• Caroline Farkas

“New Math” Terms Every Teacher Should Know

Updated: Apr 13

Raise your hand if you walked into your first teaching job and you felt like they were speaking a foreign language in math. It’s pretty common. Many of the math strategies and terms that are being used in classrooms today are completely different from how we learned math. Whether you are specifically teaching those new math terms or your students learned them earlier in their education- here are some math terms that you should be familiar with in upper elementary education teaching the “new math”.

- Decomposing- Decomposing a number is breaking a number down into parts (typically by place value in elementary) in order to solve a problem. Decomposing can also be called expanded form. An example of this is 1,245 decomposed is 1000+200+40+5.

area model in multiplication in the color blue multiplying 6 by 1,242

- Box Multiplication- This is also commonly referred to as area model multiplication. A student will decompose a number by place value and then multiply it using a box model or area model in order to solve. The model is extremely helpful because it gives students a visual way to break down larger multiplication problems into smaller pieces.

- Math Visuals- Visuals are crucial in learning mathematical concepts for all students. It helps students understand a problem, show their thinking, reason with other students, and grapple with more difficult concepts. Ultimately, visuals can help students take something that can seem very abstract to them and turn it concrete. Visuals at the elementary level can include math manipulatives, number lines, area models, ten frames, and math clipart. Visuals can be especially helpful for students with learning difficulties or ELL students.

Math Manipulatives for Upper Elementary Math

-Math Manipulatives- These are tools that are hands-on objects that students can arrange or work with in order to solve a problem. Math manipulatives can include cubes, beads, counters, base-ten blocks, or math clipart.

- Growth Mindset- This is huge in math education. It’s the idea that students believe they are able to develop good math skills through learning and growing. Many teachers teach it by telling students to add the word “yet” at the end of the sentence. For example: Instead of saying “I don’t know how to solve this problem” change it into “I don’t know how to solve this problem yet”.

- Mental Math-This is the process of using a variety of skills in order to solve a problem in your head with mental computation or estimation.

- Array- An array is a math visual used in multiplication. They are dots or objects arranged in columns or rows to help students explain multiplication or division. For example, an array of 2x3 would have two rows of three dots.

- Landmark and friendly numbers are both very similar to each other. The end goal of these strategies is to have students turn numbers into ones that would be easier to work with.

  • Landmark Numbers- Are numbers that students are familiar with such as 10, 25, 50, 100, 125 etc. Students will change a number into a landmark number in order to solve.

Example: 123 + 50. Students would turn 123 into a “landmark number” of 125 that they

could easily add to 50. 125 +50 = 175 . They would then subtract the 2 back out to make


  • Friendly Numbers- Are very similar to landmark numbers, but are numbers that end in zero (10, 20, 50, 100, etc).

Example: 18+25, Students would change the 18 to the friendly number of 20. They would

add 20 +25 = 45 and then subtract the 2 that was added to get 43.

Both friendly numbers and landmark numbers can be used with math manipulatives or number lines to make learning more visual for students. The strategies around these terms can vary widely, but the point is to allow students to be flexible with numbers in order to make solving problems with them easier.

What are tens frames? Tens frames showing 8 added to 5.

- Making Tens- This is a strategy typically used in lower elementary. It can help students see the relationship between numbers and reinforce our base-ten number system. It is often accompanied by base-ten blocks or tens frames to help students visually see the regrouping of numbers. The goal is to have students make a group of ten in order to solve.

Example: 8+5, Students would turn the 8 into a 10 by taking 2 from the 5. They could then easily see that 10 + 3 equals 13.

What other math vocabulary were you unsure about? I’d love to hear!

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New math terms every teacher should know in purple.

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