## Math

The International Academy of New York aims to achieve high, personalized standards for all students. Among other skills, the following are examples of what can be expected by the end of Nursery through Grade 4 in the core subject of

**math**.__Pre-Nursery__

- Recognize numbers 1-10 (label and recognize in and out of sequence).
- Name basic shapes.
- Utilize 1:1 correspondence to 5.
- Recognize primary colors and more.

__Nursery__

- Represent quantities in numeric form.
- Demonstrate basic number sense (Students understand when they see a number/symbol, e.g., ”1”).
- Utilize one-to-one correspondence to 10.
- Organize and express understanding of common properties and attributes.
- Extract information from graphical representations.
- Demonstrate problem-solving skills.
- Recognize explicit mathematical problems.
- Recognize and name basic shapes.
- Rote count to 20.
- Recognize and create a basic A/B pattern.

__Pre-Kindergarten__

- Count with understanding and match sets of numbers to corresponding numeral.
- Recognize geometric shapes in the environment.
- Classify and sort objects according to color, size, shape.
- Complete jigsaw puzzles and other types of spatial activities.
- Develop understanding of the concepts of “greater than” and “less than” by using concrete objects.
- Make observations, read, and represent concrete data using a pictograph.
- Use “real life” experiences such as cooking to learn basic concepts of measurement.
- Understand the basic concept of time -- today, tomorrow and yesterday.
- Understand rational counting.
- Understand and use data analysis (graphs) correctly.
- Compare and order numbers correctly.

__Kindergarten__

- Develop an identity as mathematicians and be able to explain their thinking when solving a math problem.
- Recognize two- and three-dimensional shapes and describe their attributes.
- Compare and order objects and numbers within 20.
- Compare lengths and weights of different objects.
- Count by 1’s, 5’s, and 10’s to 100.
- Use different strategies to add and subtract within 20. Students will recognize the addition, subtraction, and equal signs.
- Recognize and create growing and repeating patterns.
- Understand various aspects of past, present, and future.

__Grade 1__

- Demonstrate a beginning understanding of place value.
- Use manipulatives, number grids, and tally marks to solve problems involving adding and subtracting 1-digit whole numbers with 1 or 2-digit whole numbers.
- Tell time on analog and digital clocks.
- Read and interpret different types of graphs.
- Count by 1s, 2s, 5s, and 10s from a given number.
- Order and compare pairs of numbers up to 3 digits numbers.
- Read and write numbers up to 1,000.
- Understand ten fact families.

__Grade 2__

- Read, write, and model numbers up to 10,000, and identify place values in these numbers.
- Collect and organize data to create charts, tables, graphs, and line plots.
- Measure length to the nearest inch and centimeter.
- Read, write, and explain expressions and number sentence using the symbols +, -, =, > and <.
- Demonstrate automaticity with all addition facts through up to 20 and fluency with the related subtraction facts.
- Use manipulatives, number grids, and tally marks to solve problems involving the addition and subtraction of multi-digit whole numbers.
- Fluently add and subtract within 100.

__Grade 3__

- Relate math to real world situations and use the language of mathematics to clearly communicate ideas.
- Demonstrate an understanding of place value with seven digits.
- Demonstrate proficiency with addition and subtraction with regrouping within 1000.
- Understand Commutative and Associative Property of Addition and Multiplication.
- Use repeated addition, arrays, and knowledge of products and factors to solve multiplication problems.
- Show and solve division problems with remainders.
- Identify and show fractional parts, work with equivalent fractions, estimate and compare fractions.
- Show symbolic representations for denominations of money and understand decimals with money.
- Work with estimation and recognize when it’s appropriate.
- Collect, organize and describe data and make decisions and predictions based on data.
- Construct, read and interpret charts, diagrams, and graphs.
- Understand the concepts of probability and chance, and use fractions to represent probability and statistics.
- Recognize and draw parallel, intersecting and perpendicular lines, lines of symmetry, and different angles.
- Calculate area and perimeter.
- Show and calculate time (elapsed).

__Grade 4__

- Read, write, and compare multi-digit whole numbers using base-ten numerals, number names, and expanded form.
- Fluently add and subtract whole numbers up to 1 million.
- Round multi-digit whole numbers to any place.
- Use mental computation and estimation strategies such as rounding to assess the reasonableness of answers.
- Understand factors and multiples and find all factor pairs for a whole number up to 100.
- Multiply or divide whole numbers with and without remainders, and represent the problem using equations, rectangular arrays, area models.
- Recognize equivalent fractions and compare two fractions by using visual fraction models, creating common denominators or numerators, or using a benchmark fraction such as 1/2.
- Add and subtract fractions and mixed numbers with like denominators and multiply a fraction by a whole number by using visual fraction models and equations.
- Express a fraction with denominator 10 as an equivalent fraction with denominator 100; write fractions with denominators of 10 or 100 as decimals.
- Compare two decimals to hundredths place by reasoning about their size.
- Understand the relative sizes of measurement units, and use the four operations to solve problems involving measurement and conversion of measurements (distances, intervals of time, liquid volumes, masses of objects, and money).
- Apply the area and perimeter formulas for rectangles, irregular polygons, circles, and triangles in real world and mathematical problems.
- Draw and identify lines and angles, classify shapes by properties of their lines and angles, and recognize a line of symmetry for a two-dimensional figure.
- Understand concepts of angle measurement; measure and sketch angles in degrees using a protractor.
- Solve increasingly complex word problems, and explain orally and in writing the process used to solve a problem.