DragonBox Algebra 12+ Home School Manual

Transcription

1 DragonBox Algebra 12+ Home School Manual

2 About DragonBox Algebra DragonBox aims at supplementing the teaching of the basics of algebra to kids in a natural, fun and effective way. These pages will tell you about the game and how it works as well as how the game can be used as part of your home school curriculum. We believe that children should be actively engaged in their learning process because they are, by nature, curious and inquisitive. From birth, they learn about their world by asking questions and by experimenting, using trial and error. DragonBox was conceived and developed to draw on these traits. We want children to rely on their innate ways of learning when playing DragonBox because, in doing so, they not only become self-reliant, they also learn how to learn. DragonBox teaches how to solve linear equations but it also lays the foundation for further algebra learning. It demystifies algebra and gives players confidence in mathematics. Age recommendations: DragonBox Algebra 12+ as a learning tool: Gives students a thorough introduction to DragonBox Algebra 12+ is recommended from age 10 and up but the first three chapters could also be introduced and discussed at an earlier age It is well suited as a supplement for the older students learning the basics of algebra, in addition to younger students searching for more challenges in math algebra in a fun and intuitive way in a matter of hours Seeks to motivate and give a feeling of mastery Engages and helps those who struggles in math This guide shows parents how to integrate DragonBox Algebra 12+ into your home school curriculum and how to bridge the gap between the levels in the game and solving equations on paper. DragonBox is based on the following pedagogical principles: Students learn more when they are engaged The most important factor to learning is feedback and it should be immediate to be effective To feel mastery is key to staying motivated Students should be presented with challenges that match their level of mastery Students should be assessed in a formative, non-intrusive way Discovery learning is much more effective than instructional-based teaching Students learn differently and at different paces Learning goals Basic equation solving skills Number factoring, signs Parenthesis, distributive properties Factoring, simplifying fractions Addition of like terms Creation of parameters Chapter side A Chapter side B

3 How to play DragonBox 2 DragonBox Algebra 12+ lets the students learn algebra by using colorful and fun objects that are gradually replaced by numbers and mathematical expressions similar to equations on paper. Students should be encouraged to articulate what they observe because it enhances the learning process and they will acquire the vocabulary necessary to be cogent in their thinking. The goal of the game is to get the dragon box, representing the unknown x, alone on one side of the game board. The rules and strategies for solving each level are introdused one at a time throughout the chapters. The games consists of a side A and B. On side A, the students learn the rules, while the levels on side B allow the students to practice what they have learned. Side B also provides a way to connect the game with equations the students would solve on paper. If the student chooses to restart a level, a lightbulb will appear in the top right corner. By clicking on the lightbulb, the student will get a short animation describing the solution for this level. The student can stop the animation at any time and go back to solve the equation again. Grades are not used in the game, but the students collect stars as they play. If the students solves a level, they are awarded with a star. Solving it and simplifying will get the student another star. The last star is earned when you can successfully solve the puzzle and simplify the solution in a minimum number of moves. Symbol Meaning The Dragon Box represents the unknown x. The goal of the game is to get the box alone on one side of the game board. The Green Vortex represents 0. Example of how numbers are represented in the game. Example of cards with two sides which gradually will be replaced by numbers or letters

4 How to use Dragonbox Algebra 12+ It is possible to work with DragonBox Algebra 12+ by defining six learning blocks according to the curriculum: Målgruppe 1: Basic equation solving skills (3 hours, worksheet 1a&1b) 2: Number factoring and signs (2 hours, worksheet 2) 3: Parenthesis and distributive properties (2 hours, worksheet 3) 4: Factoring and simplifying fractions (2 hours) 5: Addition of like terms (1 hour) 6: Creation of parameters (2 hours, worksheet 6) DragonBox can be used in different ways. Each child is unique. Each parent is unique. The relationship between a parent and a child is also unique. Therefore, it is up to each homeschooling parent to decide how to use the resources we have created, simply because you know best! Here comes an example about how to use DragonBox, but it is in no way the only manner to take advantage of this powerful tool. 3 - Take a break after each mn game session Om DragonBox edu - Ask your child to explain what she does in one of the last levels she has completed - Introduce the right mathematics concepts when you are sure your child has understood the mechanics in the game - Play again as long as you feel your child is not bored and not tired of the game - After some time, it is wise to make the link between the game and numerical equations. Example: X+5=10 What is X so that X+5 is 10? On the learning resources page of wewanttoknow.com you will find worksheets to practice and transfer what you have learned to pencil and paper. Here you will also find a document describing each rule with screenshots from the game as examples. Example of how to use DragonBox Algebra 12+: - Play the game yourself to familiarize yourself with the pedagogy of the game. - Play the game with your child 20 mn at the time (we recommend not explaining the math in the game at first, it would spoil the game)

