Grades 9–10 MCAS Objectives

Mathematics Curriculum Framework (Massachusetts Department of Elementary & Secondary Education)

MCAS stands for
* Massachusetts Comprehensive Assessment System*.

As required by the Massachusetts Education Reform Act of 1993,

students must pass the grade 10 MCAS tests in English Language Arts and Mathematics

as one condition of eligibility for a high school diploma (in addition to fulfilling local requirements).

In addition, the MCAS program is used to hold Massachusetts schools and districts accountable, on a yearly basis,

for the progress they have made toward the objective of the
No Child Left Behind Act

that all students be proficient in Reading and Mathematics by 2014.

MCAS tests measure how well students have learned the academic
standards outlined in the
Massachusetts Curriculum Frameworks.

All Massachusetts public school students take MCAS tests: each year in grades 3 through 8, and at least once in high school (usually grade 10).

This page lists the Learning Standards that form the basis
for MCAS, and then provides links to my web exercises covering the material.

Of course, concepts are often covered in many different exercises; I have tried to provide the most relevant links.

Five strands organize the MCAS mathematics content:

**N**umber Sense and Operations**P**atterns, Relations, and Algebra**G**eometry**M**easurement**D**ata Analysis, Statistics, and Probability

Each learning standard has a unique identifier (like 8.N.2) that consists of:

- the grade level (
**8**.N.2) - the strand (8.
**N**.2) - the standard number (8.N.
**2**)

For example, 8.N.2 is a **8**^{th} grade standard in the ‘**N**umber Sense and
Operations’ strand, and it is the **2**^{nd} standard in this strand.

The learning standards specify what students should know at **the end** of each grade span.

Students are held responsible for learning standards listed at earlier grade spans as well as their current
grade span.

The LINKS TO FISHER SITE (right column, below) often provide a higher level of understanding than that required for
the MCAS grades 7-8 test.

However, these exercises can be used as a reference by teachers.

Also, these links illustrate that grade 7-8 MCAS objectives are being reviewed and developed in the high school curriculum,

thus preparing students for the MCAS test in grade 10.

MCAS LEARNING STANDARDS |
LINKS TO FISHER SITE | |

GRADES 7–8 LEARNING STANDARDS | ||

NUMBER SENSE AND OPERATIONS | ||

8.N.1 | Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents. |
deciding if a number is a whole number, an integer, etc. changing decimals to fractions changing decimals to percents changing percents to decimals writing fractions in simplest form rewriting fractions as a whole number plus a fraction |

8.N.2 | Define, compare, order, and apply frequently used irrational numbers, such as $\,\sqrt{2}\,$ and $\,\pi\,$. |
deciding if a fraction is a finite or infinite repeating decimal deciding if numbers are equal or approximately equal locating fractions on a number line |

8.N.3 | Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change. |
♥ Similarity, Ratios, and Proportions |

8.N.4 | Represent numbers in scientific notation, and use them in calculations and problem situations. |
scientific notation |

8.N.5 | Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems. |
Adding Fractions (This is the pdf file for Section 13, Adding Fractions) |

8.N.6 | Demonstrate an understanding of absolute value, e.g., $\,|-3| = |3| = 3\,$. |
simplifying basic absolute value expressions determining the sign (plus or minus) of absolute value expressions |

8.N.7 | Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots. |
practice with exponents practice with order of operations basic exponent practice with fractions practice with radicals |

8.N.8 | Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., $\,-7+7 = 0\,$; $\,\frac34\times \frac43 = 1\,$) and the notion of closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition). |
addition multiplication subtraction of signed numbers practice with the distributive law |

8.N.9 | Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g. multiplying by $\,1/2\,$ or $\,0.5\,$ is the same as dividing by $\,2\,$. |
multiplying and dividing fractions |

8.N.10 | Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than $\,100\,$ and less than $\,1\,$). |
writing fractions in simplest form |

8.N.11 | Determine when an estimate rather than an exact answer is appropriate and apply in problem situations. | |

