Grade 4 Practice Problems: Geometry

Examples from Standards Revision and GLEs

4G-20) Answer: 95 inches
A map of a National Forest in Alaska has a scale of one inch for every 75 miles. The perimeter of the forest is 7,125 miles. How many inches would represent the perimeter on the map? Write to help explain your best thinking using words, numbers, or pictures.

4G-19) Answer: 120
How many times does X occur in the diagram below? Write to help explain your best thinking using words, numbers, or pictures.

4G-18) Answer: 71
How many times does the letter X occur in the diagram below? Write to help explain your best thinking using words, numbers, or pictures.

4G-17) Answer: 36
How many times does the letter X appear in the diagram at the below? Write to help explain your best thinking using words, numbers, or pictures.

X	X	X	X	X	X	X
X	X	X	-	X	X	X
X	X	-	-	-	X	X
X	-	-	-	-	-	X
X	X	-	-	-	X	X
X	X	X	-	X	X	X
X	X	X	X	X	X	X

4G-16) Answer: 4x4 and 3X6
There are two rectangles whose dimensions are whole numbers and whose area and perimeter are the same number. Find them. Write to help explain your best thinking using words, numbers, or pictures.

4G-15) Answer: 15
For Gilda's party, the Hoagie House prepared a huge sub sandwich on a 7-foot long Italian roll. Gilda wants to feed 16 friends. How many cuts must she make? Write to help explain your best thinking using words, numbers, or pictures.

4G-14) Answer: 23
Candy delivers packages. Today she started on the first floor and went up 7 floors. Then she went down 3 floors, and then up 16 floors. She went up 2 more floors to the top floor of the building. How many floors were in this building? Write to help explain your best thinking using words, numbers, or pictures.

4G-13) Answer: (diagram)
Lia and Carlos went on a bike ride with Anita. They left Anita's house and went 3 blocks to Maple Street and turned right. They went straight ahead 6 blocks to Pine and turned left. They went 4 blocks to Elm and turned left. Then they went straight ahead 4 blocks when Anita stopped, and said she wanted to go back to her house. What was the shortest way back to Anita's house? Write to help explain your best thinking using words, numbers, or pictures.

4G-12) Answer: 54
Sasha's family is having a big reunion on July 4. They borrowed tables and are setting them up outside. They can put three chairs on each side of the tables. If they set up 8 tables in a long row, with the tables together on one side, how many family members can sit down to eat? Write to help explain your best thinking using words, numbers, or pictures.

4G-11) Answer: 65
Penny works in the Package Palace. It is Penny's job to stamp the sides of packages that are not touching the floor and not touching another package. Today there are 25 packages on the floor. Penny put the packages in 5 stacks, and the sides of the stacks touch. How many sides of packages must Penny stamp? Write to help explain your best thinking using words, numbers, or pictures.

4G-10) Answer: 14 inches
Alice watched an ant hunting for food. The ant was traveling in a straight line toward a crumb on the floor. Suddenly it turned around and crawled 9 inches back to Alice's shoe. Another ant joined it and together they hurried 11 inches back toward the crumb. The two ants stopped and came back 2 inches toward Alice's shoe. Finally they turned around and raced 5 inches to the crumb. How far was the crumb from Alice's shoe? Write to help explain your best thinking using words, numbers, or pictures.

4G-9) Answer: 10
Sandy and Mario are going into Tuneville Center to hear a band play. They can get in through two different entrances. Each entrance goes into a lobby that has a snack bar in it. There are five doors going from the lobby into the room where the band will play. How many different paths can Sandy and Mario take to get from outside Tuneville Center to their seats in the band room? Write to help explain your best thinking using words, numbers, or pictures.

4G-8) Answer: (diagram)
"Follow me" said Marcy to Lea. The two girls left Lea's home. They walked forward 4 blocks on Mystery Road and turned left on Wax Way. They went forward 8 blocks and turned right onto Sandy Street. Lea was puzzled by now, but she kept following Marcy down Sandy Street for 3 blocks. Marcy stopped there and went into a house. Lea followed her. "Surprise! Happy birthday, Lea!" called the girls' friends when Lea came into the house. Can you show the path from Lea's home to the house where the birthday party was? Write to help explain your best thinking using words, numbers, or pictures.

