- Adults and students work together to complete modules—at school, at home, or both.
- Students check in regularly. When their Practice Meter for a lesson is in the red, they should complete one or more modules in that lesson to get their Practice Meter to blue (or at least out of red).
- Adults check in 1 day, 1 week, and 1 month after first going through a lesson module and require that all practice levels be out of the red or in the blue on that day. End-of-module certficates are stamped at time of completion with the date and the Practice Meter level, if e-mailing certificates is something in the works in your class.
- PLEASE read the recommendations for adults at the end of this post.

First things first: click below to install the application. When you start the application each time, you start at the homepage, which shows all 15 lessons for Grade 6 (or all 16 lessons for Grades 7–8).

After you have completed at least one module in one of the lessons, this will activate your Practice Meter (explained below) for that lesson, and you will see a meter level to the right of the lesson on the homepage. This will allow you to, at a glance, see what concepts need your attention. Above, you can see that I've completed at least one module in the Ratio Names lesson (a green bar is shown to the right of the lesson). The Instructor Notes link at the bottom right allows you the ability to download the complete PDF of all the Instructor Notes for the grade level(s).

Lesson Structure

Click on one of the lessons to be taken to the lesson homepage. Every lesson (with the exception of Plotting Ratios) in Grade 6 contains five modules. At the right, the lesson homepage for Ratio Names is shown. Notice the green Practice Meter level in the center icon. This mirrors the level shown on the main home page. Hover over this icon to see the numeric Practice Meter level (the one shown is at 36 currently).

Notice also the Home button in the bottom right corner of the lesson homepage. This can be found on all lesson homepages and will take you back to the main home page.

The 3 main modules, located in the center quad-panel are numbered 1 to 3 (Algebraic Expressions shown at right). The fourth square in the quad-panel is a link to the Instructor Notes for the lesson. Click on that to download a PDF of these notes.

The modules do not necessarily have to completed in any particular order. However, completing them in the order given is recommended.

Adult Interaction Is a Must

Each of the first modules in every lesson is labeled with Guided Practice (Equations and Inequalities shown at left). This means that if it is used in a classroom, it should be used as an activity centerpiece involving teachers and students. If it is used at home, the first module in particular should be the focus of both parent(s) and student.

The Instructor Notes provide an outline for interactive teaching and learning discussions with this material. It is recommended that every module—when first completed—be done together with adult and student.

To use Guzinta Math at home, a teacher may assign a module for homework or practice. Parent and student then discuss and complete the module together and, if it is requested, return the student to school the next day with the completion certificate or email it. (Parents can follow the Instructor Notes for each module as well.) The material can be used also at school or solely at school. In that case, different modules can be completed as a class and others may be assigned for homework. It is not the case that adults should be doing all or even most of the work during these interactions, but they should attend to them, rather than plop students down in front of a monitor to complete these activities alone.

Practice Meter

At 25 and below, the Practice Meter color is red. Between 26 and 79, the color is green. And, a level of 80 or above makes the color blue. Once a module has been completed—either at school with a teacher or at home with a parent or caregiver, the time is recorded for that lesson, along with the Practice Meter level. As time passes, the Practice Meter level decreases to represent a forgetting of the content.

In the first 7 days, the meter decreases at a rate of about 54% each day. That is, it loses a little more than half its value each day. The Practice Meter level of 36 (green) mentioned above would be about 16 or 17 (red) a day later, if no work is done in the lesson. From 7 days to 28 days, the meter only loses about 17% of its value each day. From 28 to 90 days, only 6% is lost each day. And from 90 days on, only 1% is lost each day.

The purpose of the Practice Meter is to provide a visual indication of forgetting and to alert students, teachers, and parents when it is time to revisit a lesson. Forgetting is very useful for learning, so it is important to allow time for the Practice Meter level to decrease before recharging it. A good schedule to keep would be to use a module together as a class or with parents and students as homework and then check in 1 day, then 1 week, and then each month after this first start. Have students get their meters out of the red or in the blue, at least for these check-ins. The goal is to keep this content alive throughout the year—yes, even if students are repeating the same questions. Repetition is excellent for novice learners!

