Teacher s Guide. Editor s note. How to use the game

Transcription

1 Teacher s Guide Updated: January 23, 205 Editor s note Slice Fractions is designed to introduce children to the concept of fractions by solving puzzles. This guide reveals the underlying conceptual learning of the game and gives you the key content for all levels. We strive to help children discover the principles of fractions on their own, rather than assume that they have already learned them. Therefore, the first levels are designed to familiarize children with the game and teach basic concepts such as splitting groups into equal shares, slicing shapes into equal shares, comparing shapes to a common whole, etc. The game also uses symbolic representations to gradually give meaning to the numbers used as a numerator or denominator. Even without seeing numbers, kids achieve significant knowledge gains on which they will build a strong conceptual understanding of fractions. How to use the game Slice Fractions can be used to introduce fractions or to strengthen concepts and notions that have already been discussed in class. Ideally, students would have the opportunity to play the game alone so that they can experiment by themselves, learn from their own errors, and progress at their own pace. They can also play in teams of two, taking turns playing different roles and verbalizing their problem-solving strategies with their teammate. All the levels of the game, or those marked with an Essential flag, can be projected onto a screen and solved as a group. The teacher can lead the discussion and encourage students to verbalize their mathematical reasoning while using the appropriate terms. Lead the activity in three steps:. Ask students general questions about fractions such as, What s a fraction? How would you define it? Can you give examples of how fractions are used? Then, let the group of students decide among themselves if the answers that were given are correct or not. 2. Briefly introduce the game Slice Fractions. Specify that the first levels do not have any visible fractions, even though it will still be possible to understand the important concepts. Ask students to follow the normal progression of the game without skipping any levels. Devote a large amount of time for free play. 3. As a group, look back at some of the Essential levels and invite some students to share the strategy they used to solve the problem and verbalize how they analyzed the puzzles.

2 How to use this guide This guide lists all of the levels in the game so that teachers can quickly glance through the different concepts, understand the nature of the concepts that have been covered, and easily find the reference for a specific level. In addition, each level is associated with challenges related to mathematics and planning. The degree of difficulty is indicated on a scale of 0 to 3: Math: The player has to use their mathematical reasoning skills to solve the puzzle. Planning: The player has to plan his moves in a specific order to solve the puzzle. Concepts Table TAB CONCEPT DESCRIPTION PAGE How to play Learn the gameplay 3 COMMON CORE MATH CONTENT Split groups Split groups into equal shares 2.G.A.2 GREEN Slice shapes Slice shapes into equal shares 5 2.G.A.3 BLUE Shape Comparison Compare a part to its whole 7 Symbolic numerator Fractions reading Understand that a numerator counts equal parts Compare symbolic to numerical fractions Denominator Use the denominator 0 3.NF.A. Numerator Use the numerator 3.NF.A. Pie charts ORANGE Size comparison BROWN Use pie charts to represent fraction values Know that one fraction is X times bigger than NF.A. 3.NF.A.3 Equivalent Fractions (A) Understand equivalent fractions 5 3.NF.A.3 Equivalent Fractions (B) Master equivalent fractions 7 3.NF.A.3 Fractions ordering Compare fractions successfully 8 3.NF.A.3 Question marks Solving fraction values based on the information at hand 9 3.NF.A. Subtraction Subtract fractions from 20.NF.B.3.A 2

3 How to play GREEN TAB Learn the gameplay The goal of the game is to clear any obstacles that could prevent the mammoth from exploring an intriguing universe full of surprises. The first levels of the game serve as the tutorial to help the player understand the mechanisms of the game: bubbles can hold objects and they pop when the player touches them, lava cancels out an equivalent amount of ice, chains are unbreakable. Planning 2 Planning 3 Planning Planning 5 Planning 3

4 Split groups GREEN TAB Split groups into equal shares In order to melt the ice columns to the ground, the player must make an equivalent amount of lava fall onto each of them. The player will therefore learn to divide the lava into equal parts. 2 3 Badge