5 How to use Dragonbox Algebra 12+ in home school 4 Part 1: Basic equation solving skills Goal: Students will understand the fundamental process of solving literal linear equations. After session 3, they will learn how to relate the rules and strategies from the game with solving of equations on paper. They will get acquainted with the goal of the game and the first set of rules. Rules: For a description of the underlying rules for part 1, se the Rules of Algebra sheet. It is important that the teacher encourages the students to explain the rules and strategies in their own words. What to play in DragonBox: Session 1: side A, chapter 1-2 Session 2: side A, chapter 3 and side B, chapter 1-4. Session 3: Solve equations from side B, the students can work with worksheet 1 on paper Work method: 3 sessions (3 hours). In the third session, the students will start solving equations on paper and they can begin with worksheet 1 in class. The second worksheet should be completed. Goal Rules Chapters side A Levels Additive and inverse identity property 1 1 to 8 Additive property of equality 1 9 to 20 Multiplicative inverse and identity property 2 1 to 10 Basic equation solving skills Division property of equality 2 11 to 20 Shortcut 3 1 to 6 Multiplication property of identity 3 7 to 20

6 How to use Dragonbox Algebra 12+ in home school 5 Session 1 and 2: Length about 2 hours. The student works as described on page 3. Session 3: For the third session, the teacher and student solve a linear equation from side B in the game, explaining the strategies as he/she plays. They then solve tha same equation using pencil and paper. After solving the equation on paper, go back to the game and show the same level again. The students will learn to relate what they do in the game to solving equations on paper. The students could then start with the worksheets. Tips: When solving the equation on the chalkboard, write the equations with some space so that it is possible to draw the frames of cards around each element. At first, the equation will look like very difficult to many children, but by drawing the frames of the cards, students will easily relate the equations to the game. The teacher can then solve the equation as in the game, writing a new line for each change. Important: the students use good strategies and remind them of the goal or on paper and discuss with the student Encourage the student to get as many stars as possible in order to find the best solution for each equation.

7 How to use Dragonbox Algebra 12+ in home school 6 Part 2: Number factoring and signs Goal: Students will understand factoring, addition and multiplication in the game, as well as the rules for signs. Rules: For a description of the underlying rules for part 2, se the Rules of Algebra sheet. It is important that the teacher encourages the students to explain the rules and strategies in their own words. What to play in DragonBox: Session 1 and 2: side A, chapter 4-5 and side B, chapter 5. Work method: : Part 2 can be split into 2 sessions of 1 school hour. The student should have pen and paper ready to be able to note down the different strategies or rules as they play. Worksheet 3 should be completed. Goal Rules Chapters side A Levels Factoring and addition/ multiplication Addition 4 1 to 3 Factoring 4 4 to 7 Multiplication 4 8 to 20 Signs Properties of negation Rules of signs for fractions 5 1 to 20 Session 1 and 2: The student works with the game as described on page 3. As new rules are introduced, the teacher should help the student describe these rules with words. The students can start working with worksheet 3 in the last part of session 2. Important: Some students may forget the goal of the game and try to simplify the wrong side of the equation first. Make sure the students use good strategies and remind them of the goal It is important that the students understands the rules so far. If something is unclear, solve equations in the game or on paper. For part 2 it is important that the student understand the principles of factoring. The teacher could at this point show some examples of numbers that could be factorized. It is important that they understand that we factorize numbers in fractions to simplify them. Be aware that the students can be confused by the many different rules of signs and by the difference between the minus operator and the minus sign. Encourage the student to get as many stars as possible in order to find the best solution for each equation

8 How to use Dragonbox Algebra 12+ in home school 7 Part 3: Parenthesis and distributive properties Goal: Students will work with parentheses, learn when they can remove them and they will learn the distributive properties for solving equations Rules: For a description of the underlying rules for part 3, se the Rules of Algebra sheet. It is important that the teacher encourages the students to explain the rules and strategies in their own words. What to play in DragonBox: Session 1 and 2: chapter 6 on side A and B. Work method: Part 3 can be split into 2 sessionsof 1 hour. The student should have pen and paper ready to be able to note down the different strategies or rules as they play. Worksheet 4 should be completed. Goal Rules Chapters side A Levels Parenthesis 6 1 to 4 Parenthesis Distributive property I 6 5 to 6 Distributive property II 6 7 to 20 Session 1 and 2: The student works with the game as described on page 3. As new rules are introduced, the teacher should help the students describe these rules with words. The students can start working with worksheet 4 in the last part of session 2. Important: Some students may forget the goal of the game and try to simplify the wrong side of the equation first. Make sure the student uses good strategies and remind them of the goal It is important that the students understand the rules so far. If something is unclear, solve equations in the game or on the board and discuss with the students. For part 3 it is important that the students understand the principles for parenthesis and distributive properties. The teacher could explain in more detail the stategies for multiplication and parenthesis Encourage the student to get as many stars as possible in order to find the best solution for each equation

