Making 10

This week during math we focused quite a bit on making the number 10. We created different visual representations paired with our number sentences to show the different facts to 10. As you will see in some of the photos below, some number sentences are arranged with either the missing number or the sum in different positions. It is important for students to see that, with addition, the order of numbers in a number sentence can be rearranged without changing the sum. It is also helpful for students to work with number sentences both beginning and ending with the sum to reinforce the idea that the sum can come on either side of the equation (for example, 10=4+6, 4+6=10). We also spent time discussing what we call "turn around facts" this week and practiced identifying the turn around facts for each number sentence we created. (turn around facts may also be known as the commutative property of addition, an example being 4+6 and 6+4). Tomorrow we will discuss how we have created balanced equations, balancing the numbers across the equals sign (6+4=10 is balanced because it has 10 on each side of the = sign).

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Counting Project Finale

Today we completed our big counting project! Throughout the last two weeks students practiced counting many different collections of objects exploring different ways to count and adapting their counting and recording strategies as they went along. This week we worked together as a whole class to decide how to count a collection of over 1,000 unifix cubes (see my previous post about this project)! Today we finished our project, by arriving at the final answer of, "just how many unifix cubes do we have in our classroom?" The answer turned out to be 1,744! Today during math we started with our groups of 100 (created yesterday) and counted them until we knew that we had 1,700. We have been discussing place value a little bit each day at the beginning of our math block when we find many ways to make "the number of the day," so, during a whole class discussion, we used what we know about place value to add the extra 4 groups of 10 and 4 single cubes left over from our previous days' counting to reach 1,744. Wow! The students were very excited to realize that, by using grouping and organizing, they were able to count to such large number of cubes! Below are two photos of our final result (the photo with the class shows, from left to right, a group of 1 thousand, a group of 7 hundreds, a group of 4 tens, and a group of 4 ones bagged by their quantity).

Counting Project - Starting on The Big Set!

The counting project continues! Now that students in our class have had many opportunities to count different sets of objects in different ways we have moved on to our class project: deciding how to count our class set of unifix cubes (we have over 1,000). We began by pulling out our two large tubs of unifix cubes and having a discussion about different ways we could count them all. We decided, after all of our other counting work, that grouping and organizing before we count would help us to count more quickly, keep track of our counting, and give us a quick way to check our answer if we need to. The class decided on grouping unifix cubes in 10s, since we all know how to count by 10. Students set to work creating sets of 10 cubes, then putting each group into a small ziploc bag. Some of our students decided that we have several hundred cubes all together, so, after grouping all of our cubes in bags of 10, we had to decide how to proceed! Since we decided that only some of us know how to count by 10 beyond 100, we needed to choose another way to group. After discussion, students realized that they know how to count by 100 and that we could easily make groups of 100 by putting 10 small bags of 10 into a large bag. Yesterday students worked with partners to create groups of 100 in this way. Today during math time we will decide what to do next! Here are some photos of our process.

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Continuing Our Counting Project

Here in room 5 we have been moving forward with our big counting project. This week as partners continue counting sets of objects and recording their counting, we are discussing grouping. So far we explored different types of grouping and decided which were the most useful when it came to counting the groups. Students made important discoveries, learning that grouping by number is more effective than grouping by color, each group has to contain the same number of items, and we need to group items in a way that we know how to count (grouping by 5 or 10, rather than a grouping we are unfamiliar counting). Through this discovery project students have developed their thinking about how to organize and count large sets of objects effectively and efficiently in a short time! It is exciting to see how they help each other to try new strategies and, through discussion and exploration, develop more successful methods of counting and keeping track of their work! Below are a number of great photos of students at work. If you look at the photos from the first day of our counting project, then compare them to these photos from the last few days, you will see the developing organizational strategies students are using to help them count.

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Counting Project

Students in room 5 have been working hard at learning to be successful work partners during math time! Below are more photos of kids in our class practicing partner work while playing a math game yesterday.

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Today our class began our big September counting project. I did this project with my class last year and it was a lot of fun and made for some wonderful hands-on learning through discovery. Part of why I love it so much is that I get to talk students through their thinking as they problem solve with partners, then watch and support their powerful "ah-ha!" moments as we move through our discovery! Today we began by my asking the students questions like, "why do we count," and "what are some things we could count?" Students then began working with partners to count different things in our classroom (books in a basket, a bucket full of pattern blocks, a bin of crayons, etc) and to record their counting on a clipboard. Today, as the first day in the project, I did not tell the students how to count or how to record their work but rather watched students work and asked them questions to guide their thinking. As they worked together I would ask questions such as, "how are you choosing to count these things," "how are you keeping track of your counting," "what could you do if you lost count," "how could you check your answer," "how are you recording what you counted?" The way that students are able to try a counting strategy they generate, answer my questions to explain their thinking, realize where they are getting stuck, then devise a way to modify their counting/recording strategy makes for wonderful discovery of effective ways to count a set of objects and to reason through a problem. In the following days students will have more opportunities to count collections of objects, refine counting strategies, learn from what other students are trying, and find effective ways to count, record, and keep track of their counting. Our final project will be problem solving "the best way" to count our entire class collection of unifix cubes (we have over 1,000!). Last year my students loved doing this project! I will post more along the way and you may also look at last year's project in my archived posts from last September. Below are photos of our first day working on the project.

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