Lower School: K-2 – Math

Monmouth County Private School : K-2 Math

The Voyagers’ K-2 math program is a multi-pronged approach that provides activities for a variety of different math levels and learning styles. The students work in a small group that can be varied as children show progression and the teacher feel they are ready to be challenged by the next set of skills, this allows the teacher to focus on specific exercises and foundational building blocks.  

Teachers in both the K-2 and 3-5 classrooms utilize a variety of curricular components including “Investigations in Number, Data, and Space” math curriculum, in addition to a variety of activities for young learners in order to provide constructivist-based learning opportunities and real-world, meaningful situations that require mathematical solutions. An emphasis is placed on helping the students master basic numeracy concepts and building the solid foundation for future math learning. Teachers rely on instruction that is differentiated, direct, experiential, and cooperative.  The activities and experiences offered are hands-on, multisensory, visual and kinesthetic.

The youngest of our students are provided direct instruction in number recognition, counting in a one to one correspondence, learning about basic computation, the passage of time, cluster counting, patterning, comparing quantities, beginning geometry, introduction to the clock face and telling time, learning coin names and values, working with a number line, place value in the ones and tens place, using a hundreds chart, solving word problems, and learning addition facts.  These students are continuing to learn the building blocks that will lead to all their future mathematical learning.  As they progress through their school year they will be empowered to feel that they are capable in their mathematical understanding.

The teachers provide real world, meaningful situations that require mathematical thinking and solutions. The K-2 students are charged with the responsibility of providing the community a mid-morning snack every day.  This task consists of the students checking inventory, ordering supplies creating a menu, tallying classroom total, preparing and serving the snack.  This job is one exciting and challenging opportunity for the students to integrate and practice the mathematical concepts they are learning in class. 

The students will:

Develop an understanding of numbers and operations of whole numbers up to 100:  

  • Identify, read, and write, numbers up to 100
  • Count by groups of 2, 5, and 10
  • Identify coins and their values
  • Develop fluency with addition of up to 10+10
  • Add multiples of 10 and 100 to a number
  • Solve up to 3 digit addition problems using at least one strategy

Introduction to multiplication and division

  • Understand the meaning
  • Develop strategies for multiplying and dividing groups of objects

Develop an understanding of addition and subtraction of whole numbers:

  • By combining and decomposing numbers, representing numbers, combining either single or double digit numbers, finding quantities by counting on and eveloping fluency when combining two numbers
  • Develop an understanding of word problems and interpret the operation needed.
  • Understand doubles

Be introduced to Data Analysis

  • Interpret and describe data
  • Interpret graphs and change over time
  • Create a table for comparison of graphs
  • Organize data for a graph
  • Summarize data from a graph
  • Introduction to fractions of 1/2, 1/4, 1/3.
  • Introduction to Measurement
  • Use ruler, measure lengths
  • Solve problem about time
  • Introduction to  measuring perimeter
  • Introduction to measuring area
  • Recognize right angles
  • Identify triangles, rectangles and squares as well as other polygons in both 2- and 3- dimensional form
  • Understand Patterns
  • Identify beginning and ending points in a pattern
  • Be able to convert a pattern into a ration
  • Develop an understanding of 2- and 3-dimensional objects
  • Compare angles and similarities between shapes
  • Compare and contrast 2- and 3-dimensional shapes
  • Identify number of sides on polygons
  • Understand symmetry


Fall Semester

Math Workshop Time has been focused primarily on setting the tone for routines and establishing habits of learning for the school year.  Each student was invited to explore the math manipulatives they would be using for the school year.  Since we are starting a new math program called Investigations in our classroom, it was important for the students to use the materials in an open-ended manner and discover the possibilities and potential of the different math supplies.  

After taking some time to get to work with the materials, the students were slowly introduced to their math workshop routine.  Each student was given a small math notebook and a special Math Folder to hold their work completed during math.  Students were first introduced to the different math activities before the teacher assigned them to their work. As the students completed a variety of math centers, they were instructed on how to document their work in their math notebook or on the worksheets.  

Students worked on the same activities over several days as to practice the routine and tone of math time in order for the students to develop appropriate habits for their work time.  Once they began to understand the expectations of math workshop, they were told they could choose whatever math activity they wanted, keeping in mind the number of students each activity provided space for.  Some activities required partners and students would work with one another to complete their work.

