Sorting: Students begin to classify objects by noticing what they have in common and how they're different (we will refer to these properties as "attributes"). At first, I will assist students with suggesting ways they can sort a variety of materials (by color, size, shape, or objects with holes/objects without holes, fruits/vegetables, etc.). Once students have grasped the concept, they will come up with their own sorts and will even give other classmates categories to sort their objects into.
Patterns: Students will copy, create, name, and extend patterns of varying complexity throughout the year. They will use rhythm (snap, clap, stomp, etc.), colors, shapes, manipulatives, literature, artwork, letters, and a multitude of other resources to create patterns. They will need to recognize that a pattern is something that happens over and over again, and allow us to predict what will come next. Students will also learn to name patterns and recognize how many members they have. A necklace that has a red, pink, purple pattern in the order of the beads, for example, would be considered a three part- or 3 member- pattern and would be labeled ABC (a= red, b= pink, and c= purple). At times, students will be presented with the letters and they will need to create a pattern that could be named as such/ For instance, if they are given the letters 'AABC', a possible colored bead pattern would be: red (A), red (A), pink (b), purple (c). Other times, students will be required to combine patterns (ie, create a color pattern to go with a rhythm pattern: red (a), red (a), blue (b), blue (b) for tap (a), tap (a), clap (b), clap (b) ).
Making Sets: Making set is simply pairing a number with a group of objects. For instance, a set for the number five could be anything from 5 stickers, to 5 gummy bears, 5 cars, 5 people, etc. The first nine weeks we will work with sets to 5, and each additional nine weeks we will add 5 more all the way up to 20.
Number Formation: We will begin practicing number formation through a variety of ways each of which is very similar to the techniques we use for practicing letter formation (see the 'Going Deeper' tab for Language Arts and scroll down to the purple "Letters" section or periwinkle "Handwriting" section). As a rile of thumb, we will practice forming numbers by writing from left to right and top to bottom. The following sites also offer poems and visuals that can help support your child if they are struggling to form their numbers: http://www.littlegiraffes.com/mathnumberformationpoems.html; http://www.hwtears.com/files/Number%20Formation%20Chart.pdf.
In conjunction with the sets, we will begin with numbers 1-5 and move our way up to 20 by the end of the year.
Number Sense: Number sense can be described as a student's understanding of the different combinations that can be used to make numbers (2 and 3 make 5, for example), how numbers relate to each other, and how they can be changed. We will practice using sets of manipulatives to make different numbers, combine different groups of objects to make one whole set for each number, and use the number bond bracelets described above to strengthen students' development in this area. Our district implements the Singapore Math approach to building students' number sense and mathematical skills foundation (more information can be found at: http://childparenting.about.com/od/schoollearning/a/what-is-singapore-math.htm).
Find the Number:
Counting: By the end of the year, Kindergarten students will be expected to 'rote count' (count aloud) to 100 by ones and tens (we practice counting by 2's and 5's as well), and should be able to do this when starting from any number (i.e., start at '29' and count from there to 100). They should also be able to count forwards and backwards from 20. We practice counting together everyday according to the number of days we have been in school. We pair our counting with rhythm and kinesthetic activities (body movements) in order to help with memory retention. We also practice recognizing patterns in the '100s chart' that we track while we are counting. Counting to 100 is an activity that you can easily do at home with your child. You can practice counting on the way to and from school, during bath time, or having them count to 100 before watching a TV program, to count the seconds they have to clean their room, to count how long they need to make their bed or brush their hair, etc. There are also numerous videos that you can download to your computer, tablet, or smartphone. I placed a different selection of counting videos on each 'month' page that can be accessed from the 'Month by Month' link on the 'Going Deeper' tab.
As students orally practice counting to 100, they will also need to know how to count out 20 objects and recognize and write numbers 1-20. As students learn how to count objects, it is important that they physically touch, move, and line up the objects to avoid counting the same objects multiple times. Watch the video below to see what this looks like:
Addition/Subtraction: These concepts will not be studied until the end of the year, but the foundations for effectively applying these number operations will be built on all year with the number sense activities we practice. Concrete practice (using their own bodies and manipulatives) is the most effective way for a Kindergartner to internalize these concepts.
One way students will become accustomed to addition and subtraction is by creating 'number bonds'- all of the different combinations that can be made to create a number:
Students will also practice using the sentence stems below to create addition and subtraction stories:
They will also use what is called a 'part-part-whole' mat to understand how numbers are formed and taken apart:
Measurement (non-standard units): Students will use tools such as a balance scale and everyday objects to measure the weight/mass, height, length, area, size, capacity, and volume of various items. For instance, in January we measure the height of snowmen with cotton balls- 5 cotton balls are equal to the height of one snowman.
