Math Progression

One of our first "big ideas" in math this year was to notice how numbers are used in the real world and recognize what numbers tell us about ourselves and the world around us.  

When young children see how numbers have a purpose in their everyday life they can begin to develop number sense.  

Number sense refers to a child's ability to use and understand numbers by:

* knowing their value

* how  to use numbers to make judgements

* how to use numbers flexibly when adding or subtracting

* having strategies for counting, measuring and estimating

To begin our year-long journey toward number sense we have focused on counting by ones to ten, recognizing those numerals, comparing them and ordering them in sequence.  We are learning that numbers and their amounts can be represented in a variety of ways.  When counting to answer "how many" the last number said tells the number of objects counted and the number of objects stays the same regardless of how they are arranged.  When counting, the next number refers to an amount that is larger by one.  These foundational skills fall within the domain known as Counting and Cardinality of the Common Core State Standards (CCSS) which we follow for mathematics instruction.  We want children to know the number names and the counting sequence, along with counting to tell how many and how numbers and amounts can be compared. 

We learned two useful counting strategies to help keep track of a group of counted objects. The first is what I call the "doorbell" strategy where one touches an object and pauses for a split second to finish saying the number name before moving to touch the next. This pause helps ensure children are touching each object counted in a one to one correspondence fashion. The second is the "pull away" strategy where one ensures they pull away the counted object from the group that is uncounted so that two distinct piles are made.  You may see your child counting with these strategies a bit more dramatically as they have been introduced and you will see photos here of our practice. 

To help us recognize amounts that match a numeral, we are using cards called "five frames" and “ten frames” throughout our day.  The five frames helped us grasp a solid understanding of what one of my math instructors calls a sense of "fiveness."  By knowing how five can be composed and decomposed, young children can use this as a building block for ten, twenty, and so forth.  They can begin to apply what they know about five to larger numbers and use that other math computational skills.

Ten frames consist of a grid with two rows of five.  The spaces can be filled in with dots or materials to represent a corresponding number.  These grids help children recognize an amount that matches a number.  We use several types of printed five and ten frames with dot patterns that help kids make a mental picture of an amount that matches a number.  Once children are able to recognize dot patterns quickly, we can use them in a various mathematical ways, including for addition and subtraction. 

For several days we have worked with partners to represent number amounts while remembering the social strategies for working with a partner and finding solutions to problems together. This is a great link to the social conflict resolutions activities we are doing throughout the day.  In one photo here you will see children showing their collection of “five” while practicing social skills of listening in a group, keeping their eyes on their speaker and focusing with their brain on what the speaker is saying.  Being able to listen to peers in a group is a skills we will practice all year, adding more steps as we go along.

I will keep sending home the Home Links that support our EverydayMath program.  This homework will greatly support your child's learning in school.  Once you have completed the activity, you can send it to school and I will check it, acknowledge your child’s work and send it back home.  Thanks for partnering in your child’s education!

Learning to recognize the color and name of pattern block shapes.

Explaining out mathematical ideas using a document camera.  Here children are explaining how a particular shape looks and comparing those observations to other shapes and real life objects.

Practicing the "doorbell" and "pull away" counting strategies.

Learning to recognize numbers, counting and matching amounts to numbers.

Showing ways to represent an amount of five... and recognizing how is can look different, yet be the same amount.

Taking five apart and counting to ensure how two smaller amounts can add up to five.  We love singing and chanting a variety of counting songs and poems.  Using the game, "spin a number" to identify numbers and count to match that number.

Partner games to strengthen our mathematical thinking as we explain our answers to partners:  How many more needed to make ten with Race to Ten and Ten Frame Draw.  Domino dot patterns help strengthen recognizing those patterns on dice which are used for many math games.

Fiveness: How can five be represented in dot patterns, addition number stories and on ten frames.

Learning to subitize:  Subitizing is a skill we practice to help kids automatically recognize and amount, especially between 0-10.  

Life Cycle Studies: Painted Lady Butterfly

Our study of the life cycle of a painted lady butterfly covered an array of learning goals for our class. We were able to observe each stage of its life cycle beyond the egg stage.  Key to this learning is that a life cycle continues to flow, with butterflies laying more eggs to continue the pattern.  We also read about other life cycles happening simultaneously that affect butterflies... plant, tree and flower growth and the four seasons.   Along the way we kept a journal to record what we observed, just like a scientist. It might have been tempting to use rainbow colored crayons, but we were careful to keep in mind that our journal was a non-fiction piece with real information and diagrams to show changes from day to day.

