5G-12) Answer: 15 times
Joan went fishing. On the first cast she hooked a trout 80 feet from the boat. Each time she reeled in 10 feet of line the trout would take out 5 feet. How many times did she have to reel in to get the fish to the boat? Write to help explain your best thinking using words, numbers, or pictures.
5G-11) Answer: 24 inches
A square piece of paper is folded in half as shown and then cut into two rectangles along the fold. The perimeter of each of the two rectangles is 18 inches. What is the perimeter of the original square? Write to help explain your best thinking using words, numbers, or pictures.
5G-10) Answer: top: Lana-Gerald-Lara; bottom: Meredith-Farley-Sam
Teresa built a 2-story apartment house for her hamsters: Gerald, Farley, Sam, Meredith, Lana, and Lara. She put each hamster in one of the 6 apartments. She put Gerald next to Lara and above Farley. Lana was at the other end from Lara. Sam was not directly below Lana. Where did Teresa put each of the hamsters? Write to help explain your best thinking using words, numbers, or pictures.
5G-9) Answer: 246 square feet
A rectangular garden is 14 feet by 21 feet and is bordered by a concrete walk 3 feet wide. How many square feet are in the surface area of just the concrete walk? Write to help explain your best thinking using words, numbers, or pictures.
5G-8) Answer: 132
Muriel and Betty are stacking cartons in the middle of the room. They are stacking the cartons side by side, 2 rows of 9 cartons across and 6 cartons high. They have to mark each carton where there is a side facing out, except for the tops of the cartons. How many sides do they have to mark? Write to help explain your best thinking using words, numbers, or pictures.
5G-7) Answer: 11 cages
Troy was feeding the animals at the zoo. He started at the monkey's cage. Then he walked down the hill 3 cages to feed the birds. The birds are in the first cage in the zoo. Then Troy went up the hill 7 cages to feed the seals. From there he went down the hill 5 cages to feed the bears. Next he went up the hill 8 cages to the elephants. They are in the last cage in the zoo. How many cages are there in the zoo? Write to help explain your best thinking using words, numbers, or pictures.
5G-6) Answer: row l: records & tapes-books-toys row 2: t-shirts-jewelry-posters
Libby and Kay were setting out records and tapes, jewelry, toys, books, posters, and T-shirts for the White Elephant Sale at school. They were setting up six tables in two rows. They put the records and tapes across from T-shirts and next to the books. They put the posters at the Opposite end of the row from the T-shirts. The toys were not put next to the T-shirts. How did Libby and Kay set up the tables for the White Elephant Sale? Write to help explain your best thinking using words, numbers, or pictures.
5G-5) Answer: 40 boxes
There are 4 separate large boxes, and inside each large box there are 3 separate small boxes, and inside each of these small boxes there are 2 separate smaller boxes. How many boxes, counting all sizes, are there altogether? Write to help explain your best thinking using words, numbers, or pictures.
5G-4) Answer: 28
Clayton is getting some friends together to go to a movie. He is getting his friends who live on his floor of the apartment building. First he walks down the hall 6 apartments to get Martha. Martha lives in the last apartment on the floor. Then Clayton goes up the hall 10 apartments to get William. Next he goes down the hall 3 apartments to find Rita. From here he goes up the hall 6 apartments to pick up James. He lives in the last apartment on the floor. If there are the same number of apartments on both sides of the hall, how many apartments are there altogether on Clayton's floor? Write to help explain your best thinking using words, numbers, or pictures.
5G-3) Answer: 112 feet
Mr. Granger is building a fence. He places 15 fence posts 8 feet apart. What is the distance from the first fence post to the last? Write to help explain your best thinking using words, numbers, or pictures.
5G-2) Answer: 75 seconds
Five flags are spaced evenly around a track. It took a runner 30 seconds to get from the first flag to the third flag. If the runner continues at the same speed, how long will it take her to get completely around the track? Write to help explain your best thinking using words, numbers, or pictures.
5G-1) Answer: 144 rectangles
Rectangular cards, each 2 inches by 3 inches, are cut from a rectangular sheet 2 feet by 3 feet. What is the greatest number of cards that can be cut from the sheet? Write to help explain your best thinking using words, numbers, or pictures.
Expectations & Examples of Geometry from the 2008 Math Standards Revision (draft) - Grade 5
Represent the relationship of the surface area of a rectangular prism to the areas of its faces using words, numbers, pictures, or physical objects. Students can use the area formula for rectangles here. Representations may include graph paper, nets, or a sum of the areas of the faces. Find the approximate volume of rectangular prisms using cubic units. Students might find approximate volume by filling boxes with cubes or by using small cubes to build larger cubes or larger rectangular prisms. Develop and use formulas for finding the volumes of cubes and other rectangular prisms. Use rectangular layers (area of the base) along with the number of layers to determine the volume of a rectangular prism. Solve word problems that involve surface area or volume and explain solutions using words, numbers, pictures, physical materials, or equations. Graph ordered pairs on a coordinate grid for two sets of data related by a linear rule and draw the line they determine. Example:
Graph the ordered pairs (0,0), (2,10), and (5, 25) and the line connecting the ordered pairs. Use the line to determine the missing value in the table. Sketch and identify acute, right, and obtuse angles. Classify triangles as acute, right, or obtuse based on their angle measures. |
Examples of Geometric Sense from the 2006 GLEs – Grade 5
Explain the difference between a regular and irregular polygon. Describe a 2 dimensional shape and/or figure using properties including number of sides, number of vertices, and types of angles. Draw a simple 2 dimensional shape and/or figure having given characteristics including number of sides, number of vertices, types of angle(s), and/or congruence. Use and/or explain mathematical conventions used to label vertices, line segments, and angles. Describe parallel and perpendicular lines and/or lines of symmetry. Draw, describe, and/or label a figure or design that includes a given set of properties including parallel or perpendicular lines and/or line of symmetry. Draw, describe, and/or label angles, quadrilaterals, parallel and/or perpendicular lines, lines of symmetry, and congruent 2 dimensional shapes or figures. Sort, classify, and label shapes and figures using the properties of parallel lines, perpendicular lines, and lines of symmetry. Complete a picture or design using a line of symmetry. Complete pictures or designs from a variety of cultures that incorporate parallel line(s), perpendicular line(s), and/or a line(s) of symmetry. Plot points with positive coordinates on a number line. Describe the relative position of fractions and/or decimals on a positive number line. Identify or move the coordinates of points on an incomplete number line involving fractional or decimal increments. Draw a translation or reflection of a given figure on a grid. Use translations or reflections to describe patterns in art, architecture, or nature. Describe whether a figure has been translated or reflected. Create designs using translations and/or reflections. Identify a picture or diagram of a particular translation or reflection. |