A Problem Solving Approach to Mathematics for Elementary School Teachers (13th Edition)
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; Divide the given circle into 4 parts by drawing... more
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Ratio is approximately .Average is approximately .... more
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All metric units of length are related to the base... more
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Since and is 5 times , multiply 5 by 1,000 to ... more
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; Use to convert into centimeter,Use to ... more
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; Substitute for into the formula of ... more
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The circumference of the circle gets doubled. ; ... more
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; The length of an arc of a circle of radius is... more
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; Let the radii of the circles be , , and . ... more
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; Use the conversion .Convert into centimeter.... more
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; Circumference is the distance around the circle... more
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To explain the reason because of which triangle ... more
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The radius of the circle gets doubled. ; The ... more
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; The length of an arc of a circle of radius is... more
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; Let the radii of the circles be , , and . ... more
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Runners must complete the lap of the track from ... more
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Centimeter because it is a small measurement unit... more
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The required ratio is .The length of the arc of a ... more
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If the diameter of the larger semicircle is , then... more
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The spot on Object W touches the sidewalk 8 times.... more
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Triples can be used: 1, 1, and 1; 2, 2, and 1.... more
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Observation and research show that the size of ... more
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The circumference of Container C is greater as ... more
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To make the calculation easier, sometimes is used... more
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Yes, because the wire will be approximately above... more
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YesLet the length of the diameter be and the ... more
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No; There are 1000 meters in 1 kilometres, so 5 ... more
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Millimetersare used for the measurement of very ... more
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Person F's rope is 12 inches long, and it is ... more
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; The circumference of a circle is given by , ... more
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; Let be the side of the first square and be ... more
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The area of the triangle, that is , can be ... more
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The parallelogram is transformed into a rectangle... more
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YesThe area of the rectangle will be decreased by... more
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The resultant figure will be a parallelogram and ... more
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Person A is of the opinion that the area of a ... more
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This is not true as a thread of the same length ... more
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No, it is not possible to find the area of a thing... more
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"are" and "hectare" are the units of area, so it ... more
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The claim of Person D is not correct since it is ... more
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The formula of the area of a rectangle is the ... more
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; A quadrilateral with its diagonal perpendicular... more
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A: B: Total area: Area of Object C: ; The ... more
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; The circumference for an arc with angle is .... more
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; Redraw the figure with label of measure of ... more
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; The length of arc of the sector is given by the... more
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Estimated Area: ; Actual area: Difference in the ... more
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Area would be same in both the cases. ; If the ... more
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Total area: ;Area of Object C: square feet ; The ... more
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A composite shape is made up of simple geometric ... more
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Estimate area of appliance D: 6 times the area of ... more
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; As described, draw the triangle inside the ... more
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; Assume that is a constant. Then, the side of ... more
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To find the area of a parallelogram, its base ... more
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; A rhombus is in the shape of a kite, with all ... more
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; It is given that .Multiply and by 100 ... more
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; The area of a circle is , where is the radius... more
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; The area of the shaded region is obtained by ... more
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; The area of a circle is , where is the radius... more
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; Area of a triangle is , where is base and ... more
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; The area of a circle is , where is the radius... more
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; The area of a sector with radius is .... more
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; The area of a parallelogram is , where is the... more
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; The area of a trapezium with base and , and ... more
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; In a regular hexagon, the side is equal to the ... more
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The estimated area is of 3 hands and the actual ... more
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Entire Proof Answer: From the figure in part 6(a... more
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The third vertex of the triangle will be outside ... more
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; It is known that Multiply by to convert it... more
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; The area of a rectangle is , where is the ... more
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; The area of a rectangle is , where is the ... more
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The circular Object P inside the square has less ... more
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The areas of the inside and the outside of the ... more
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; The area of the square is , where is the ... more
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; Label each region of the given figure. ; Let ... more
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Determine the area of four small rectangles which ... more
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First pack ; The area of a rectangle is , where... more
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; Rotate square along the center of square ... more
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The area of is 9 times of the area of . ; When ... more
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; The area of a circle is , where is the ... more
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; The radius of the circle is half of its ... more
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; The area of a sector with radius is .... more
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; The area of a trapezium with base and , and ... more
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; In a regular hexagon, the side is equal to the ... more
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180 ; The area of a rectangle with length and ... more
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The area of a triangle is , where is the base ... more
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; The area of a rectangle with length and width... more
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The perimeter of a rectangle with length and ... more
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There are about 48 squares in the shaded region.... more
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In a right triangle, the sum of squares of lengths... more
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Consider a with side lengths , , and , where is ... more
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According to the Pythagorean Theorem, , where and... more
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As , the given triangle is not a right triangle... more
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A geometric proof is based on reason, logic, and ... more
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The converse of Pythagorean Theorem states that if... more
