Showing math in many ways

The students are encouraged to show their mathematical thinking in more than one way. This encourages deeper level thinking and more solid conceptual knowledge of mathematical concepts and ideas. Here are some pictures to show that traditional mathods, such as using diagrams, writing number sentences and unifix cubes can also be used in conjunction with digital tools such as an iPad!

Justifying and Conjectures

The students are continuing to justify their mathematical thinking. They are encouraged to show their mathematical understanding in more than one way as a way to back up and prove their work and understanding. The above picture illustrates some of the work we have done on odd and even numbers. The students have explored what happens to numbers as odd and even numbers are added together in a very systematic way. Each time 2 numbers were added together, the students showed their thinking using tiles and a traditional number sentence and sketch. The students started by adding 2 odd numbers together. As they added more number sentences using only 2 odd numbers, they were challenged to see if any patterns or similarities occured. Then, the students added 2 even numbers together, following the same systematic sequence as described above. Lastly, the students added an odd and an even number together (once again, following the same overall structure mentioned above). As the students explored the numbers and shared their findings, we were able to come up with a classroom conjecture: If you add 2 odd numbers together, you always get an even number. The students also discovered that if you add 2 even numbers together, you get an even number.
Ask your child to prove to you that this holds true for us now. For example, ask your child to show you how 3+5, or 5+7 can show this, or how 2+4 or 6+6 proves this. Challenge your child to show you with many more number sentences. Have fun and Happy Math!

Justifying

First grade mathematicians are learning about the importance of justifying our thinking. As discussed previously (please scroll down for older posts), justification not only allows students to "back up" their thinking with real evidence, it also allows students an opportunity to choose their own math strategy for solving a particular problem. Here are some examples of how we justify and "prove" our mathematical thinking in addition to using traditional number sentences and verbal proofs.

What number are we showing with tally marks?
 How can tally marks help us? Why do mathematicians use tally marks?

What number is this?  Is it an odd or an even number? Why?
How many different number sentences can you create?  Is there a limit?  If so, why?
Why do we use two different colors?

How can traditional writing/sketching help us in math?

How many different shapes do you see? How many hexagons?   How many traingles/trapeziods? How many trapeziods fir inside a hexagon? How many triangles fit inside a hexagon?
What are the different number sentences for each?

Figuring Friday

Every Friday in Bridges, the students explore the date in many different ways. This provides an opportunity to look at numbers in different ways, composing and decomposing numbers while recognizing the patterns between numbers and their connections to everyday life. Here are two pictures, representing two different Fridays. The first yellow picture, show a connection between the numbers and our calendar grid used in class. We discovered 10 butterflies, 10 praying mantises and 10 beetles on our chart. 10+10+10=30, the date we completed this chart!
We can also write the number 30 as 5x6. WOW, this is 3rd grade math! The students, through visual manipulatives and aids disscovered that we can take 5 six times to make 30! There are, of course, many other connections between numbers and everyday situations. This month, we explored how money can provide us with an example, as seen in the last number sentence. Ask your child to explain how many different number sentences are possible for the number 30 if we use the American coins only. Ask your child if those possibilities differ from all the possible ways we can express 30? Comment on this blog post to share your ideas. Thank you!

This picture represents the beginning half of the calendar grid for the month of October. It is hard to see in this picture, but the first "card" asks the question "Where is the lady bug?". The second question asks "Where is the butterfly?" This month, in addition to finding hidden patterns in our number grids, the students are challenged to use their vocabulary to explain where things are located. We have learned that specific words help us and add details. Mathematicians use VERY precise language. Ask your child to explain.

Justification

Students are encouraged to justify their thinking in our math classes and back it up.  They are encouraged to use evidence and proof to show their understanding.
Our favorite word is because-simply because it allows us to show why we think what we think.  We like because so much, we even have a song and dance for it!
Ask your child to explain how he/she justifies his/her thinking every day.

Using technology to enhance math thinking

Today, our first grade mathematicians had the opprtunity to use our iPads to further deepen their understanding of numbers as we were composing and decomposing numbers. The students worked together to solve number sentences (such as 14+11=?) using various mathematical strategies. Students were encouraged to use a variety of strategies. While the students worked together to show the components of each number sentence, they also used unif cubes toi visually show their understanding. They did an amazing job. Ask your child to explain how the app "Touch Math" allowed us to show the components of each number sentence.

Dyad Partners

As part of our school-wide math initiative and continued work around problem-solving and conceptual math thinking, our first grade mathematicians learned how to effectively share their math thinking with their dyad partners. A dyad partnership is a structured math grouping of two students, who not only work together, but also share their math thinking together. While the students still work as a class and rotate through our regular math stations, they now also have the time to check in and reflect on their own math thinking with their dyad partner. Another name for a dyad math partner could be "Math Buddy". For example, the students have learned that when two friends share ideas, we allow "Private Think Time" to our partners so they can think through what they wish to share. We have also learned that dyad partners give each other eye contact and pay attention to what is being said or shown (if, for example, the task was a more collaborative hands-on activity). Lastly, the students also learned that when we work in dyad math partnerships, we always "back up" our thinking. This is called justifying and the students are very effective justifying their own thinking mathematically.
It is amazing to see the collaboration and sharing that takes place in our classroom during math time! I am so proud of them.

Our First Homework

Our first math homework will come home on Monday next week.  I hope you will play the game many times at home, but return it to school so the teachers can check it.  We will send it back.  Our hope is that your child has a math corner or folder at home to collect all the games from math.  The homework is primarily interactive games, games that can be played over and over again.  We hope you and your child will discover that math is a social activity and should be explored, discussed and experienced.  Thank you.
In addition, your child will bring home their Work Place Planners soon.  These planners represent work stations your child has explored during the math unit.  Many of work places also represent games that can be played at home.  We hope you will take the time and carefully look through these packets as well.  Let me know if you have any questions!

Update

Dear Families,
I wanted to let you know that 1st grade mathematicians have learned what dyads are and how we can work together.  A dyad is a partnership.  Students are paired up with a friend and share their mathematical thinking.  They take turns talking and listen and respond to what their partner is saying.  The students practice "private think time" in these dyads, which means that they patiently wait for their partners to finish their thoughts or ideas about math.  The students will be dyad partners for a while and we will switch partnerships periodically.  Ask your child to explain and also share the benefits from having a partner in math.  As we practiced this together this week, some students shared that it was "nice to have friend who you knew would always listen to your ideas."  Amazing discussions also resulted as the students showed respect and kindness for each other.

Dyad partnerships are sometimes used during our Number Corner section in math.  Each math class begins with Number Corner.  Number Corner allows us to practice basic number sense every day as we explore the calendar, through mathematical investigations of patterns and numbers.  For example, the students "Turn & Talk" to their partners about what patterns and predictions they discover in our calendar every day.  They also "Turn & Talk" to share how numbers can be composed and decomposed as we investigate time, temperature, money and geometric patterns together.