We also compare measurements by determining which object(s) is/are heavier, lighter, hotter/colder, etc. or equal to another and then ordering them according to those measurements (i.e.- tallest to shortest). Students begin by comparing 3 objects and then moving up to 5.
Graphs: The first few weeks of school we will begin to recognize graphs as a way to answer questions and gather information. Students will discuss what they notice when they look at the graph and they will orally explain how they were able to arrive at that conclusion. For instance, on a favorite food graph, students may conclude that most of the students in our class prefer pizza because that category had more stickies than all of the others. As the year progresses, students will be introduced to 'more', 'fewer', 'equal', 'least', 'more than/less than' vocabulary, and will be asked to compare the differences between the categories. They will also begin to gather information and construct their own graphs.
More/Less: Students will learn how to compare objects by how many more/less are in each group. We begin by doing this with our classmates (such as are there enough chairs for all of the students, how many are we missing, or how many extra chairs are there, etc.). Later, we move on to manipulatives. Students who are struggling with this concept can line up the objects in 2 separate rows and pair them up. They can then use a pipe cleaner or similar item to 'hook' the pairs together. Whatever is left over or 'extra' is 'more', and whatever is missing is 'less'. As we are beginning to study this concept, we use a sentence stem and sticky notes to support students with the oral language piece. Watch the video below to see what this looks like:
Sequencing: Sequencing is a skill that our Kindergartners will practice across content areas. They will be ordering story events to retell stories, follow steps to conduct Science investigations, and creating 'how to' writing pieces, just to name a few examples. The emphasis on this concept is whether or not the child is able to determine if the sequence of events follows a logical order and the ability to orally defend this reasoning and to use transitional words (next, later, finally, etc.) and ordinal numbers (first, second, third, etc.).
Positional Words/Spatial Awareness: Spatial awareness is a student's ability to understand where objects are in relation to each other. This includes determining direction, distance, and location. We will practice using 'positional words' such as 'next to', 'beside', 'under', 'over', etc. to describe where objects are and where we move them. Students will even make a video of themselves on the playground to give them an opportunity to utilize this vocabulary!
Shapes (2d and 3d): Students will learn how to identify flat and solid shapes according to their attributes (number of sides and vertices for flat shapes and number of edges, faces/bases, and vertices for three dimensional shapes) and will be able to orally describe and compare them. We will practice sorting shapes from home and describing shapes for their peers to find and build.
The blocks center is a place where students can strengthen their spatial awareness skills as well as invent, manipulate, and explore while using flat and geometric shapes. Research has proven the benefits of engaging in blocks activities on a daily basis and also suggests that students creativity in writing can also be enhanced by their time spent here. I give students free reign at this center to see what they come up with, but I also leave inspirational pictures and challenges for those who need the extra boost. I rotate the types of blocks to keep students motivated and I try to relate the tasks to what we are currently working on in class. For instance, when we are studying geometric shapes, I pull out the the 3D blocks and challenge students to build their dream home with the blocks, and when we are studying Lincoln and SFA, I challenge students to use Lincoln logs to build their log cabins. To ensure students' accountability at this center, I require that they fill out a sentence stem and glue it in their journal to tell me what they made while visiting. They may either draw or write their answer.
Financial Literacy: In April, after culminating a unit on cowboys and how products travel from farm to market, we will begin a study on financial literacy. The students will learn about the different places we receive money (through gifts and/or income), and we will combine what we have already learned about needs and wants earlier in the year to practice making decisions with money (using money to purchase what we need and want and why we save money). Our district is fortunate to work with the Junior Achievement Program (http://www.ja.org/), and pairs our classrooms with high school students who will visit our class to supplement our instruction as we learn about these concepts. We also take a field trip to the neighborhood HEB and set up a grocery store in our own classroom. Students will be able to use these opportunities to practice identifying coins by name as well.
Math Stories/Problem Solving: If there are two words that could not be stressed enough in Kindergarten they would be 'oral language'. The veteran Kindergarten teacher on our team is faithful in reminding us that before a child can write something, they have to be able to say it. Language development, meaningful experiences with print, and writing all are critically dependent upon a child's ability to be able to explain in words what they are thinking and justify the reasoning behind their choices. For this reason, a great deal of the problem solving that we expose our Kindergartners to requires them to be able to orally respond to questions and create their unique solutions. In order to avoid gaps in later years, talking about their thinking in solving math problems is essential. One way we do this is by modeling ways to create math stories and then solve them. Students are then given the opportunity to use either the same manipulatives, story line, or numbers to reproduce their own stories. The focus isn't necessarily on whether they are right or wrong, but can they explain why they made their choices while using mathematical vocabulary and can they find the solutions in multiple ways. The pictures below show an example of what this may look like: