Warm-ups in Math Education

According to About.com, Daily warm ups or do nows are tools that every teacher should have in their educational arsenal. Warm ups can be given to students at the beginning of the period to review a previous topic or to introduce new material. They give students something to accomplish of an educational nature while allowing the teacher time to take roll and perform other housekeeping duties.They can also reinforce the key points that you want students to remember. Therefore, every teacher can benefit from including warm ups each day.

Warm-ups in math education serve many purposes for both teachers and students. The purposes it can serve for the teacher are: Student assessment, focused students in the class, introduces or reviews materials, promotes individual and group work, and allows the teacher to complete clerical tasks. Warm-ups can become something the students expect when they walk into the classroom. They serve as a "jump start" for students.

The purposes it can serve for the student are: Allows practice or review of the material, test preparation, provides a stress-free environment for students to make mistakes, and allows them to work on individual or group work.

In my experience with warm-ups in the classroom so far, I have seen a few strategies implemented that I thought to be effective use of the time. The first was a warm-up activity focused on individual students. Students were to complete the task alone and then be ready to explain to the class their reasoning. The second was a group-based activity. Essentially the same idea as before, but promoting group work and roles as a focus. Material in the warm-ups was a variety of review and an introduction into new knowledge.

In all, math warm-up are good for both student and teacher. It provides that first 10 or so minutes of class to focus and initiate the "math brain." I know I will use warm-ups in my classroom.

Appropriate Use of Technology

Fraction Models

Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages. Additionally, there are length, area, region, and set models. Adjust numerators and denominators to see how they alter the representations and models. Use the table to keep track of interesting fractions. http://illuminations.nctm.org/ActivityDetail.aspx?ID=11

 

For my project, I had numbers and operations related to fractions and decimals. I copied and pasted the above description of the activity I found and used to relate to this topic. The mathematics that it reinforces is fractions, decimals, mixed numbers, and percents. As the numerator and denominators are adjusted, the student can see the related decimal, mixed number, and percent. The activity also displays a visual representation of the fraction. 

 

I thought the activity could be very effective as is addresses the kinestetic and visual learner. The technology offers a quick reference to fractions that may be difficult to picture in a students mind. It teaches the student what a mixed number or a percent looks like. This technology should be coupled with a supporting teacher lesson, using many types of materials to explain fractions as they relate to other numbers (ratios, percents, and decimals). If I were to teach the lesson, I would either do this activity as a warm up to the lesson, or after I taught an introductory lesson.

Standards, Standards, Everywhere

My group had numbers and operations and the associated standards. I found the NCTM standards/expectations for numbers and operations were pretty general as they covered 6 - 8 in general terms. There were a total of seven general standards for three grade levels. These were:

• work flexibly with fractions, decimals, and percents to solve problems;
• compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line;
• develop meaning for percents greater than 100 and less than 1;
• understand and use ratios and proportions to represent quantitative relationships;
• develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation;
• use factors, multiples, prime factorization, and relatively prime numbers to solve problems;
• develop meaning for integers and represent and compare quantities with them. 

In deciphering the above standards, I found action verbs being utilized such as, work, use, and develop. As one can see they are very general, but point to the overall concepts that students should know and demonstrate before going on to high school.

As I viewed the Common Core and CMP standards, I found they were more difficult to decipher. For example, for the number system in the common core standards, there were broad headings like "Apply and extend previous understandings of numbers to the system of rational numbers." After the heading there are more specific objectives or benchmarks for the student to achieve.

In the CMP standards, there were focused objectives for Number and Operation goals. It also had guided objectives in relation to standards and the texts being used for the material. In my middle school classroom, we are using Connected Math and I have found it user friendly and comprehensive. It breaks down the standards into daily student objectives.

Overall, I found the National Standards to be broad concepts and Common Core and CMP standards more focused. It was like a "funnel effect" for the standards, as I got to CMP, they were more focused and deliberate to daily or lesson objectives.