Number+Talks

Number talks are a great way for students to use mental math to solve and explain a variety of math problems. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide. A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum. A great place to introduce a Number Talk is during Number Corner. It is important to keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics. In fact, teachers need to spend only 5 to 15 minutes on Number Talks. Number Talks are most effective when done every day. As prior stated, the primary goal of Number Talks is computational fluency. Children develop computational fluency while thinking and reasoning like mathematicians. When they share their strategies with others, they learn to clarify and express their thinking, thereby developing mathematical language. This in turn serves them well when they are asked to express their mathematical processes in writing. In order for children to become computationally fluent, they need to know particular mathematical concepts that go beyond what is required to memorize basic facts or procedures.

Students will begin to understand major characteristics of number, such as:
 * Numbers are composed of smaller numbers.
 * Numbers can be taken apart and combined with other numbers to make new numbers.
 * What we know about one number can help us figure out other numbers.
 * What we know about parts of smaller numbers can help us with parts of larger numbers.
 * Numbers are organized into groups of tens and ones (and hundreds, tens and ones and so forth).
 * What we know about numbers to 10 helps us with numbers to 100 and beyond.

All Number Talks follow a basic six-step format. The format is always the same, but the problems and models used will differ for each number talk.
 * 1)  Teacher presents the problem. Problems are presented in many different ways: as dot cards, ten frames, sticks of cubes, models shown on the overhead, a word problem or a written algorithm.
 * 2) Students figure out the answer. Students are given time to figure out the answer. To make sure students have the time they need, the teacher asks them to give a “thumbs-up” when they have determined their answer. The thumbs up signal is unobtrusive- a message to the teacher, not the other students.
 * 3) Students share their answers. Four or five students volunteer to share their answers and the teacher records them on the board.
 * 4)  Students share their thinking. Three or four students volunteer to share how they got their answers. (Occasionally, students are asked to share with the person(s) sitting next to them.) The teacher records the student's thinking.
 * 5) The class agrees on the "real" answer for the problem. The answer that together the class determines is the right answer is presented as one would the results of an experiment. The answer a student comes up with initially is considered a conjecture. Models and/or the logic of the explanation may help a student see where their thinking went wrong, may help them identify a step they left out, or clarify a point of confusion. There should be a sense of confirmation or clarity rather than a feeling that each problem is a test to see who is right and who is wrong. A student who is still unconvinced of an answer should be encouraged to keep thinking and to keep trying to understand. For some students, it may take one more experience for them to understand what is happening with the numbers and for others it may be out of reach for some time. The mantra should be, "If you are not sure or it doesn't make sense yet, keep thinking.
 * 6) The steps are repeated for additional problems.

Similar to other procedures in your classroom, there are several elements that must be in place to ensure students get the most from their Number Talk experiences. These elements are:
 * <span style="font-family: Arial,Helvetica,sans-serif;"> A safe environment
 * <span style="font-family: Arial,Helvetica,sans-serif;">Problems of various levels of difficulty that can be solved in a variety of ways
 * <span style="font-family: Arial,Helvetica,sans-serif;">Concrete models
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Opportunities to think first and then check
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Interaction
 * <span style="font-family: Arial,Helvetica,sans-serif;">Self-correction