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The coordinates of two points on the -plane are ... more
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; Let the vertical and horizontal distances ... more
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units ; Let the vertical and horizontal distances... more
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; Let the length of the smaller leg of the given ... more
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; Assume that the length of the diagonal of a ... more
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; Use the coordinate axes to plot the route of ... more
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; As the surface and object W are perpendicular, ... more
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; Label the given trapezium as , and draw a ... more
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; The measurements made by the company are the ... more
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Entire Proof Answer:Each side of the quadrilateral... more
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; Join the centers of the circles with a line ... more
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unitsAccording to triangle relationship, the ... more
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; Draw the right-angled triangle which shows the ... more
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; The diagonals of a rhombus bisect each other at... more
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Entire Proof Answer: The triangles similar to the ... more
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If a polygon has interior vertices, then its ... more
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Use the conversion to convert the length of ... more
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; As, a right-angle triangle is formed with the ... more
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; The circle formed by the range has centre and ... more
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; As a right-angle triangle is formed by the ... more
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to the nearest ; Mark the point in the diagram... more
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; Divide the length of by 2 to find the length ... more
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; Observe the home base, first base, and third ... more
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Entire Proof Answer: It is given that , which ... more
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In the given figure, the outside quadrilateral is ... more
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Entire Proof Answer: Area of a circle can be ... more
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; Substitute 0 for , 0 for , for , and for... more
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Entire Proof Answer: Calculate the lengths of all ... more
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or ; Plot the given triangle having as the ... more
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; Let be the inner circle having the first ... more
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; The tangent touches the circle at point .... more
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; Two diagonals divide the rhombus into four ... more
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Entire Proof Answer: Let , , and be the three ... more
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Entire Proof Answer: Let and represent the ... more
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Join and . Draw a perpendicular from to the ... more
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Let the lengths of the sides of the right triangle... more
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Draw a right triangle with two legs of the lengths... more
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Entire Proof Answer: Determine the areas of the ... more
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The area of the can be found by adding the areas... more
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; Let there be an equilateral triangle , whose ... more
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Approximately To find the area between the given ... more
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; Compare the given equations with the equation ... more
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Take a right triangle and construct two squares ... more
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An equilateral triangle does not satisfy the ... more
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Entire Proof Answer: Assume a right triangle with... more
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Yes. If the sides of the right triangle are ... more
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The statement given by an individual B is not ... more
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Individual J made a mistake by taking addition of ... more
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All the points that satisfy the given condition ... more
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Since the price of Item C is dependent on the ... more
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Square rod is a unit that is used to measure the ... more
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, , , ; To compare the quantities, convert them ... more
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; The object W is fenced around a shape of a ... more
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Individual S got a good deal than Individual M as ... more
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; The coin of the given currency of Country U has... more
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The measures of the hypotenuse, base, and ... more
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Mid-point of a line segment can be found by adding... more
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The triangle has the perpendicular of length 5... more
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When the figure will be folded from the dashed ... more
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; Substitute 6 for , for , and 4 for into the ... more
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; Since , convert the given radius and height ... more
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; Substitute 6370 for into the formula to find... more
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; Substitute 4 for into the formula . ; Simplify... more
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; Draw a right triangle inside the hexagon such ... more
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; The can is in the shape of a right circular ... more
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; Let length, width and height be , and of the ... more
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; Take the square root of the given area to find ... more
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; Substitute for into to find the ... more
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; Let and be the length and radius of the first... more
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; Divide the diameter by 2 to find the radius. ; ... more
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; Let and be the edges of the first and the ... more
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; Substitute 10 for , for , and for into the ... more
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; There are 6 faces in a hexagonal prism.Multiply... more
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; Convert the dimensions given in the feet into ... more
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In the given figure, there are 4 rectangles and 2 ... more
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; Area of a rectangle is given by , where is ... more
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; The height, slant height and half of the base ... more
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; The lateral surface area of the right circular ... more
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; Calculate the base, , from the area of the ... more
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Calculate the surface area with as and as .As ... more
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; Let be the length of the first cone and be ... more
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The surface area of planet J will be 121 times as ... more
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; Calculate the surface area of the first cube by... more
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; Calculate the surface area of the outer cube ... more
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; Dissect the figure to show the cross-section... more
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; Find the slant height as the height of ... more
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Substitute for into to find the surface area of... more
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No effectThis is because there is a loss of and a... more
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Entire Proof Answer: For the given result to be ... more
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; Draw a labeled right circular cone containing ... more
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Radius: ;Find the circumference of the given ... more
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; Substitute for , for , and for into the ... more
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; Consider a right triangular prism with the ... more
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No; the person needs nine times of the previous ... more
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Person G is not correct because the surface area ... more
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YesThe formula used by Person A is in factored ... more
