### Math

PS 62's Vision is to prepare students for their future.  Therefore, we believe that young children need many opportunities to engage collaboratively with math through games and problem solving activities in order to feel comfortable and be resourceful with problem solving and number sense. Our philosophy is for all students at PS 62 to gain a conceptual understanding of the big ideas (below) and to be innovative in how they apply their knowledge.  Students are challenged to show multiple representations or models in response to a task rather than simply provide an answer and move on. We believe that when there is equitable opportunity for every student to participate and experience success, they can feel hopeful for a future career that may or may not include mathematics.

To this end, the daily math lesson will often include 'Number Talks' to develop student discourse as they make sense of algorithms and word problems.  In this forum, students learn to agree or disagree without judgement and be ready to talk about their reasoning.  Students are encouraged to value mistakes as learning opportunities and to persevere in problem solving even when things get difficult.  They work together and alone, depending on the task and get regular feedback from their teacher.  Real world applications of math are experienced via our Project Based Learning Units and experiences with computer science and innovation.

What are the 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.
What are the Big Ideas from Common Core?

Numbers represent quantity.

Description of 2-D and 3-D shapes.

Fluency Goal

• Add and subtract within 5

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).

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.

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.

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.

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 at a Glance

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: