数学の仲間たち: 兄弟や友達と一緒に探検、実験、遊びましょう

**This is a self-scheduled class.  To sign up your learner(s) please click on "Show Alternative Times", and there you can select a date and time that work for your family.  

One-on-one tutoring gives learners individualized instruction catered to all of their needs.  It's almost perfect, but missing one really beneficial component: collaborating with peers.  

According to Jo Boaler, a great inspiration of mine, collaborating with peers helps with the following: 
-Reasoning - Can you convince someone else you are right, even if they disagree with you?
-Questioning - Approach data with skepticism; challenge why and how it works
-Engagement - Students are more engaged with games and activities they can do with their peers than adults.  
  (Despite my feeble attempts to NOT be boring, I am still, regrettably, an adult)
 
In short, learners can have more fun and deepen their conceptual understanding of math ideas when they work together.

This class was originally created for siblings that I tutor to be able to get together and reinforce key ideas, but it is open to any sibling or friend group that would like to do the same.  

The minimum class size is 2 for this class.  If you are interested, but cannot find an appropriate partner for your child, please reach out to me, and I can then communicate with other families that may be a good match. 

Typical 5th grade topics: 

-Writing & Interpreting numerical expressions
-Analyzing Patterns and Relationships
-Understanding the Place Value System
-Performing operations with multi-digit whole numbers and with decimals to hundredths
-Using equivalent fractions as a strategy to add and subtract fractions
-Applying and extending previous understandings of multiplication and division to multiply and divide fractions
-Convert like measurement units within a given measurement system
-Represent and interpret data
-Understanding concepts of volume and relate volume to multiplication and division
-Graph points on the coordinate plane to solve real-world mathematical problems. 
-Classify two-dimensional figures into categories based on their properties. 

Typical 6th grade topics: 
-Understanding Ratio concepts and use ratio reasoning to solve problems
-Apply and extend previous understandings of multiplication and division to divide fractions by fractions
-Compute fluently with multi-digit numbers and find common factors and multiples 
-Apply and extend previous understandings of numbers to the system of rational numbers
-Represent and analyze quantitative relationships between dependent and independent variables.
-Solve real-world and mathematical problems involving area, surface area, and volume.
-Develop understanding of statistical variability.
-Summarize and describe distributions.

Typical 7th grade topics: 
-Analyze proportional relationships and use them to solve real-world and mathematical problems.
-Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
-Use properties of operations to generate equivalent expressions.
-Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
-Draw, construct, and describe geometrical figures and describe the relationships between them.
-Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
-Use random sampling to draw inferences about a population.
-Draw informal comparative inferences about two populations.
-Investigate chance processes and develop, use, and evaluate probability models.

Typical 8th grade topics: 
-Know that there are numbers that are not rational, and approximate them by rational numbers.
-Work with radicals and integer exponents.
-Understand the connections between proportional relationships, lines, and linear equations.
-Analyze and solve linear equations and pairs of simultaneous linear equations.
-Define, evaluate, and compare functions.
-Use functions to model relationships between quantities.
-Understand congruence and similarity using physical models, transparencies, or geometry software.
-Understand and apply the Pythagorean Theorem.
-Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
-Investigate patterns of association in bivariate data.


**The weekly schedule will vary based on the individual needs of the students.  This is, essentially, a group tutoring class.