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Person J is wrong as four times the previous ... more
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Person R is wrong because the surface area of ... more
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; Let and denote length and width of the ... more
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; As the diagonals of the rhombus bisect each ... more
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; Use the Pythagorean theorem on triangle to ... more
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; The diagonal of a cube is given by , where ... more
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Consider a circular ring of any radius. The given ... more
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The given prism has five faces.The figure given in... more
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If heights and radii of a cone and a cylinder are ... more
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The required volume is about cubic inches. ; The... more
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Multiply the volume of the cone by 3. ; Let the ... more
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; Calculate the number of drops in 30 days by ... more
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; The given Structure GP is similar in shape with... more
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; For (a), the given value is . Use the ... more
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; Substitute 4 for , 4 for , 4 for , and for ... more
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It becomes 8 times the volume of the original ... more
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(a)(b)(c)(d) ; The volume of a rectangular prism ... more
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; If the diameter of a sphere is times the ... more
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; Substitute 50 for , 25 for , and 2 for into ... more
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; Object S is cylindrical.If the diameter is 4 mm... more
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Great pyramid Ch has approximately times greater... more
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; Let be the height and be the radius of the ... more
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; Let be the side of the given cube. Then, the ... more
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; Find the volume of one Object B by substituting... more
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; The shape of Object C is cylindrical. So, the ... more
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The volume of prism is equal to the volume of ... more
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To measure the weight of heavy objects, the unit ... more
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The given object cannot have a mass of 340 grams ... more
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; The mass of water in the tank is equal to the ... more
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; There are approximately grams in a pound.The ... more
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Fish AG: Fish C: ; Convert to English ton by ... more
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; Find the weight of the single sheet by dividing... more
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; Convert the width of the floor, , to inches ... more
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; Use the conversion to convert the required ... more
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; The volume of the stones is equal to the ... more
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; Find the increase in the height by subtracting... more
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; For (a), the given value is . Use the ... more
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27 times of the volume of the original sphere ; ... more
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; The volume of a rectangular prism is given by... more
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Larger Fruit M; At the price of times of the ... more
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; The given figure is made of two prisms. One is ... more
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; Find the radius, , when the diameter is using ... more
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; Find the outer radius by adding and .Convert ... more
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No, the amount of Item P reduces to one-third for ... more
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; It is known that .The volume of a cylinder is ... more
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Second Item F ; Substitute for , for , and for... more
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; First, find the volume of sphere by ... more
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; Let the edge of the box be . So, the volume of ... more
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About times the radius of the original Object B... more
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; Observe that a square of size has been cut ... more
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To measure the weight of light objects, the unit ... more
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To measure the weight of light objects, the unit ... more
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; There are approximately grams in a pound.The ... more
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Fish AG: Fish C: ; Convert into kilograms by ... more
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; Find the weight of the single sheet by dividing... more
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; Convert the width of the floor, , to inches ... more
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; Use the conversion to convert one kilogram ... more
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The volume of an irregular shape can be found by ... more
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The second problem is easier because the ... more
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The feasibility can be justified by the fact that ... more
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Any box can be used because the length of the ... more
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; The diagonal of a cube is the hypotenuse of the... more
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; The volume of cylinder is , where is the ... more
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A box of length , width , and height is the one ... more
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Design a cylinder having a radius of and a height... more
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Yes because weight depends on density that depends... more
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Yes, the volume and the surface area of a cube can... more
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The volume of cube is not . Students do not ... more
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Person A is right as the volume will be increased ... more
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The choice of Person B was wrong because she had a... more
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Yes, any cube is similar to another cube and any ... more
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; Use the Pythagorean theorem to determine the ... more
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The length of the nonface diagonal is more because... more
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The total available volume is very small, and it ... more
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The given unit is used to measure the area of ... more
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The diameter of the cylinder is , which implies ... more
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; Convert the diagonal of the rectangle into ... more
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; The circumference of a circle with radius ... more
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Individual M is incorrect because the ... more
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The area of the rectangle in the given second ... more
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Since the base of all the triangles is same, the ... more
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; Reconstruct the diagram and determine the height... more
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; Find the length of the right triangle using... more
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; Surface area is the sum of areas of all sides ... more
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; Find the lateral side, , of the right circular... more
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The year 2020 figure shows that company’s growth ... more
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; The area of a kite with diagonals and is ... more
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; Convert the value of the diagonal of the ... more
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; The area of a triangle with base and height ... more
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Width: ; Using the given information, draw the ... more
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; The formula for the volume of cylinder is and ... more
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; The length and width of the cut of a rectangle ... more
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; The capacity of sphere is the volume of the ... more
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; Using similarity principle, if two similar ... more
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In both plans, the area covered by Object S is the... more
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Entire proof answer: Side is equal to side ... more