# Educating for learners in today’s world

Within a society whose structures are largely mathematical it is important that citizens be educated in the methods of mathematics: first in terms of general numeracy but also in terms of understanding mathematics as a discipline which has formatting power in society.

Teaching students to identify and pose problems, to explain themselves in terms others can understand and to question the invisible structures of mathematics is key to developing informed, active and critical learners.

Mathematics has a role in learners education because it has the potential to help us understand our society and our role in shaping it.

Fifth grade is a milestone and a pivot point for students. The classroom focus on arithmetic during the elementary grades will develop into a more formal study of algebra in middle school. To be ready for algebra, students must have an understanding of fractional arithmetic, in part because even simple equations cannot be solved without fractions. Because of this, whole-number arithmetic comes mostly to a close in 5th grade, while multiplying and dividing fractions becomes a major focus. In Grade 5, instructional time should focus on three critical areas:

• Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions).

• Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.

• Developing understanding of volume.

The skills and understanding that your child will gain during 6th grade are among the most important foundations for college and career readiness. These include working with ratios and rates and working with variables and variable expressions — the building blocks of algebra. Many of this year’s topics will remain a major emphasis throughout the middle school years and into high school.

• Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems

• Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers

• Writing, interpreting, and using expressions and equations

• Developing understanding of statistical thinking.

In 7th grade, your child will grow in skill and understanding as he or she continues the previous grade’s work in proportional relationships, equations, and positive and negative numbers. These topics will remain a major emphasis throughout the middle school years and into high school. A good command of rates and proportional relationships, including percentages, is also an important life skill.

• Developing understanding of and applying proportional relationships

• Developing understanding of operations with rational numbers and working with expressions and linear equations

• Solving problems involving scale drawings and informal geometric constructions, and working with twoand three-dimensional shapes to solve problems involving area, surface area, and volume

In 8th grade, your child will learn a number of skills and ideas that he or she must know and understand to be ready for college and career. Your child will continue to learn how to write and reason with algebraic expressions. Your child also will make a thorough study of linear equations with one and two variables. Building on previous work with relationships between quantities, your child will be introduced to the idea of a mathematical function. And your child will prepare for high school geometry by understanding congruence (same shape and size) and similarity of geometric figures.

• Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations

• Grasping the concept of a function and using functions to describe quantitative relationships

• Analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.