Accelerated High School

Standardized Curriculum of General Mathematics-III

Mathematical knowledge and skills are essential for navigating the complexities of the 21st century. Understanding and applying mathematical concepts is crucial for personal decision-making, civic participation, and career readiness. Accelerated High School (AHS) aligns its curriculum with various educational standards to ensure comprehensive coverage of mathematical principles and their practical applications.

Mission:

All students will understand the mathematical concepts and processes required for personal decision-making, participation in civic life, and preparation for future academic and career pursuits.

Vision:

Prepare students to become mathematically literate individuals who can effectively:

• Apply mathematical thinking and skills to solve real-world problems.
• Engage in logical reasoning and develop problem-solving strategies.
• Conduct investigations, analyze data, and interpret results.
• Discuss mathematical concepts and their applications.
• Read and evaluate multiple sources of mathematical information.
• Communicate mathematical ideas through various forms, including reports, presentations, and visual displays.

Spirit and Intent:

The AHS mathematics curriculum has been prepared and standardized following The New Jersey Student Learning Standards (NJSLS), including the Student Learning Standards for Career Readiness, Life Literacies, and Key Skills, as well as the Student Learning Standards for Personal Financial Literacy. These standards outline the expectations for what students should know and be able to do, promoting a comprehensive approach to mathematical instruction. From the earliest grades, students are expected to engage in learning experiences that develop their understanding of mathematical concepts, improve their problem-solving skills, and enhance their ability to apply mathematics in various contexts.

Four Dimensions of AHS Mathematics Curriculum:

In Grade 3, instructional time should focus on four critical areas:

(1) developing an understanding of multiplication and division and strategies for multiplication and division within 100;

(2) developing an understanding of fractions, especially unit fractions (fractions with numerator 1);

(3) developing an understanding of the structure of rectangular arrays and of area; and

(4) describing and analyzing two-dimensional shapes. 

(1) Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division. 

(2) Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. 

(3) Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication and justify using multiplication to determine the area of a rectangle. 

(4) Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of the part of a shape as a unit fraction of the whole.

Curriculum for Grade-III Mathematics

Standard 1: Number and Operations in Base Ten

Learning Objectives:

• Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Use place value understanding to round whole numbers to the nearest 10 or 100.
• Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 
• Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. 

Topics of AHS-GM:

Place Value:

• Place value names up to ten thousands
• Value of a digit up to ten thousands
• Convert to/from a number 
• Convert between place values

Ordering and comparing:

• Compare numbers
• Which number is greatest/least?
• Order numbers
• Make the largest or smallest number possible

Rounding:

• Round to the nearest ten or hundred using a number line
• Round to the nearest ten or hundred
• Round to the nearest ten or hundred in a table

Mixed operations: addition and subtraction:

• Relate addition and subtraction sentences
• Add and subtract three-digit numbers

Multiplication Tables:

• Table 2-10

Standard 2: Operations and Algebraic Thinking

Learning Objectives:

• Multiply and divide within 100.
• With accuracy and efficiency, multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 8 = 5) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Topics of AHS-GM:

Multiplications:

• Multiply by 0
• Multiply by 1
• Multiply by 2
• Multiply by 3
• Multiply by 4
• Multiply by 5
• Multiply by 6
• Multiply by 7
• Multiply by 8
• Multiply by 9
• Multiply by 10
• Multiplication facts for 2, 3, 4, 5, and 10
• Multiply by a multiple of ten
• Multiply three numbers

Division:

• Divide by 1
• Divide by 2
• Divide by 3
• Divide by 4
• Divide by 5
• Divide by 6
• Divide by 7
• Divide by 8
• Divide by 9
• Divide by 10
• Division facts for 2, 3, 4, 5, and 10   

Standard 3: Number and Operations – Fractions

Learning Objectives:

• Develop an understanding of fractions as numbers.
• Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by parts of 1/b size.

Topics of AHS-GM:

Fractions:

• Match unit fractions to models
• Match fractions to models

Standard 4: Measurement

Learning Objectives:

• Geometric measurement : understand concepts of angle and measure angles.
• Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
• An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360th of a circle is called a "one degree angle," and can be used to measure angles.
• Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
• Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Topics of AHS-GM:

Lines and Angles:

• Lines, line segments, and rays
• Angles greater than, less than, or equal to a right angle
• Parallel, perpendicular, and intersecting lines

Read and write times:

• Match clocks and times
• Match analog and digital clocks
• Read clocks and write times
• A.M. or P.M.
• Write times