Time-Released Practice Questions

Because the application timestamps the beginning of a student's work in a lesson, this allows it to reveal new practice questions over time. The table below shows the number of questions (excluding Module 0) asked in each lesson of Grade 6, starting on Day 1 and then the extra questions revealed on Days 4, 9, and 22. These days are measured separately for each lesson, and the timer doesn't start until after adults and students together complete at least one module in the lesson.

Lesson | Day 1 | Day 4+ | Day 9+ | Day 22+ |
---|---|---|---|---|

Ratio Names | 31 | +5 | +8 | +6 |

Ratio Tables | 28 | +10 | +7 | +5 |

Comparing Ratios | 45 | +0 | +0 | +0 |

Plotting Ratios | 12 | +0 | +0 | +0 |

Measurement Conversions | 26 | +6 | +12 | +6 |

Fraction by Fraction Division | 28 | +6 | +12 | +4 |

Long Division | 22 | +6 | +10 | +6 |

GCF and LCM | 33 | +6 | +6 | +5 |

Negative Numbers | 31 | +0 | +0 | +0 |

Quadrants in the Plane | 31 | +7 | +6 | +6 |

Order and Absolute Value | 34 | +7 | +6 | +3 |

Numeric Expressions | 28 | +8 | +8 | +6 |

Algebraic Expressions | 46 | +0 | +0 | +0 |

Equations and Inequalities | 29 | +0 | +0 | +0 |

Across the entire Grade 6, students have 424 practice questions on Day 1. Then, over time, this number grows to 651 total practice questions. The zeros in the table show 5 lessons which do not time-release new questions over time (at the moment). The other 10 lessons do.

There are a few reasons for time-releasing new questions: (1) This ratchets up the challenge level for a lesson. The answers for questions revealed on and after Day 4 are not included in the Instructor's Notes. And, more questions in a lesson means that it becomes slightly more difficult to raise one's practice meter up to any given level (though the difficulty increase is very minor in most cases). (2) It helps break the repetition a little. (3) Transfer is facilitated when students revisit a previously learned topic in a slightly new context.

Contact and Future Work

I've written here about work on Guzinta Math that I'll be getting to in the near and farther future. If you have any questions or technical issues, please email me at qanda[at]guzintamath.com.

Some Polite Suggestions

Here are some recommendations for how to think and behave around this material.

- Ideally, provide guidance in one form or another on EVERY module the first time students go through it. The Instructor Notes provide the answers and some guiding questions for adults for the original practice questions (not the time-released ones). Use those notes to help you guide students. Guidance doesn't mean you are perched on top of their shoulder, making sure they don't get anything wrong.
- Take. Your. Time. Students should live with this content—revisiting it regularly to maintain their Practice Meter levels—throughout the entire year. They don't need to "get through" the content fast.
- It's possible to revisit the same module of a lesson every time to raise one's Practice Meter level. That's okay! But encourage students to complete other modules over time as well.
- Forget whatever label you've assigned to your student. "Quick learner"? They still need to work through and revisit this material throughout the year, just like everyone else. Revisiting deepens their understanding and often reveals patches of misunderstanding—where they learned to play the game well but don't really get it. "Slow learner"? They should be challenged and given high expectations like other students. Again, revisiting over the entire year is key.
- If your student has memorized the answers to questions, that's fine, at least once. That's a good cue to let that module sit and allow forgetting to set in for a while and do other things. Also, if you suspect that a student is moving through stuff without thinking, that's a clue to SIT DOWN WITH THEM AGAIN and work together. Watch the videos again and discuss. Have them explain things to you. Read the Notes. Have them generalize. Work through the exploratory module even when it doesn't have questions to answer. In short, make them think and elaborate when otherwise they wouldn't.
- After a while, the bulk of a student's time with the app will be revisiting already completed lessons. This is the reason for the time-released questions—to help keep students on their toes a little. But, a great idea for revisiting lessons is to have students teach you the content that they're going over. Take notes and ask questions, and make them explain the worked examples and videos and questions!