Happy Monday!

I once saw a quote that read, “Do not let the littleness in others bring out the littleness in you.” That quote is a founding practice in my daily life. People can challenge us, kids can challenge us, and our environments can be challenging, but we have the power to find the best in each situation, focus on the good we want to see, and highlight the goodness all around us. Be kind, you never know what challenges someone is facing.

Kids need kind, persistent coaching.

Last week, I posed a multi-digit division problem to a group of fifth graders.

Mrs. Castillo has _______ pencils. She is going to give ____ pencils to every classroom. How many classrooms will get pencils?

I asked the students, “How many strategies can you use to solve this problem?” a few students offered suggestions, while one broke down in tears and had to leave the classroom to regroup. When asked, he said, “I don’t have any strategies.”

I inferred from the student’s response that he was intimidated by what he believed his peers could do and what he believed couldn’t do and therefore suffered from a lack of confidence. He was looking at his friends and telling himself a story that brought him to tears and caused him to cry. Low self-confidence is no way to begin the school year. I reached into my toolkit and pulled out all I knew to build up his self-confidence and ensure he saw himself as a confident problem solver.

I reread the problem to him.
I changed the context of the problem by asking him to name the classroom by a real teacher’s name.
I gave him smaller manageable numbers to use.
(24, 6)

I gave him base ten blocks and ones to solve.
I asked him to act out the wording of the problem using the tools.
After every action, I asked him, Does what you just did make sense? Why?”
When he successfully solved the problem using the first set of numbers.

I gave him a second set of easier numbers to use.
(32, 4)
I repeated the cycle by asking him if creating groups of 4 cubes makes sense and why.
He successfully solved the division problem with the new numbers.

The third time around, I gave him a division with 3-digits. He was so excited and displayed so much confidence in himself. I tried coaching him through the problem, but he shooed me away and said,  “I got it.”
(320, 4)
He was successful!

He ultimately went on to solve a four-digit by a one-digit equation within the span of 45 minutes.
There are 3,240 pencils. Each classroom will get 40 pencils. How many classrooms will get pencils?

Start small, make sense of the problem, try it out again, challenge students a little more, make sense of the problem, and coach students to try something they never believed they could. Kindness and patience bring out the best in them.

Don’t assume they know.

I showed an image of base ten blocks to a group of students and asked them to write as many different equations as they could. I assumed the students would be able to complete the assignment with ease. They could not.  Rather than giving in and telling students what to write, I coached them through the image.

First, we counted how much was represented in the image (452). I told the students this number should appear in the equation.

Next, I asked them, “How many hundreds did you add together? We wrote that as an equation.
100  + 100 + 100 + 100 = 400

How many tens did you add together?
We wrote that as an equation.
10 + 10 + 10 + 10 = 40

How many ones did you add together?
We wrote that as an equation.
3 + 3 + 3 + 3 = 12

400 + 40 + 12 = 452

I then nudged students to connect their images to multiplication by asking, “How many times did you multiply 100, 10, and 3?”
We wrote that as an equation.
(4 x 100 ) + (4 x 10) + (4 x 3)  =  4 x 113 = 452

We repeated the process for division.
“How many blocks do we have in total?
452
How many groups do we have?
4
How many blocks are in each group?
113

452 /4 = 112

Many of the students wanted to give up at the beginning. Many more students wanted to stick with addition sentences. However, if I succumbed, I would not have provided them with an opportunity to grow. If I showed them how to write the equations, I would not be bringing out the best in these 4th and 5th-grade students and lifting them to a higher understanding of mathematics. Instead, I asked guiding questions and elicited their thinking, and coached them to analyze the images.

Start small, make sense of the problem, try it out again, challenge them a little more, make sense of the problem, and coach students to try something they never believed they could. Bring out the best in them.

Give Them Opportunities To Shine

All students bring value to the math community. Some students are great with tools, number lines, and equations. Some students are excellent at understanding the strategies of others, and some kids are fantastic at thoroughly explaining their thinking.

We just have to be patient, kind, and consistent and that will always bring out the best in them.

Ways To Connect

I love to stay in touch.  Please reach out via email, Danielle@TeachingOneMoore.org, or follow me on Instagram @Teaching1Moore is probably the fastest way to connect.

If you would like to take a deep dive into students’ thinking consider enrolling in my online Cognitively Guided Instruction (CGI) math course through the University of San Diego.
Enroll anytime, take up to 6 months to complete the course, go at your own pace, and earn up to 3 graduate-level units.

Go to www.pce.sandiego.edu to learn more today.