The Public Schools of Northborough and Southborough

Click below to find an overview of the mathematics at each grade level.

. A triangle featuring the text "making sense of mathematical concepts" in a clear, bold font.

In Kindergarten, instructional time should focus on two critical focus areas:

(1) representing, relating, and operating on whole numbers, initially with sets of objects

(2) describing shapes and space

The Fluency Expectation for Kindergarten is that students will be able to fluently add & subtract within 5.
In Grade 1, instructional time should focus on four critical areas:

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

(2) developing understanding of whole number relationships and place value, including grouping in tens and ones;

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

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

The Fluency Expectation in Grade 1 is that students will be able to fluently add & subtract within 10, and add & subtract within 20.
In Grade 2, instructional time should focus on four critical areas:

(1) extending understanding of base-ten notation;

(2) building fluency with addition and subtraction;

(3) using standard units of measure; and

(4) describing and analyzing shapes.

The Fluency Expectation in Grade 2 is that students will be able to fluently add & subtract within 20 (know single digit sums from memory) and add & subtract within 100.
In Grade 3, instructional time should focus on four critical areas:

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

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

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

(4) describing and analyzing two-dimensional shapes.

The Fluency Expectation in Grade 3 is that students will be able to multiply & divide within 100 (know single digit products from memory), and add & subtract within 1,000.
In grade 4, instructional time should focus on three critical areas:

(1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends;

(2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers;

(3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

The Fluency Expectation in Grade 4 is that students will be able to add & subtract within 1,000,000.
In Grade 5, instructional time should focus on three critical areas:

(1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions);

(2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and

(3) developing understanding of volume.

The Fluency Expectation in Grade 5 is that students will be able to complete multi-digit multiplication.

Fluency

Below are a number of resources you can use to help develop your child's love of math and strengthen their ability to think flexibly about numbers.

Fluency: Each grade level K-5 has fact fluency expectations (see chart below). Fluency "means quickly and accurately. It means more or less the same as when someone is said to be fluent in a foreign language. To be fluent is to flow: Fluent isn’t halting, stumbling or reversing oneself. A key aspect of fluency in this sense is that it is not something that happens all at once in a single grade but requires attention to student understanding along the way" (PARCC, Math Model Content Frameworks, 2011). According to Jo Boaler in her article "Fluency Without Fear", "the best way to develop fluency with numbers is to develop number sense and to work with numbers in different ways, not to blindly memorize without number sense" (2015).

A chart outlining phonics expectations for fourth-grade students, including key skills and learning objectives.

Math Flips
Math Flips are flashcards with a problem on the front and a similar problem on the back (instead of a problem and an answer) to encourage relational thinking rather than answer-getting. Click …

Combinations of 10 Flashcards

Math Flips (Addition/Subtraction and Multiplication)/Google Slides
- See site below for instructions on how to use
Subitizing Multiplication Flashcards
- Video (make note of child's thinking process and how father guides thinking)
  - Child can also practice saying the fact first, then giving the solution.

- Free games for children to practice various computational skills
  - K: Ten-Frame Mania, How Much How Many?, Numtanga Jr
  - 1-2: Ten-Frame Mania, How Much How Many?, Numtanga Jr, Math Limbo, Kakooma (addition), Coin Bubble (grade 2); Break Apart (addition/subtraction); Numskill; Missing Numbers (addition/subtraction); Place Value (whole numbers- grade 2)
  - 3-5: How Much How Many? (Level 5 and up), Numtanga Jr and Sr, Kakooma (multiplication); Break Apart (multiplication/division); Expresso; Missing Numbers (multiplication/division- grade 3); Place Value (whole numbers- grade 3; decimals- grade 4 and 5); Satisfraction
Multiplication and Division Fact Practice

The math game your kids will play for hours!

Stick and Split is a deceptively simple, addictive game. But what makes it so special is while they are playing it, children learn and practice their times tables, perhaps without even realizing it.

Research shows the more you think about something, the more likely you are to remember it.

Most times tables games try to get children to answer simple questions like ‘what is 3 x 6?’ many, many times. The problem with this approach is it aims to get children to answer with minimum of thought. So it’s no wonder children have to answer them thousands of times before they remember the answers. Many get bored and switch off before the memory sticks. Some children get anxious when they don’t know the answers, and research also shows feeling anxious is not a great way to make memories.

Stick and Split has been carefully designed to encourage children to think much more about multiplication and division facts. There are no right or wrong answers, so it won’t induce anxiety. Instead, they need to be constantly thinking about what they need to do. The more they think, the more they remember.

For students in grades 3-5, download the app on your computer or tablet. Your teacher will provide you with your own unique 9-digit code. Enjoy!

SMPs

Standards of Mathematical Practice
We can all support student development of the mathematical “habits of mind” as described by the Massachusetts Common Core State Standards, Standards for Mathematical Practice (SMP). These behaviors ensure the understanding of math and focus on developing reasoning skills and mathematical communication.