Accelerated High School

Standardized Curriculum of General Mathematics-I

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 1, instructional time should focus on four critical areas:

(1) developing an understanding of addition, subtraction, and strategies for addition and subtraction within 20;

(2) developing an understanding of whole number relationships;

(3) developing an understanding of linear measurement and measuring lengths as iterating length units;

(4) reasoning about attributes of, and composing and decomposing geometric shapes.

(1) Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, takefrom, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction. 

(2) Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes. 

(3) Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement. 

(4) Students compose and decompose plane or solid figures and build an understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement. 

Curriculum for Grade-I Mathematics

Standard 1: Geometry

Learning Objectives:

• Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
• Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Topics of AHS-GM:

Shapes and Space:

• Bigger – Smaller
• Biggest – Smallest
• Top - Bottom
• Near – Far
• Geometric shapes

Standard 2: Operations and Algebraic Thinking

Learning Objectives:

• Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
• Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
• Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Topics of AHS-GM:

Numbers from One to Nine:

• Tracing numbers
• Writing numbers

Addition:

• Add with cubes - sums up to 10
• Add with pictures - sums up to 10

Subtraction:

• Subtract with cubes - up to 10
• Subtract with pictures - up to 10

Numbers from Ten to Twenty:

• Counting 10 to 20

Standard 3: Number and Operations in Base Ten

Learning Objectives:

• Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Topics of AHS-GM:

Numbers from Twenty-one to Fifty:

• Writing numbers

Numbers from Fifty-one to One Hundred:

• Writing numbers

Standard 4: Measurement and Data

Learning Objectives:

• Order three objects by length; compare the lengths of two objects indirectly by using a third object.
• Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
• Tell and write time in hours and half-hours using analog and digital clocks.
• Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Topics of AHS-GM:

Measurement:

• Compare objects: length and height
• Wide and narrow
• Light and heavy
• Holds more or less
• Compare size, weight, and capacity

Time:

• Morning
• Afternoon
• Evening

Data Handling:

• Sorting data addition, subtraction

Patterns: 

• Sorting data with shapes and numbers