Math

PS 62 participates in the Algebra for All Citywide Initiative for math.  

We believe that young children need many opportunities to engage with math through games and problem solving activities in order to meet and exceed the requirements of common core standards.  The goal is for all students at PS 62 to gain a conceptual understanding of the big ideas (below).  This challenges students to show multiple representations or models in response to a task and simply provide an answer and move on.  

During the math lesson, teachers model 'Number Talks' in order to engage the whole class in making sense of algorithms and word problems.  In this forum, students must agree or disagree and be ready to talk about their reasoning.  

Math Practices
  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics.
  • Use appropriate tools strategically.
  • Attend to precision.
  • Look for and make use of structure.
Big Ideas from Common Core


Grade K 

Numbers represent quantity.  

Addition and subtraction equations.  

Description of 2-D and 3-D shapes.


Fluency Goal

  • Add and subtract within 5


Grade 1

Strategies to develop addition and subtraction within 20

Links between addition and subtraction and counting, number line, construction and destruction

Understanding of length and its units

Composition of plane and solid figures


Fluency Goals

  • 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).


Grade 2

Understanding of Base ten notation and place value

Counting by 5’s, 10’s, 100’s

Use of tools to measure and the understanding of standard units of measure

Analyze shapes by their sides and angles

Use building and drawing as a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades


Fluency Goals

  • Fluently add and subtract within 20 using mental strategies.
  • By end of Grade 2, know from memory all sums of two one-digit numbers.
  • Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.


Grade 3

Students understand the relationship between multiplication and division

Develop understanding of fractions as a part relative to a whole

Area is an attribute of 2-D regions, and the connection of rectangular area to multiplication

Students relate fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole


Fluency Goals

  • Fluently 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 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
  • 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.


Grade 4

Multiplication procedures work, based on place value and properties of operations and use them to solve problems.

Different fractions can be equivalent

Fractions are a composition of unit fractions

Shapes can be classified by properties of their lines and angles


Fluency goals

  • Fluently add and subtract multi-digit whole numbers using the standard algorithm.


Grade 5

Fractions are the division of numbers

Explain why the procedure for multiplication and division of fractions makes sense

Place value systems relation to computational methods

Multiplication as scaling

Volume of solid objects can be calculated and is additive


Fluency Goals

  • Fluently multiply multi-digit whole numbers using the standard algorithm.




Fluencies

Students must learn to perform calculations and solve problems both quickly and accurately. At each grade level in the Standards, one or two fluencies are expected: 


 Grade  Fluency
 Kindergarten add/subtract within 5
 Grade 1 add/subtract within 10
 Grade 2 add/subract within 20
 add/subract within 100 (pencil and paper)
 Grade 3 Multiply and Divide within 100
 add/subtract within 1000
 Grade 4 add/subtract within 1,000,000
 Grade 5 Multi-digit multiplication