District 196 Curriculum

Middle School Math (Grade 6)

Student Learnings: What students should know and be able to do

Mathematical Reasoning Standard

Apply skills of mathematical representation, communication and reasoning throughout the remaining four content strands.
Assess the reasonableness of a solution by comparing the solution to appropriate graphical or numerical estimates or by recognizing the feasibility of a solution in a given context.
Appropriately use examples and counterexamples to make and test conjectures, justify solutions and explain results.
Translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context.
Support mathematical results by explaining why the steps in a solution are valid and why a particular solution method is appropriate.
Determine whether or not relevant information is missing from a problem.
Use accurately common logical words and phrases such as “and,” “or,” “if … then …,” “unique,” “only if.”

Number Sense Standard

Use positive and negative rational numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.
Find, represent and use percentages in real-world and mathematical problems, including percentages greater than 100% and less than 1%.
Use the relationship between moving the decimal point and the operations of multiplication or division by powers of ten to simplify calculations.
Determine the prime factorization of positive integers.
Order and compare integers, fractions, decimals and mixed numbers with >, < and =.
Locate and compare positive and negative rational numbers on a number line.

Computation and Operation Standard

Compute fluently and make reasonable estimates with positive and negative rational numbers in real-world and mathematical problems.
Understand the meanings of arithmetic operations and factorization, and how they relate to one another.
Appropriately use calculators and other technologies to solve problems.
Apply the correct order of operations and grouping symbols when using calculators and other technologies.
Use addition, subtraction, multiplication and division of multi-digit whole and decimal numbers to solve multi-step real-world and mathematical problems.
Multiply and divide, without a calculator, numbers containing up to three digits by numbers containing up to two digits, such as 347 / 83 or 4.91 x 9.2.
Add, subtract, multiply and divide common fractions and mixed numbers as well as fractions where the common denominator equals one of the denominators.
Apply the correct order of operations including addition, subtraction, multiplication, division and grouping symbols to simplify and evaluate numeric expressions.
Use rounding and estimation with integers, decimals and fractions to solve real-world and mathematical problems.

Algebra (Algebraic Thinking) Standard

Apply arithmetic operations in the correct order to simplify and evaluate numeric expressions in real-world and mathematical problems.

Measurement Standard

Make calculations of time, length, area and volume within standard measuring systems, using good judgment in choice of units.
Solve problems requiring conversion of units within the U.S. customary system and within the metric system.
Find the area and perimeter of rectangles, squares, triangles and parallelograms by measuring, using a grid or using a formula.
Express measures of time and distance as fractions, mixed numbers and decimals to solve real-world and mathematical problems.
Measure, identify and draw perpendicular and parallel lines, angles and rectangles by using appropriate tools such as straightedge, ruler, compass, protractor or software.

Spatial Sense Standard

Recognize the relationship between different representations of two- and three-dimensional shapes. Understand the effect of various transformations.

Geometry Standard

Identify a variety of simple geometric figures by name, calculate various quantities associated with them and use appropriate tools to draw them.
Use facts about angles including the relationship between complementary angles, supplementary angles and the angles within triangles to solve real-world and mathematical problems.
Classify triangles as equilateral, isosceles or scalene, and the right, acute or obtuse.

Patterns and Functions Standard

Demonstrate understanding of the rectangular coordinate system.
Demonstrate understanding of the four quadrants in a rectangular coordinate system by writing and plotting ordered pairs.
Predict the position and orientation of simple geometric shapes under transformations such as reflections, rotations and translations.
Identify symmetries in three-dimensional shapes.
Create models of three-dimensional geometric shapes from two-dimensional representations.

Data and Statistics Standard

Represent data and use various measures associated with data to draw conclusions and identify trends.
Understand the differences and appropriate use of mean, median and mode.
Find the median and possible outliers.
Collect, organize and represent categorical and numerical data with tables and bar graphs.

Probability Standard

Calculate and express probabilities numerically, and apply probability concepts to solve real-world and mathematical problems.
Generate and display data in graphs and tables to estimate experimental probabilities.
Represent all possible outcomes for a probability problem with tables, grids and tree diagrams to calculate probabilities and draw conclusions from the results.

Instructional resources used for this curriculum:

Copyright 2004, Holt Rinehart Winston Publishing
Middle School Mathematics, Course 1