MAT1236 Study Guide - Final Guide: Platonic Solid, Problem Solving, Triangular Number
14 Jun 2018
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Teaching)volume:!!
Students!will!sometimes!assume!that!the!tallest!container!has!the!largest!volume,!so!have!students!
compare!volume!by!pouring!liquid!from!one!container!to!another,!provide!examples!where!the!
tallest!container!is!not!the!largest,!and!have!students!explain!their!reasoning.!Platonic!solids:!convex!
regular!polyhedral,!the!faces!of!each!platonic!solid!are!congruent!regular!polygons,!with!the!same!
number!of!faces!meeting!at!each!vertex.!5!platonic!solids:!tetrahedron,!cube,!octahedron,!
dodecahedron,!icosahedron.!!
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Percentages:!a!special!ratio!that!represents!parts!per!hundred.!Models!for!teaching!%:!
rectangular!grids!shaded!to!show!50%,!percent!bars,!10x10!grid!to!illustrate!percentages.!Smaller!
percentages!may!be!difficult!to!grasp.!Problem!solving:!students!should!learn!to!solve!problems!with!
percentages!using!common!benchmarks!and!estimation.!Convert!factions!to!decimals:!use!division,!
¾=3!divided!4=0.75.!Decimals!to!fractions:!use!place!value,!0.136=1/10+3/100+6/1000=136/1000.!
Fractions!to!percentages:!make!the!denominator!100,!or!convert!to!decimal!and!multiply!by!100.!!
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Patterns:!Two!types;!Repeating!patterns,!Growing!patterns.!Children!should!work!on!patterns!by!
exploring!extending!and!describing!patterns!(continuing!patterns),!being!with!counting!sequence,!
then!skip!counting,!then!Arithmetic!sequences:!have!a!constant!difference!graphing!arithmetic!
produces!a!straight!line!–!linear!pattern)!Geometric!sequences:!found!by!multiplying!or!dividing!by!a!
constant!amount.!Example!of!a!continuing!pattern:!Fibonacci!(1,1,2,3,4,8,13…)!Triangular!numbers!
(1,3,6,10…)!Square!numbers)
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Document Summary
Platonic solids: convex regular polyhedral, the faces of each platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex. 5 platonic solids: tetrahedron, cube, octahedron, dodecahedron, icosahedron. Percentages: a special ratio that represents parts per hundred. Models for teaching %: rectangular grids shaded to show 50%, percent bars, 10x10 grid to illustrate percentages. Problem solving: students should learn to solve problems with percentages using common benchmarks and estimation. Fractions to percentages: make the denominator 100, or convert to decimal and multiply by 100.