5 Slice shapes GREEN TAB Slice shapes into equal shares In this series of levels, the player learns to slice shapes and to divide them into equal parts. Some blocks have predefined slice lines while others show a pattern with scissors to indicate that they can be freely sliced. Planning 2 Planning 3 Planning Planning 5 Planning 6 Planning 7 Planning 8 9 Planning 5

6 Slice shapes GREEN TAB Slice shapes into equal shares In this series of levels, the player learns to slice shapes and to divide them into equal parts. Some blocks have predefined slice lines while others show a pattern with scissors to indicate that they can be freely sliced. Badge 0 Planning 6

7 Shape Comparison GREEN TAB Compare a part to its whole The white lines in the background can be used to compare the ice blocks and the lava blocks to a common whole. When the smoke hides a lava block, the player must subtract the value of that block, by interpreting the symbol located in front of the smoke. Planning 2 Planning 3 Planning Badge 7

8 Symbolic numerator BLUE TAB Understand that a numerator counts equal parts In this series, symbols imitate fractions: the number of the red blocks epresents the numerator, and the whole in the dotted sections represents the denominator. The player is guided to understand how to read a fraction by interpreting the numerator value based on the denominator. Planning 2 3 Planning 5 Planning Badge 8

9 Fractions reading BLUE TAB Compare symbolic and numerical fractions By associating the numerical representation of a fraction to its corresponding symbol, the player learns to read and interpret the numerator and the denominator of a fraction. Planning 2 3 Planning Planning Badge 5 9

10 Denominator BLUE TAB Use the denominator In this series of levels, the player will strengthen his or her understanding of the denominator by exploring different ways to divide a whole into equal parts. Planning 2 3 Planning Badge 0

11 Numerator BLUE TAB Use the numerator The player solves puzzles by deducting the amount of ice needed from the numerator of each fraction. This series aims to show that: a fraction /B as the quantity formed by part when a whole is partitioned into B equal parts; a fraction A/B as the quantity formed by a parts of size /B. Planning 2 Planning 3 5 Planning 6 7 Planning 8 9 Planning

12 Numerator BLUE TAB Use the numerator The player solves puzzles by deducting the amount of ice needed from the numerator of each fraction. This series aims to show that: a fraction /B as the quantity formed by part when a whole is partitioned into B equal parts; a fraction A/B as the quantity formed by a parts of size /B. 7 Planning Badge 9 Planning 2

13 Pie Charts ORANGE TAB Use pie charts to represent fraction values In this series, the player practices cutting a circle in half, quarters, and learns to combine these fractions based on the different denominators. eighths, and Planning 2 Planning 3 Planning 5 Planning 6 Badge 8 Planning 3

14 Size comparison ORANGE TAB Know that one fraction is X times bigger than another one The player learns to compare fractions to each other based on the numerator and the denominator, in order to determine which represents the largest quantity and in what proportion. Planning 2 Planning 3 Planning 5 Planning 6 Planning Badge

15 Equivalent fractions (a) ORANGE TAB Understand equivalent fractions The player manipulates fractions with different denominators to find out which ones are equivalent. Planning 2 Planning 3 Planning Planning 5 Planning 6 Planning 7 8 Planning 9 5

16 Equivalent fractions (a) ORANGE TAB Understand equivalent fractions The player manipulates fractions with different denominators to find out which ones are equivalent. Badge 0 Planning 6

17 Equivalent fractions (B) ORANGE TAB Master equivalent fractions The player recognizes the equivalent fractions in various contexts to find the solution to the puzzles. Planning Planning 6 Planning Badge 0 Planning 7

18 Fractions ordering BROWN TAB Compare fractions successfully By associating the different sized ice blocks to fractions, the player places the fractions in ascending order according to size, based only on the value of their numerator and their denominator. Planning 2 3 Badge Planning 8

19 Question marks BROWN TAB Solving fraction values based on the information at hand The player deduces the value of the parts of a whole based on the information that is available to him or her. He or she therefore learns to calculate the complementary fraction to form a whole. Planning 2 3 Planning Badge 5 Planning 6 9

20 Subtraction BROWN TAB Subtract fractions from The player finds the result when a fraction is subtracted from a whole represented by or A/A. 2 3 Planning 5 Planning Badge 20