District Curriculum Overview

Subject: Mathematics Grade Level: Sixth Grade

Concepts/Enduring Understanding/Themes	Topics/Units	Content/Skills	Essential Activities/Agreements
Number Sense and Operations Patterns, Relations, and Algebra Geometry Measurement Data Analysis, Statistics, and Probability	Connected Math (CMP) units: --Prime Time --Bits & Pieces I --Bits & Pieces II Hands On Algebra Scott Foresman Addition Wesley (SFAW) text, Selected Lessons in Chapter 1, 2, 3, 4, 5, 7, 8 Hands On Algebra (with support from selected lessons in SFAW , Chap. 8 &12 and CMP units Connected Math unit: --Shapes & Designs --Covering and Surrounding SFAW Chap. 9 Connected Math unit: --Shapes & Designs -Covering/Surrounding SFAW Chap. 10 Connected Math unit: --Data About Us --How Likely Is It? SFAW Chap. 11	*Represent and compare positive numbers to billions and thousandths in various forms using concrete models, expanded notation for whole numbers without exponents; and word form. *Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line. *Apply number theory concepts – including prime and composite numbers, common factor, common multiple and divisibility rules for 2, 3, 5 and 10. *Demonstrate an understanding of the properties of arithmetic operations: the commutative, associative, distributive, identity, and zero properties of operations on whole numbers, fractions and decimals. *Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ÷) *Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals. *Accurately and efficiently add, subtract, multiply, and divide positive fractions and mixed numbers. Simplify fractions. *Add and subtract integers, with the exception of subtracting negative integers. *Create, analyze and determine the rules for extending, symbolic, arithmetic, and geometric patterns and progressions, (e.g. ABBCCC; 1,5,9,13…; 3,9,27,…. ). *Use physical models to investigate and describe how change in one variable relates to change in a second variable, (e.g., doubling problems, flat rates, etc.). *Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant. *Graph points and identify coordinates of points on the Cartesian coordinate plane, *Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions, e.g. translations, rotations, and reflections. Investigate tessellations and tilings. *Match three-dimensional objects and their two-dimensional representations objects, (e.g., nets, projections and perspective drawings). *Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area (e.g. d = 2r; p = C/d), and use the concepts to solve problems. *Find volumes and surface areas of rectangular prisms. *Find the sum of the angles in simple polygons (up to eight sides) with/without measuring the angles. *Use tree diagrams and other models, (e.g. lists and tables) to represent possible or actual outcomes of trials. Analyze the results. *Predict the probability of outcomes of simple experiments, (e.g. using coins, number cubes (dice), spinners, and counters) and test the predictions. Use the appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with he likelihood of the event.	The mathematics period in the sixth grade classroom should be at least 60-80 minutes long each day. This period may be broken down into time for the general lesson (45-50) minutes and 15-30 minutes each day for individual and small group extension, reinforcement, and re-teaching. Teachers will also need to select activities and suggestions in the MCAS Preparation Section (pages T36-T47) in Volume 1 of the SFAW Teachers’ Manual. [Note: A decision will need to be made about incorporating the Connected Math-Revised Program. In particular, there is now a Bits & Pieces III for the sixth grade.]