Monday, May 24, 2021

Springtime Stories

Here are some 'springtime stories' that can be used when applying the "3-Read Strategy" (outlined in this blog).  Students create their own math problems, which allows ownership and leads to good discourse.

Sherry planted three rows of flowers in her garden.  Each row has 14 flowers.  Half of the flowers she planted are pink, and half of the remainder are yellow.

We had a rainy day yesterday. It rained steadily for two hours in the morning, then it stopped for a little while.  Later it rained again for 90 minutes.  Finally, we had another steady rain for three hours and fifteen minutes.

Springtime brings warmer temperatures, but sometimes there is quite a range of temperatures in a given day.  The other day it was 42 degrees when I woke up, and when I went to lunch it was 64 degrees.  When I started mowing the lawn around 2:00 it was 70 degrees.  As I was wrapping up my day, I noticed the temperature was 58 degrees.

Everyone is excited to see the pool open this year! There are three children in my family. It costs $1.50 for one child to get into the pool.  Adult entry prices are $1.75.  Our babysitter and her friend are adults and they like to go to the pool with us.

Monday, May 17, 2021

Subtraction Work Out

Subtraction can be challenging for students.  Often, students do not develop strong strategies for this operation and specifically struggle with regrouping.  They need lots of practice and encouragement.

Ask students to solve subtraction problems (mentally) such as "20 minus 13."  Although such a problem does, theoretically, require regrouping, encourage students to focus on the 'difference' between the two numbers.  Let them share their strategies orally and talk through the steps.  The teacher might need to model a strategy for the students in some cases.

Later, move on to a problem like this one:  "Beth had 25 buttons in her collection.  She lost three of the buttons and then gave 12 buttons to her sister.  How many buttons does she have now?"  Such a problem is multi-step and does require keeping track of numbers, but the operation is rather basic.  Again, encourage students to talk through the steps and to share their strategies.

Assigning problems like these on a daily basis can be a great help to all students, but for those students who might struggle with subtraction, this sort of work is vital.  Hearing their classmates share strategies is most helpful.

Move away - far away - from worksheets as "practice." Focus on the strategies that students use.  Subtraction may continue to challenge our students, but we can help them become more confident and more comfortable with this operation.

Monday, April 12, 2021

How Far Away?

Engage students in a great thinking activity - "how far away?"

Set a number as the "goal" and then say another number.  Ask "how far away is my number from the goal?"  Students will have to think and use their counting skills, addition skills, and subtraction skills to come up with an answer.


The goal is 50.  I say, "39 - how far away?"  A student might say, "11 ... I counted up from 39 to 40, which was 1, then I added 10."

The goal is 100. I say, "75 - how far away?" A student might say, "25. I thought of quarters ... 75 cents is one quarter away from a dollar."

Activities like this can generate a variety of strategies and can allow students the chance to shine as they explain their mental math.  Also, number sense is being built for everyone as strategies are shared.  Such activities do not take very long and the benefits are big.

Later, the teacher can incorporate time in the activity.


The goal is 4:00.  I say, "It is 2:35 - how far away?" A student might say, "That is one hour and twenty-five minutes. From 2:30 to 4:00 is one hour and thirty minutes, but this is five minutes past 2:30, so I subtracted five minutes from the amount."

At some point the number can be past the goal, so "how far away?" can be altered as "how far past?" This allows good use of subtraction strategies.

Tuesday, April 6, 2021

Higher-Order Thinking

Everyday, teachers try to encourage students to engage in higher-order thinking. It is not always easy to get the results we want, but it is definitely worth the effort.

Here are a few tips to encourage higher-order thinking:
(1) ask students to explain how/what they are thinking about the task
(2) do not expect students to quickly come up with profound answers - allow for "think time"
(3) build tasks on students' prior knowledge
(4) scaffold the thinking with a goal in mind
(5) model the higher-level thinking

Teachers who utilize appropriate questioning technique can get "more" from their students.  It is important to have such questions ready.  The teacher may not be able to think of such questions on the spur of the moment, so have a list of questions ready and it is okay to ask questions more than once.  Repeating the appropriate question will eventually lead to students taking ownership of their thinking, as they know what to expect from the teacher.