8.N.12 | Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives). | |

PATTERNS, RELATIONS, and ALGEBRA | ||

8.P.1 | Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding. |
arithmetic and geometric sequences loans and investments the compound interest formula |

8.P.2 | Evaluate simple algebraic expressions for given variable values, e.g., $\,3a^2 - b\,$ for $\,a = 3\,$ and $\,b = 7\,$. | |

8.P.3 | Demonstrate an understanding of the identity $\,(-x)(-y) = xy\,$. Use this identity to simplify algebraic expressions, e.g., $\,(-2)(-x+2) = 2x - 4\,$. |
practice with products of signed variables practice with the distributive law |

8.P.4 | Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations. |
introduction to variables going from a sequence of operations to an expression going from an expression to a sequence of operations |

8.P.5 | Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems. |
introduction to the slope of a line practice with slope |

8.P.6 | Identify the roles of variables within an equation, e.g., $\,y = mx + b\,$, expressing $\,y\,$ as a function of $\,x\,$ with parameters $\,m\,$ and $\,b\,$. |
solving linear equations in one variable (This is the pdf file for Section 32, Solving Linear Equations in One Variable) graphing lines finding equations of lines |

8.P.7 | Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs. |
practice with the Addition Property of Equality practice with the Multiplication Property of Equality solving simple linear equations with integer coefficients solving more complicated linear equations with integer coefficients solving linear equations involving fractions solving linear equations, all mixed up solving simple linear inequalities with integer coefficients solving linear inequalities with integer coefficients solving linear inequalities involving fractions |

8.P.8 | Explain and analyze—both quantitatively and qualitatively, using pictures, graphs, charts, or equations—how a change in one variable results in a change in another variable in functional relationships, e.g., $\,C = \pi d\,$, $\,A = \pi r^2\,$ ($\,A\,$ as a function of $\,r\,$), $\,A_{\text{rectangle}} = lw\,$ ($\,A_{\text{rectangle}}\,$ as a function of $\,l\,$ and $\,w\,$). | Getting bigger? Getting smaller? |

8.P.9 | Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. | |

8.P.10 | Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and $\,x$- and $\,y$-intercepts of different linear patterns. | |

GEOMETRY | ||

8.G.1 | Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons. | |

8.G.2 | Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems. |
♥ Triangle Congruence ♥ Similarity, Ratios, and Proportions |

8.G.3 | Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal. | ♥ Parallel Lines |

8.G.4 | Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems. | the Pythagorean Theorem |

8.G.5 | Use a straight-edge, compass, or other tools to formulate and test conjectures, and to draw geometric figures. | Constructions |

8.G.6 | Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure, e.g., predict how tessellations transform under translations, reflections, and rotations. | |

8.G.7 | Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces. | |

8.G.8 | Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings. | |

MEASUREMENT | ||

8.M.1 | Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. |
Tables of Unit Conversion Information classifying units as length, time, volume, weight/mass practice with unit abbreviations practice with unit names practice with unit conversion information |

8.M.2 | Given the formulas, convert from one system of measurement to another. Use technology as appropriate. |
one-step conversions multi-step conversions |

8.M.3 | Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate. | ♥ Area Formulas: Triangle, Parallelogram, Trapezoid |

8.M.4 | Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement. |
♥ Similarity, Ratios, and Proportions ♥ Perimeters and Areas of Similar Polygons |

8.M.5 | Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density. | rate problems |

DATA ANALYSIS, STATISTICS, and PROBABILITY | ||

8.D.1 | Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling. | |

8.D.2 | Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box-and-whisker plots, histograms, tables, and charts. Differentiate between continuous and discrete data and ways to represent them. | |

8.D.3 | Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. |
mean, median, and mode measures of spread |

8.D.4 | Use tree diagrams, tables, organized lists, basic combinatorics ("fundamental counting principle"), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice. |
basic probability concepts more probability concepts probability tree diagrams choosing things: does order matter? |