Mathematics K-5

Mathematics is a dynamic, interactive field of study that enables students to move from hands on storytelling activities and word problems, to more abstract problem solving.  By connecting mathematical concepts with prior knowledge and using authentic contexts, students can apply strategies as well as algorithms with purpose and understanding. 

Our instructional program addresses arithmetic, conceptual understandings, higher order thinking and problem solving strategies. Ample and productive opportunity is provided for students to become fluent in basic skills and computations; to develop critical and analytical reasoning; master the mathematical vocabulary needed to communicate universally in proper mathematical language; and to include technology as a vehicle for enhancing and extending learning. 

The Common Core State Standards outline the need for computational reasoning, applied problem solving and strong knowledge of foundational skills.  In addition to memorizing and practicing procedures, our instructional program emphasizes students’ work toward the recall of number facts, as well as flexible ways of looking at numeracy and arriving at solutions. Solving problems with whole numbers, fractions and decimals without calculators; understanding the underpinnings of algebraic thought; and creating the capacity of students to explain and demonstrate their reasoning in pictures, words, and numbers are components of the mathematics program. New concepts are introduced through a concrete-pictorial-abstract (CPA) approach. This approach means that students first learn concepts with the use of concrete manipulatives to allow students to develop understanding through their own experiences before progressing to the pictorial and abstract representations of the concept. 


Authentic situations, such as the use of a calendar, corresponding cardinality and problem solving are highlighted throughout the course of the year.  Observing graphing patterns, such as the differences between school days and weekdays on a calendar, counting with one to one correspondence and grouping objects by ones and tens allow students to understand how mathematics plays a role in their everyday lives and experiences.

Activities such as counting the number of days school has been in session, tallying the number of sunny or rainy days, using stories with number or word problems enables pupils to interact with mathematical concepts and make sense of the world around them.  Sorting, estimating and organizing also serve to enhance conceptual understandings and higher order disciplines such as geometry and algebra are addressed through the introduction, recognition and use of patterns and shapes.


Students understand and apply basic geometric concepts, such as recognizing and describing defining attributes, using multi-dimensional shapes to create new shapes (such as two triangles creating a rectangle), and using pattern blocks to conceptualize and build fractions as part of a whole.  Measurement and data are supported through the use of standard and non standard units of measure, as well as graphing and analyzing information.  

Fluency with addition and subtraction are honed through hands on activities and the use of story problems as a vehicle for more abstract thinking.  The utilization of concrete models and drawings demonstrate understanding of place value, properties of operations, and/or the relationship between addition and subtraction. These skills are further developed with the study of two-digit addition and subtraction, with and without regrouping. The use of mathematical vocabulary and symbols, such as <,  >, and = are employed as students explain their reasoning and strategies when arriving at solutions to problems. 


The second grade curriculum incorporates understanding and applying the commutative and associative property of addition and subtraction.  Problem solving and the use of mental math strategies as a complement to arithmetic are advanced as the year progresses. Common experiences, such as identifying, counting and working with monetary amounts are infused throughout the curriculum. Enhanced uses of a number line and identifying odd and even quantities are also important components of the curriculum as well as the use of proper mathematical vocabulary to express mathematical ideas and solutions. 

The role and relevance of place value and approaches to finding the missing addends and subtrahends are included as students use their understanding to estimate, round numbers, and compare amounts using skip counting, adding multiples and regrouping. Multiplication is introduced as repeated addition and arrays; division is introduced as repeated subtraction (quotative) and distribution or sharing (partative).  Students’ hands on experiences and the use of modeled number stories aid in the preparation of higher order and analytical thinking skills. 


Third grade begins with a review of the major concepts in mathematics that will be extended as the year progresses.  Place value patterns, problem solving strategies, comparing and ordering numbers, and understanding the relationships between numbers and operations are key components.  The study of fractions is deepened and advanced as students examine equal parts of a whole, name fractional parts, and plot and identify fractions on a number line with multiple fraction names e.g. 1/2 = 2/4. 

The important skill of writing to explain and provide support for problem solving strategies is introduced and refined through a variety of activities.  Students are expected to use proper mathematical vocabulary and demonstrate understanding using numbers, models, pictures, and words to explain their own thinking and that of their classmates. Fluency with multiplication and division are further honed, as students learn and practice facts through hands-on activities and apply their learning as they solve real-world problems.  This understanding supports students in learning to estimate products, find area and perimeter, and convert measurements within the metric system to demonstrate the inverse nature of many mathematical concepts.


Reading and writing numbers in standard, word and expanded forms provide a significant foundation for the year’s study as place value extends to decimals and hundred millions.  Using this information, students are expected to calculate the sum, difference and product of whole numbers, use estimation appropriately and recognize patterns in various multiples. Computing equivalent fractions by finding common denominators, adding and subtracting fractions and mixed numbers, composing and comparing fraction values and using decimal notation for respective fractions are expectations in fourth grade. 

Geometric shapes are classified, prime numbers are introduced and multiplication and division are applied through a wide variety of word problems and problem solving activities.  The role of relevance of graphing as it relates to data analysis and the importance of selecting appropriate tools for measurement are reinforced, and line plots are used to display a data set of measurements in fractions of a unit. Students are expected to explain their own solutions, as well as be able to understand and use an alternative method when solving a similar problem.


The distributive property, as a resource for multiplication and a building block of Algebra, is incorporated into teaching and learning. Fractions are interpreted as a form of division and addition, subtraction, multiplication, and division of fractions complement foundational precepts. 

Using coordinate planes, graphing equations and using operations to solve equations prepares students for algebraic study. This process includes understanding equivalence, estimating,  and using number sense to apply math to everyday situations. The study of measurement in terms of finding area, perimeter and volume, calculating time lapses and measuring with fractions of an inch offer a well rounded foundation for problem solving skills.

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