126
Problem solving
Textbook: Part 4, lesson 126, pp. 55–57
GoalProblem solving: sorting solids into sets, finding a part of a set of shapes, problems on surface area and data.
New words
set · to‘plamelement · elementsolid shape · hajmli shaklcurved surface · egri sirt
Explanation
Solids can be sorted into sets by their features: shapes with only flat faces (cube, prism, pyramid) and shapes with a curved surface (sphere, cylinder, cone). To find a part of a set of shapes, use the rule for finding a part of a number. For the total surface of a pyramid or prism, add the areas of all faces. In each problem first decide what to find, then write an expression.
Worked examples
A set has 60 shapes: 1/4 are cubes and 1/3 are spheres. Cubes: 60 : 4 = 15, spheres: 60 : 3 = 20, other shapes: 60 − 15 − 20 = 25.
In the set {cube, sphere, cone, pyramid, cylinder} the shapes with a curved surface are the sphere, cone and cylinder: 3 elements.
Class activity
“Two baskets”: the teacher puts different objects on a table (a box, a ball, a glass, a paper hat, a toy cube). Children sort them into the sets “only flat faces” and “curved surface” and say how many elements each set has.
Practice
1
From the set {cube, sphere, prism, cone, pyramid, cylinder}, pick the shapes with only flat faces. How many are there?
cube, prism, pyramid – 3
2
A shop has 120 toy shapes: 1/4 are cubes, 1/5 are pyramids and the rest are balls. How many balls are there?
66
3
A square pyramid has a base of 25 cm² and each side face is 20 cm². What is the total surface area of 3 such pyramids in cm²?
315
4
Three towers are 120 m, 85 m and 64 m tall. How many metres taller is the highest than the lowest?
56
5
A cyclist rode 18 km up a hill in 2 hours and came down in 1 hour. What was his speed going up, in km/h?
9