NUMBER AND OPERATIONS

Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will apply these concepts and associated skills in real world situations.

M6N1. Students will understand the meaning of the four arithmetic operations as

related to positive rational numbers and will use these concepts to solve

problems*.*a. Apply factors and multiples.

b. Decompose numbers into their prime factorization (Fundamental Theorem of

Arithmetic).

c. Determine the greatest common factor (GCF) and the least common multiple

(LCM) for a set of numbers.

d. Add and subtract fractions and mixed numbers with unlike denominators.

e. Multiply and divide fractions and mixed numbers.

f. Use fractions, decimals, and percents interchangeably.

g. Solve problems involving fractions, decimals, and percents.

MEASUREMENT

Students will understand how to determine the volume and surface area of solid figures.

They will understand and use the customary and metric systems of measurement to measure quantities efficiently and to represent volume and surface area appropriately.

M6M1. Students will convert from one unit to another within one system of

measurement (customary or metric) by using proportional relationships.

M6M2. Students will use appropriate units of measure for finding length, perimeter,

area and volume and will express each quantity using the appropriate unit.

a. Measure length to the nearest half, fourth, eighth and sixteenth of an inch.

b. Select and use units of appropriate size and type to measure length, perimeter,

area and volume.

c. Compare and contrast units of measure for perimeter, area, and volume.

M6M3. Students will determine the volume of fundamental solid figures (right

rectangular prisms, cylinders, pyramids and cones).

a. Determine the formula for finding the volume of fundamental solid figures.

b. Compute the volumes of fundamental solid figures**,**using appropriate unitsof measure.

c. Estimate the volumes of simple geometric solids.

d. Solve application problems involving the volume of fundamental solid figures.

M6M4. Students will determine the surface area of solid figures (right rectangular

prisms and cylinders).

a. Find the surface area of right rectangular prisms and cylinders using

manipulatives and constructing nets.

b. Compute the surface area of right rectangular prisms and cylinders using

formulae.

c. Estimate the surface areas of simple geometric solids.

d. Solve application problems involving surface area of right rectangular prisms

and cylinders.

GEOMETRY

Students will further develop their understanding of plane and solid geometric figures, incorporating the use of appropriate technology and using this knowledge to solve authentic problems.

M6G1. Students will further develop their understanding of plane figures.

a. Determine and use lines of symmetry.

b. Investigate rotational symmetry, including degree of rotation.

c. Use the concepts of ratio, proportion and scale factor to demonstrate the relationships between

similar plane figures.

d. Interpret and sketch simple scale drawings.

e. Solve problems involving scale drawings.

M6G2. Students will further develop their understanding of solid figures.

a. Compare and contrast right prisms and pyramids.

b. Compare and contrast cylinders and cones.

c. Interpret and sketch front, back, top, bottom and side views of solid figures.

d. Construct nets for prisms, cylinders, pyramids, and cones.

ALGEBRA

Students will investigate relationships between two quantities. They will write and solve proportions and simple one-step equations that result from problem situations.

M6A1. Students will understand the concept of ratio and use it to represent

quantitative relationships.

M6A2. Students will consider relationships between varying quantities.

a. Analyze and describe patterns arising from mathematical rules, tables, and

graphs.

b. Use manipulatives or draw pictures to solve problems involving proportional

relationships.

c. Use proportions (a/b=c/d) to describe relationships and solve problems,

including percent problems.

d. Describe proportional relationships mathematically using y = kx, where k is

the constant of proportionality.

e. Graph proportional relationships in the form y = kx and describe

characteristics of the graphs.

f. In a proportional relationship expressed as y = kx, solve for one quantity given

values of the other two. Given quantities may be whole numbers, decimals, or

fractions. Solve problems using the relationship y = kx.

g. Use proportional reasoning (a/b=c/d and y = kx) to solve problems.

M6A3. Students will evaluate algebraic expressions, including those with exponents,

and solve simple one-step equations using each of the four basic operations.