9 How to use Dragonbox Algebra 12+ in home school 8 Part 4: Factoring Goal: Students will play with factoring and simplifying fractions. In addition it is important that the students understand and practice the strategies for parenthesis. Rules: For a description of the underlying rules for part 4, se the Rules of Algebra sheet. It is important that the teacher encourages the students to explain the rules and strategies in their own words. What to play in DragonBox: Session 1 and 2: chapter 7 on side A and chapter 7-9 on side B. Work method: Part 4 can be split into 2 sessions of 1 school hour. The student should have pen and paper ready to be able to note down the different strategies or rules as they play. Goal Rules Chapters side A Levels Factoring I 7 1 to 4 Factoring Creating parenthesis 7 5 to 9 Factoring II 7 10 to 13 Fractions 7 14 to 20 Session 1 and 2: The students work with the game as described on page 3. Remember to take a small break after the individual sessions. As new rules are introduced, the teacher should help the students describe these rules with words. In the second session, the students can work with the levels on side B. Important: Some students may forget the goal of the game and try to simplify the wrong side of the equation/board first. Make sure the students use good strategies and remind them of the goal It is important that the students understand the rules so far. If something is unclear, solve equations in the game or on the board and discuss with the students. Some students struggle to understand that the distributive property applies to all terms in a parenthesis and with the priority parenthesis rule and when they can remove the parentheses. Encourage the students to get as many stars as possible in order to find the best solution for each equation

10 How to use Dragonbox Algebra 12+ in home school 9 Part 5: Addition of like terms Goal: Students will learn how to add like terms. Rules: For a description of the underlying rules for part 5, se the Rules of Algebra sheet. It is important that the teacher encourages the students to explain the rules and strategies in their own words. What to play in DragonBox: Session 1: chapter 8 on side A and B Work method: Part 5 can be completed in 1 school hour. The student should have pen and paper ready to be able to note down the different strategies or rules as they play. Goal Addition of like terms Rules Chapter side A Levels Strategies for addition of like terms 8 1 to 20 Session 1: The student works with the game as described on page 3. As new rules are introduced, the teacher should help the students describe these rules with words. For part 5, the teacher should introduce the new rules first with some simple examples before they start playing, in addition to relating this to the use of the box in the game to gather cards. After they have played for about 15 minutes, there should be a group session where the teacher or students solve some levels and equations on paper. Important: Some students may forget the goal of the game and try to simplify the wrong side of the equation first. Make sure the student uses good strategies and remind them of the goal It is important that the students understand the rules so far. If something is unclear, this could be discussed while solving levels in the game or equations on paper. For part 5, it is important the the students understand the principles for addition of like terms (both simple and more complex examples). The teacher should remind the students of the strategies used earlier in the game and to put all of this together for more advanced equations and game levels. Encourage the student to get as many stars as possible in order to find the best solution for each equation

11 How to use Dragonbox Algebra 12+ in home school 10 Part 6: Substitution Goal: Students will create parameters to be able to solve literal equations that require factoring expressions Rules: For a description of the underlying rules for part 6, se the Rules of Algebra sheet. It is important that the teacher encourages the students to explain the rules and strategies in their own words. What to play in DragonBox: Session 1: chapters 9 and 10 on side A Session 2: chapter 10 on side B Work method: Part 6 can be split into 2 sessions of 1 hour each. The student should have pen and paper ready to be able to note down the different strategies or rules as they play. The last worksheet should be completed. Goal Rules Chapter side A Levels Substitution Substitution (creating parameters) 9 to 10 1 to 20 Session 1 and 2: The student works with the game as described on page 3. Remember to take a small break after the individual sessions. As new rules are introduced, the teacher should help the students describe these rules with words. The students can start working with the worksheet in the last part of session 2. Important: Some students may forget the goal of the game and try to simplify the wrong side of the equation first. Make sure the students use good strategies and remind them of the goal It is important that the students understand the rules so far. If something is unclear, this could be discussed while solving levels in the game or equations on paper. For part 6, it is important the the students understand the principles for solving equations with x i the denominator. At this point, the students have learned many different rules and strategies for solving equations.

12 How to use Dragonbox Algebra 12+ in home school 11 From playing the game to solving equations on paper In the last hour of part 1, you can show your child on paper how the strategies and rules learned in the game relate to solving equations on paper. Here are some tips on how you can do this: Take out some examples from side B and solve the same equations on paper When writing the equations on paper, make enough space between each element in order to draw squares around them to resemble the cards in the game. In that way, the students would be able toassociate between the strategies used in the games and equations on paper Solve the equations specifying the strategies and rules from the game. Use one new line for each change in the equation. stress that operations have to be made on both sides of the equation. Let your child solve equations on paper. They will commit errors, like not balancing the equation, but after two or three mistakes, they will remember it.