Recently, the students were introduced to a checklist to keep track of the work completed for the week during Math Workshop Time.  After completing an activity, the students go to the clipboard, find their name and scroll over to find the name of the activity they completed and check it off.

The students have been focusing on a variety of math concepts through their work.  They are making math connections about numbers and quantity up to ten and twenty, depending on the activity.  As the students work with these numbers, they are developing the concepts of breaking quantities up into smaller parts and then putting them back together again.  By focusing on quantities, the students are building an understanding of the relationship between the 10’s and 1’s, parts and whole, and reciprocals, and they are thinking in units of ten.  Students are grouping numbers in a variety of ways as they think about the patterns in numbers and the logical sequences.

Students are also learning about the calendar; they are learning the days of the week, names and order of the months, how many weeks make up a month/year, and how to read a calendar.

They spent months preparing for serving snack. Beginning with taking surveys to determine the number of students in each class, as well as any diet restrictions the students should be made aware of. The students compiled their data into a bar graph that will be used when determining the amount of food served to each class.

The students also created an overall inventory of the staples it will be necessary to keep in the kitchen once we get started.  After discussing snacks that the students enjoyed last year and starting a list of possibilities, the students broke into small groups and began looking at snack possibilities on the class iPads.  These ideas were then added to the list.

Once all the ideas were compiled together a list of all the snack possibilities was created.  The students are now thinking of ways to create a balanced, nutritious, and delicious for the community.  When we begin to serve snack it is the student’s intention to create a weekly menu for each classroom to have.

The students have been interacting with 2-dimensional shapes and are beginning to understand the similarities between shapes.  Working with pattern blocks, the students combine hexagons, trapezoids, rhombuses, squares, and triangles to create different larger shapes.  The students are noticing what happens when shapes are combined to form new shapes, for example, two trapezoids placed together creates a hexagon.  These connections help students see the relationships between shapes.

The class, as part of our calendar and date keeping work, count the number of days we have been in school.  One of the ways we are doing this is to create a word problem every day that will equal the number of days we have been in school.  The students may use any operation they choose to create their problem.   The students first draw the pictures that match their problem and then write the corresponding number sentence to match the graphic representation.

The students continue to build their fluency with quantities up to ten and twenty.  Using a variety of materials and engaging in multiple activities, the students are grouping and writing number sentences and drawing representations in their Math Notebooks to show their work.

The students have their exploration of 2-dimensional shapes as one of their activities of their Math Workshop.  They have been looking more closely at the variety of combinations when creating larger shapes.

The students have begun thinking about subtraction along with addition.  Some students are beginning to see the relationship between addition and subtraction, especially when looking at problems that contain addition facts they have memorized and can recall easily.

The students also play board games and other tabletop games. The students engage in a variety of mathematical thinking skills as they play these games and compete in a good natured manner.

The students have begun adding more than two numbers together.  At the present time, they are adding numbers no larger than 6 together, keeping the totals manageable.

Winter Semester

After returning from Winter Break the students were ready and eager to get back into the Math Workshop portion of our schedule.  The students are busy learning about using base ten for their addition and understand the concept of place value through many of the purposeful routines we embed into our schedule on a daily basis.  One of these routines is our stick calendar, which a student cares for every day as part of the Date Keeper’s job within the classroom.  On the classroom wall, a small box is hanging that is divided in half.  On the left side, the word Tens is written, on the right half, Ones.  The Date Keeper places one popsicle stick in the one’s box for every day on the monthly calendar.  When 10 sticks add up in the One’s box, the Date Keeper takes the ten sticks and bundles them into one bundle and places it in the Tens box, creating one ten and zero ones.  The students are taken through the process of place value in a natural and important part of their day.

We have begun to serve snack and, at the present time, all is going well.  The students are heading down to the kitchens as soon as their Independent Reading Time is over and checking the menu for the day’s snacks.  The students must count out serving portions, keep track of how much snack has been counted, and take care to maintain sanitary practices.  The students then announce to the classes that snack is ready for pick up in the Dining Hall.  

The students have started planning their snacks on a monthly basis.  Before the beginning of the month, the students planned out the menu for the next month.  Using pre-printed labels for the different menu options, the students placed the desired snack for each day that we are in school for the upcoming month on the calendar.  The students first blocked off Hot Snack Tuesday with oatmeal for the entire month before moving forward.  As they worked the students were reminded to think about variety when planning the menu, trying not to serve the same item too often and to vary the fruit and vegetables. The students are beginning to learn how to take inventory of the kitchen for supplies in the pantry, the refrigerator, and fruits and vegetables bins.

