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- https://math.libretexts.org/Courses/Coastline_College/Math_C104%3A_Mathematics_for_Elementary_Teachers_(Tran)/12%3A_Geometry/12.04%3A_PolygonsYou know that the sum of the interior angles in any triangle is 180°. Can you say anything about the angles in other polygons? Show that each of them can be split into exactly three triangles in such ...You know that the sum of the interior angles in any triangle is 180°. Can you say anything about the angles in other polygons? Show that each of them can be split into exactly three triangles in such a way that the vertices of the triangles all coincide with the vertices of the pentagon. Show that each of them can be split into exactly four triangles so that the vertices of the triangles all coincide with the vertices of the hexagon.
- https://math.libretexts.org/Courses/Coastline_College/Math_C104%3A_Mathematics_for_Elementary_Teachers_(Tran)/11%3A_Fraction_Operations/11.09%3A_Problem_BankIf the small square (the single tangram piece) is one whole, assign a fraction value to each of the seven tangram pieces. If the medium triangle (the single tangram piece) is one whole, assign a fract...If the small square (the single tangram piece) is one whole, assign a fraction value to each of the seven tangram pieces. If the medium triangle (the single tangram piece) is one whole, assign a fraction value to each of the seven tangram pieces. If you place a full container of flour on a balance scale and place on the other side a \(\frac{1}{3}\) pound weight plus a container of flour (the same size) that is \(\frac{3}{4}\) full, then the scale balances.
- https://math.libretexts.org/Courses/Coastline_College/Math_C104%3A_Mathematics_for_Elementary_Teachers_(Tran)/01%3A_Problem_Solving/1.05%3A_Problem_BankArrange the digits 0 through 9 so that the first digit is divisible by 1, the first two digits are divisible by 2, the first three digits are divisible by 3, and continuing until you have the first 9 ...Arrange the digits 0 through 9 so that the first digit is divisible by 1, the first two digits are divisible by 2, the first three digits are divisible by 3, and continuing until you have the first 9 digits divisible by 9 and the whole 10-digit number divisible by 10. Find the largest eight-digit number made up of the digits 1, 1, 2, 2, 3, 3, 4, and 4 such that the 1’s are separated by one digit, the 2’s are separated by two digits, the 3’s by three digits, and the 4’s by four digits.
- https://math.libretexts.org/Courses/Teachers_College_Columbia_University/Book%3A_Mathematics_for_Elementary_Teachers_(Manes)/05%3A_Problem_Solving/5.06%3A_Careful_Use_of_Language_in_MathematicsIt is important that the statement is either true or false, though you may not know which! (Part of the work of a mathematician is figuring out which sentences are true and which are false.) If it is ...It is important that the statement is either true or false, though you may not know which! (Part of the work of a mathematician is figuring out which sentences are true and which are false.) If it is true, then we conclude that it is false. (Why?) If it is false, then we conclude that it is true. (Why?) Paradoxes are no good as mathematical statements, because it cannot be true and it cannot be false.
- https://math.libretexts.org/Courses/Teachers_College_Columbia_University/Book%3A_Mathematics_for_Elementary_Teachers_(Manes)/01%3A_Counting/1.07%3A_Problem_Bank\[3, \quad 6, \quad 9, \quad 12, \quad 21, \quad 27, \quad 33, \quad 60, \quad 81, \quad 99 \ldotp\] \[5, \quad 10, \quad 15, \quad 25, \quad 55, \quad 75, \quad 100, \quad 125, \quad 625, \quad 1000 ...\[3, \quad 6, \quad 9, \quad 12, \quad 21, \quad 27, \quad 33, \quad 60, \quad 81, \quad 99 \ldotp\] \[5, \quad 10, \quad 15, \quad 25, \quad 55, \quad 75, \quad 100, \quad 125, \quad 625, \quad 1000 \ldotp\] What is the largest number that can be produced by erasing one hundred digits of the number? (When you erase a digit it goes away. For example, if you start with the number 12345 and erase the middle digit, you produce the number 1245.) How do you know you got the largest possible number?
- https://math.libretexts.org/Courses/Coastline_College/Math_C104%3A_Mathematics_for_Elementary_Teachers_(Tran)/01%3A_Problem_SolvingSolving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one...Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. – Yoko Ogawa
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/07%3A_Geometry/7.08%3A_Geometry_in_Art_and_ScienceSo if you make six copies of a single triangle and put them together at a point so that each angle appears twice, there will be a total of 360° around the point, meaning the triangles fit together per...So if you make six copies of a single triangle and put them together at a point so that each angle appears twice, there will be a total of 360° around the point, meaning the triangles fit together perfectly with no gaps and no overlaps. The best material for this is mini marshmallows; you can stick the ends of the toothpicks into the marshmallows to connect them.
- https://math.libretexts.org/Courses/Las_Positas_College/Math_27%3A_Number_Systems_for_Educators/02%3A_Problem_Solving/2.05%3A_Problem_BankArrange the digits 0 through 9 so that the first digit is divisible by 1, the first two digits are divisible by 2, the first three digits are divisible by 3, and continuing until you have the first 9 ...Arrange the digits 0 through 9 so that the first digit is divisible by 1, the first two digits are divisible by 2, the first three digits are divisible by 3, and continuing until you have the first 9 digits divisible by 9 and the whole 10-digit number divisible by 10. Find the largest eight-digit number made up of the digits 1, 1, 2, 2, 3, 3, 4, and 4 such that the 1’s are separated by one digit, the 2’s are separated by two digits, the 3’s by three digits, and the 4’s by four digits.
- https://math.libretexts.org/Courses/Teachers_College_Columbia_University/Book%3A_Mathematics_for_Elementary_Teachers_(Manes)/02%3A_Spatial_Relations/2.01%3A_IntroductionIt is probably the oldest field of mathematics, because of its usefulness in calculating lengths, areas, and volumes of everyday objects. The study of geometry has evolved a great deal during the last...It is probably the oldest field of mathematics, because of its usefulness in calculating lengths, areas, and volumes of everyday objects. The study of geometry has evolved a great deal during the last 3,000 years or so. Like all of mathematics, what’s really important in geometry is reasoning, making sense of problems, and justifying your solutions. You have to reason through the situation and figure out what you know for sure and why you know it.
- https://math.libretexts.org/Courses/Hartnell_College/Mathematics_for_Elementary_Teachers/01%3A_Problem_Solving/1.02%3A_Problem_or_ExerciseArrange the digits 1–6 into a “difference triangle” where each number in the row below is the difference of the two numbers above it. Find the largest eight-digit number made up of the digits 1, 1, 2,...Arrange the digits 1–6 into a “difference triangle” where each number in the row below is the difference of the two numbers above it. Find the largest eight-digit number made up of the digits 1, 1, 2, 2, 3, 3, 4, and 4 such that the 1’s are separated by one digit, the 2’s are separated by two digits, the 3’s by three digits, and the 4’s by four digits.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Mathematics_for_Elementary_Teachers_(Manes)/05%3A_Patterns_and_Algebraic_Thinking/5.07%3A_Problem_BankCat Machine: Place a cat in the input bin of this machine, press the button, and out jump two dogs and a mouse. Calculate the number of toothpicks you would need to build the 10th figure in the patter...Cat Machine: Place a cat in the input bin of this machine, press the button, and out jump two dogs and a mouse. Calculate the number of toothpicks you would need to build the 10th figure in the pattern. Calculate the number of toothpicks you would need to build the 100th figure in the pattern. Objects that are the same shape have the same weight. (So all circles weigh the same, all squares weigh the same, etc.)