We watched as each caterpillar ate food,  grew and eventually hung in a "j" shape.  After transforming (metamorphosis) into a chrysalis we waited patiently for any signs of a butterfly to come.  We were able to watch several emerge during the school day and observe them as they opened and closed their wings to dry them and pump blood throughout their wings.  After resting we transferred each butterfly to a green net, giving them sugar water as food.  We them took them outside, placed them high on evergreen branches and watched as they got accustomed to being outside.  We wished each a safe journey to Mexico and a warmer climate as it prepared to migrate for survival.  What a miracle to witness!

We recorded our observations in our science journals.

Observing the daily changes until they formed a chrysalis.

Once each chrysalis was formed, we transferred them to a glass tank, securing them along the inside. Then we watched and waited.  Finally a butterfly emerged!

After gaining their strength and time to nourish themselves, we release each butterfly together.  We took time to get a closer look and watched as they acclimated to the outside weather and prepared for their migratory trip.

After placing them carefully on evergreen branches, we wished them a safe trip to Mexico and hoped their kin would return to Vermont to lay more eggs and continue the life-cycle.

We observed the symmetry in their wings and noted that the colors were vibrant on the top of their wings and more dull on the underside.

Our final journal entry began with a Shared Writing session where all contributed to the words that described each page.  As children recalled what occurred, I projected my typing on the screen so that they could see their words come alive.  We reread our work before printing and gluing the words into our journals.

Emotions, Perspective Taking and Solving Conflicts

To build a classroom community kindergartners need to learn how to work together and resolve conflicts that may arise. For this to happen they must learn to recognize emotions and understand the perspective of others. Understanding how others feel is often a challenge for young children.  However, once kindergartners begin to recognize the emotions of other people around them, they can start to recognize how their actions affect others as well.  Once they can understand what another person feels and why they feel a certain way due to something that happened, both children can come up with solutions to conflicts that satisfy them both, or what we call “Win-Win” solutions. Being able to recognize facial expressions and name emotions is a first step. 

We are reading books whose characters exhibit different emotions in various situations. We are discussing why a character feels a particular emotion and the actions that occurred to cause the character to feel that way.  We are looking at how one character’s actions and emotions also have an effect on other character’s emotions and actions. We are discovering that a person can feel a range of emotions, especially when they are hurt or angry. Our discussions related to characters have been a springboard to real life experiences These conversations have given children in our class the opportunity to express how they have felt in a similar situation or a time when they felt the same emotion. 

An amazing comment that has helped our class to focus on identifying emotions came when a child said that a person's eyes tell you what they are thinking and how they feel.  This insightful comment has led us to always look at the characters in our books and figure out what they are feeling.  Most importantly, we look to connect the actions that the character did or that happened to him/her to the emotion they are feeling or may have caused another character to feel.  We have discovered that a person’s eyebrows can also reveal how a person is feeling.  For example, someone may have a smiling mouth, but “crinkled” eyebrows, which may signal a feeling of uncertainty or confusion.  In our classroom we will look to one another and read what our eyes and brows are saying to each other as well.

A few weeks ago we made feeling puppets with interchangeable facial expressions and role-played different emotions that your child took home on Open House Night.  We made a list of ideas describing what Partners do and experienced several partner lessons in which each partner had to give over control to the other.  This often took some negotiation and practice listening to and following what their partner said to do!  Our partner work extends into our math and literacy work as we remember to follow the guidelines of what a good partner does when working with another.  We have met the famous Penny and Danny, a.k.a. The Problem Puppets, too!   Penny and Danny have a knack for getting into conflicts with one another.  In several play scenarios, the puppets were able to work out their conflict with some easy solutions, but this week their problems become more complex and require more thinking to come up with Win-Win Solutions that they BOTH agree to follow.  My scenarios for Penny and Danny problems come from actual conflicts I have witnessed in our class so that children can begin to make the connection between practicing the steps to Conflict Resolution with Penny and Danny to their very own lives here in school and beyond.  Our conflict resolution steps include:

1. Please Stop

2. State the Problem: Both children state what they feel is the problem

3. Brainstorm several Win-Win Solutions or Ways to Solve the Problem

4. Agree on One Solution to follow

5. Follow through on the agreement. 
6. Gain adult support if needed

For several weeks we have been reading and studying about a character named David, especially in the book, David Goes To School who seems to stir up many emotions within himself and others.  We have linked his actions with his own emotions and what others around him feel due to his actions.  We even explored what David might do next to resolve a conflict and thereby change how others might feel.  

This week we will role-play more conflict situations and use what we have learned about understanding emotions to resolve them so that each person agrees.  We started making our own problem puppets to act this out!  Next week we will read about two Dr. Seuss characters, The Zax, who actually never agree on a solution and discuss how that affects their lives and those around them!