Students continue to reinforce the concept of combining numbers together to make ten.  This type of repeated exercise encourages the students to process the number facts to get to base ten over and over again in a variety of ways, eventually becoming rote.  An activity that builds upon this skill is combining numbers together and visually looking at the combinations on a twenty frame.  This extension of making ten, shown on a 5×4 grid that is filled in, allows students to call to mind the numbers being combined together and how they relate to base ten.

Besides combining numbers together, the students have also been comparing quantities using the terms, “greater than” and “less than.”  Working together through games, the students practiced using the symbols for these math terms and understanding the relation between numbers and quantity.  Counting backward is another activity that helps students think more abstractly about numbers and their relationship to one another based on quantity.

Another number activity that the students have been engaging in is the doubling of numbers. This quick thought process helps students engage in computations that they can do in their head, which will then be assimilated into their ever-increasing knowledge of number facts.

The students are being introduced to telling time to the hour and half hour on both an analog and a digital clock through a variety of games and activities.   The class created their own clock that included both the hour and minute numerals for each space on the clock face, before finally adding an hour and a minute hand.  This activity was intended to introduce the student to the hour and minute correlation on the clock face, a concept that is confusing for students beginning to tell time.  The students are engaging in activities that require them to tell the hour and minutes, match analog and digital times, and draw hands on clock faces to record times.  

Students are also being introduced to coins through a variety of activities planned by the teacher.  Being able to identify and distinguish between coins is a skill that must be practiced to become rote.  Students are sorting coins, comparing the heads and tails, and looking at the wide variety of commemorative coins produced in recent years.   

The teacher also uses this time to assess students knowledge and retention of previous topics.  Calling the students to work in small groups the teacher can see which subjects need further review and which have been mastered by the group.

Spring Semester

The students have been using their Snack Math time to continue to plan, inventory, and prepare the snack for the community.  They have become efficient at all of the tasks they have worked on throughout the year.  Recently, our assistant was away for quite some time.  She typically works in the kitchen with the students to prepare snack while the rest of the class is having Morning Meeting upstairs with the teacher.  While she was away, the students were able to work independently in the kitchen and prepare the trays for each class in the school.  They followed the preparations she had helped them to understand.  Although the aide had done much to organize the snack prior to her absence, the students were able to follow through and do it well.

The students have continued to work with coins and have been able to move beyond identification of each coin.  The have played a variety of games that required them to use combinations of coins to reach different totals adding up to 29 cents.    

The students were introduced to a game called minute math.  It’s a race against the clock, but also against oneself.  The game required the students to solve as many number problems as possible in a given set of minutes, usually two to five.  The students chose either addition, subtraction, or multiplication problems, to solve.  They are eager to try to outperform their previous attempts.  Once the students run out of time they show their results to the teacher to check for accuracy.  They quickly fix any errors discovered.  The students have noticed an increase in their performance and are happy to share with one another their accomplishments and to encourage one another.

As a follow up to the number of days in school, which the students worked on during the first half of the school year, they are now solving personal word problems about themselves. The teacher uses their interests and skill level when composing word problems  Student find their personal word problems, glue them into their math notebook, and then go about solving them.  Students must show their thinking in their notebook along with their final answer.  Students use a variety of strategies to solve these problems. They are motivated as they enjoy the stories about them and about their families and friends.

The students continue to practice telling time with an analog clock.  They are often asked to identify times during the day when daily events occur, such as breakfast or dinner.  The students were surprised to discover such a variety of times during which students do the same things, like getting up in the morning and going to bed.  The students drew a clock face to show 6 common events and then drew the hour and minute hand to indicate the variety of times.  They demonstrated an increasing understanding of time on a clock and of the passing of time

The students are continuing to play games to increase and solidify their understanding of coins, including values and combinations.  They often play a shopping game with items to buy and money to use.  The student’s draw picture cards of different children’s toys marked with a price between 3 and 27 cents.  They take coins out of a money bowl and add these up to the total needed.  Each student has a recording sheet to mark the prices and the coin combinations used.  After purchasing 5 items the students totaled their purchases and identified how many pennies, nickels, dimes, and quarters they used.

TEACHER: Sandy Miller