How Do I Teach 6th Grade Math Vocabulary?
'Doing' math isn't enough; students must also be able to 'describe' how to solve math problems, which requires using math vocabulary. Math vocabulary is useful because it provides a common language and can ensure that explanations are accurate. Therefore, math vocabulary is an important part of teaching math.
Teaching Math Vocabulary to Sixth Graders
Vocabulary in Every Lesson
Because math vocabulary is essential for good math communication, it is important to include it in every math lesson. This includes teaching new vocabulary, using accurate terms whenever discussing problems and playing vocabulary review games before tests.
Teach Vocabulary First
Research has shown that students grasp concepts better if the math vocabulary has been specifically taught (http://usablealgebra.landmark.edu). Therefore, when you teach the vocabulary at the beginning of a lesson, as an introduction to a new concept, you're preparing your students to use the new information to the fullest. When you model a new concept, label the work with the terms. For example, before you show a problem such as 48 ÷ 6 = 8, write Dividend ÷ Divisor = Quotient. Then write the problem with the numbers under the correct term.
Tie New Concepts to Familiar Ones
No matter what grade students are in, they already know facts that can be compared to new math information. Find ways to tie the new concepts to what they already know to make the new information less intimidating. For instance, if you're presenting fractions, they may already know that four quarters or ten dimes are the same as one dollar. If the new information is about parallelograms, they may already be familiar with the parallel bars that athletes use.
Use Repetition
Most students need to hear a word 1011 times in order to learn it; if the students have a learning disability, that number rises to as high as 40 (http://usablealgebra.landmark.edu). Expose students to the words through different contexts. Repeating the terms every single time you do a problem is helpful because you're giving the students repeated exposure to the term; however, that's only one medium. Other contexts might include having the students:
 Write the definition in their own words
 Draw pictures depicting the term
 Play games that use the terms
 Read or write stories that include the term
 Sing songs about the terms
 Make their own flashcards or notebook of the terms
Compare and Contrast Terms
Showing how a new term is similar or different to other terms is also helpful. For example, compare rational numbers with irrational numbers. A rational number can be written as a simple fraction or ratio (e.g., 2/3). An irrational numbers can't be written so simply, and is written as a decimal number.
Probably the best known irrational number is pi, which is approximately 3.1415. In this comparison, have the students write examples of other rational numbers (e.g., 13/3) and irrational numbers (e.g., the square root of two, which is approximately 1.4142).
Use Terms in Other Contexts
Encourage students to use the terms in other contexts. For example, at lunch time they might say something like, 'The sum of the sandwiches in the lunch room is 49.' Or after gym, 'The difference between the 3 baskets John made and the 5 Eric made is 2.' Or 'We had pizza last night and I ate 1/4 of it.'
Use the Proper Labels
Descriptive phrases like turning the fraction upside down for reciprocal sometimes become substitutes for the real vocabulary term. This method may not be beneficial because students are defining of word rather than using the word itself. The teacher must use  and expect the students to use  the correct terms consistently.
Include Vocabulary in Tests
Just as it's important that the students understand how to do a math operation, it's important that they can identify what that process is called. For example, students should know how to add 23 + 14, as well as the terms 'sum' and 'addition'. To be sure they know math vocabulary, include it in math tests. This will help ensure that they are able to accurately communicate mathematical concepts.
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