4G-7) Answer: 180
The Wizard at Windows is washing all the windows in the building at 946 Third Street. There are 9 floors in the building and 12 offices on each floor, 6 offices across the back of the building and 6 offices across the front of the building. The outside wall of each office has 2 windows. How many windows does the Wizard have to wash? Write to help explain your best thinking using words, numbers, or pictures.

4G-6) Answer: alike (4 sides, opposite sides equal and parallel ,all angles equal); different (rectangles may have 2 longer sides)
Describe a square and a rectangle. How are they alike? How are they different? Write to help explain your best thinking using words, numbers, or pictures.

4G-5) Answer: South
Suppose that you are facing west. If you turn left three times, then twice to the right, what direction is behind you? Write to help explain your best thinking using words, numbers, or pictures.

4G-4) Answer: 50 inches
Ryan made 9 cuts in a board to divide it into equal 5-inch-long pieces. How long was the board? Write to help explain your best thinking using words, numbers, or pictures.

4G-3) Answer: South 10 blocks
Ellen leaves school and walks 25 blocks south. Then she turns east and walks 16 blocks. Then she turns north and walks 15 blocks. Then she turns west and walks 16 blocks. Is she north, south, east, or west of the school and how far? Write to help explain your best thinking using words, numbers, or pictures.

4G-2) Answer: 130 inches
Jake plans to make 12 cuts in a board. There will be a 10-inch interval between cuts. How long is the board? Write to help explain your best thinking using words, numbers, or pictures.

4G-1) Answer: (clockwise) Kim, Mike, Mary, Dave
Mary, Dave, Kim and Mike are sitting around a table. Kim is sitting across from Mary. Mary is sitting at Dave's right. Where is each person sitting? Write to help explain your best thinking using words, numbers, or pictures.

Expectations & Examples of Geometry from the 2008 Math Standards Revision (draft) - Grade 4

Find the approximate area of a two-dimensional figure using square units. This might involve filling a shape with square-inch tiles.

Develop and use formulas for finding the perimeters and areas of squares and other rectangles.

Outline on graph paper a rectangle that is 4 units long and 3 units wide. Without counting the squares, how can you determine the area?

Solve problems that involve perimeters and areas of rectangular shapes and explain solutions using words, numbers, pictures, physical materials, or equations. Include customary and metric units, such as square inches, square feet, square yards, square centimeters, and square meters.

Find the areas of nonrectangular shapes that can be composed or decomposed into rectangles. Non-rectangular shape decomposed in two ways.

Demonstrate that rectangles with the same area can have different perimeters, and that rectangles with the same perimeter can have different areas. Example:

Draw several different rectangles with an area of 24 square units and compare their perimeters. What patterns do you notice in the data? Record your observations.

Locate and name points in the first quadrant of a coordinate grid using ordered pairs of whole numbers.

Examples of Geometric Sense from the 2006 GLEs – Grade 4

Explain parallel and perpendicular and give examples to demonstrate them.

Explain symmetry and use examples to demonstrate symmetry in 2 dimensional shapes and figures.

Draw one or more lines of symmetry in a given 2 dimensional figure.

Describe properties of 2 dimensional figures including parallel and perpendicular lines or lines of symmetry.

Draw and label 2 dimensional figures given particular attributes, including congruence.

Sort, classify, and label congruent 2 dimensional shapes and figures in multiple orientations.

Locate points or objects in the first quadrant on a coordinate grid in terms of horizontal and vertical position.

Plot a given set of ordered pairs in the first quadrant of a coordinate grid.

Use ordered pairs to name the location of points or objects in the first quadrant of a coordinate grid.

Show and explain a translation or reflection using a 2 dimensional shape or figure.

Record results of a translation or a reflection on a grid by listing the ordered pairs of the new vertices.

Demonstrate or draw and describe a single translation or a single reflection.

Describe translations and/or reflections in designs.

Draw the figure resulting from a particular translation or reflection on a grid.

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Grade 4 Practice Problems: Geometry