In the effort to encourage higher-order thinking, which is always worth the effort, teacher do not always "win." Sometimes the higher-order thinking does not happen or (at least) is not evident.  That is okay.  Profound responses from children will not happen every day, and teachers must not see that as a "fail."  On occasion, children might need more than one day to ruminate on a question.  Planting the seed is of value.

Higher-order thinking is always a "win."  Work towards it every day.

Tuesday, March 23, 2021

Do You Know What Your Student Are Doing?

Teachers are always interested in the work their students complete.  We grade that work and make a decision about the competency exhibited.  Here is a good question - "do you know what your students are doing?"   Here is a better question - "do you know what your students are thinking?"

Recently, I was in a classroom in which many students were 'copiers.'  They did a nice job of copying my work from the board, but I am not sure they were actually thinking.  That became evident when I made an error in my arithmetic, and no one caught it.  The students kept on copying me.  Eventually, the work that would be turned in would have "looked" good (even with the error), but I am not sure it was evidence of learning.

Sadly, many students go through several years of instruction as 'copiers.' They may copy the teacher's work or copy a friend's work and "get by." Their work may be neatly done, but their competency may be mis-judged.

The only way to know what a student is thinking is to engage the student in discourse.  They need to share their thinking orally, and they need to model their thinking through the use of drawings or manipulatives. A math class should be a rather noisy place - lots of talking - lots of sharing - lots of "out loud" thinking.

When that happens, the competency can be better-judged.  Learning is richer and even more fun when students share their thinking.  The teacher can also share his/her thinking, which has great benefits.  Be careful that the teacher does not talk too much, however.  Encourage the students at every turn to be open with their sharing.

Tuesday, March 9, 2021

Tables and Charts

 Teachers can greatly enhance learning by using tables and charts during math instruction.  Encouraging students to create tables and charts is a great idea as they explore strategies for solving math problems.

Some students need help with organizing their thoughts (or, maybe they need help with simply being neat). A table or chart can be of great benefit to such students.  This allows them to enter data in an organized and clear manner.  When they need to look at the data later, it is easy for students to refer back to the table or chart.

Patterns often exist in math.  They sometimes emerge as a problem is being solved.  Again, a table or chart is a great way to illustrate patterns.  Students can often see a pattern emerging as the data is presented in the form of a table or chart, even if they were not able to see a pattern otherwise.

Using color in a table or chart is a good idea.  

There are many ways to impact learning, and this suggestion seems rather simple and do-able.  Try to include tables and charts in instruction and model their function for students. 

Monday, March 8, 2021


"Routine" can be a synonym for "boring."  But, in mathematics instruction, "routine" can be effective and even comforting.  Consider establishing routines during instruction.

The provided curriculum may include some instructional routines. If so, follow them and make sure the students know about them.  If not, create some routines such as "Monday is preview day" or "Friday is always extension day."  Even within a lesson there can be some routines that encourage student engagement and help to keep a lesson flowing.

Other routines can be beneficial.  For example, including a counting activity every day can become a routine.  These counting activities will allow students to experience numbers in a fun way - almost like a game - and are typically not stressful.  

"Number Talks" can become a daily routine. It works best that way! Decide on a time for "Number Talks" and do an activity every day at that time (it does not have to be during math time, as it sometimes works best right after recess or right before lunch-time).  A daily "Number Talks" activity and a daily counting activity allow students to develop number sense and to gain confidence.  When these are routines, students know what/when to expect.  That is often comforting to a child who might face some anxiety in the academic setting.

Learning is not routine - it is fun and flexible and fantastic - but a good instructional routine will help the learning to happen!