__DATA ANALYSIS AND PROBABILITY __

Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. They will represent, investigate, and use data to answer those questions. Students will understand experimental and theoretical probability.

M6D1. Students will pose questions, collect data, represent and analyze the data,

and interpret results.

a. Formulate questions that can be answered by data. Students should collect data

by using samples from a larger population (surveys), or by conducting

experiments.

b. Using data, construct frequency distributions, frequency tables, and graphs.

c. Choose appropriate graphs to be consistent with the nature of the data

(categorical or numerical). Graphs should include pictographs, histograms, bar

graphs, line graphs, circle graphs, and line plots.

d. Use tables and graphs to examine variation that occurs within a group and

variation that occurs between groups.

e. Relate the data analysis to the context of the questions posed.

M6D2. Students will use experimental and simple theoretical probability and

understand the nature of sampling. They will also make predictions from

investigations.

a. Predict the probability of a given event through trials/simulations

(experimental probability), and represent the probability as a ratio.

b. Determine, and use a ratio to represent, the theoretical probability of a given

event.

c. Discover that experimental probability approaches theoretical probability when

the number of trials is large.

** **__Process Standards __

Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.

M6P1. Students will solve problems (using appropriate technology).

a. Build new mathematical knowledge through problem solving.

b. Solve problems that arise in mathematics and in other contexts.

c. Apply and adapt a variety of appropriate strategies to solve problems.

d. Monitor and reflect on the process of mathematical problem solving.

M6P2. Students will reason and evaluate mathematical arguments.

a. Recognize reasoning and proof as fundamental aspects of mathematics.

b. Make and investigate mathematical conjectures.

c. Develop and evaluate mathematical arguments and proofs.

d. Select and use various types of reasoning and methods of proof.

M6P3. Students will communicate mathematically.

a. Organize and consolidate their mathematical thinking through communication.

b. Communicate their mathematical thinking coherently and clearly to peers,

teachers, and others.

c. Analyze and evaluate the mathematical thinking and strategies of others.

d. Use the language of mathematics to express mathematical ideas precisely.

M6P4. Students will make connections among mathematical ideas and to other

disciplines.

a. Recognize and use connections among mathematical ideas.

b. Understand how mathematical ideas interconnect and build on one another to

produce a coherent whole.

c. Recognize and apply mathematics in contexts outside of mathematics.

M6P5. Students will represent mathematics in multiple ways.

a. Create and use representations to organize, record, and communicate

mathematical ideas.

b. Select, apply, and translate among mathematical representations to solve

problems.

c. Use representations to model and interpret physical, social, and mathematical

phenomena.

MRC. Students will enhance reading in all curriculum areas by:

a. Reading in All Curriculum Areas

• Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas

• Read both informational and fictional texts in a variety of genres and modes of discourse

• Read technical texts related to various subject areas

b. Discussing books

• Discuss messages and themes from books in all subject areas.

• Respond to a variety of texts in multiple modes of discourse.

• Relate messages and themes from one subject area to messages and themes in another area.

• Evaluate the merit of texts in every subject discipline.

Reading Standard Comment

After the elementary years, students are seriously engaged in reading for learning. This process sweeps across all disciplinary domains, extending even to the area of personal learning. Students encounter a variety of informational as well as fictional texts, and they experience text in all genres and modes of discourse. In the study of various disciplines of learning (language arts, mathematics, science, social studies), students must learn through reading the communities of discourse of each of those disciplines. Each subject has its own specific vocabulary, and for students to excel in all subjects, they must learn the specific vocabulary of those subject areas *in context. *

Beginning with the middle grades years, students begin to self-select reading materials based on personal interests established through classroom learning. Students become curious about science, mathematics, history, and literature as they form contexts for those subjects related to their personal and classroom experiences. As students explore academic areas through reading, they develop favorite subjects and become confident in their verbal discourse about those subjects.

Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.