When Laura Kretshmar of Lighthouse Community Charter School in Oakland, California, told her sixth graders that they
were going to have a number talk, smiles, claps, and “Yessss!” were heard from the students as they waited in anticipation. Laura invited students to share expectations for number talks and move closer and sit on the carpet if they needed to.
In Laura’s classroom, number talks are short, strategic conversations that focus on flexible mental problem solving as well as strategy sharing and critiquing. Strings of related equations are used to help students see patterns and help them transfer strategies from one equation to the next.
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Before beginning, Laura took a obtain at low price generic pills online – http://chezee.mhs.narotama.ac.id/2016/11/30/obtain-at-low-price-generic-pills-online/ pause and look around the room while her students sat in excited anticipation, then wrote the first equation up on the whiteboard:
160 ÷ 8
The room was full of intense looks gazing upward in thought,, whispered numbers, furrowed brows, and fingers moving to keep track of numbers. After a moment, Laura said “Raise your hand if you have a solution.” Hands shot acquire cheaply generic pills without prescription – http://kartika92.blog.unsoed.ac.id/2016/11/30/acquire-cheaply-generic-pills-without-prescription/ into the air from all directions. Laura picked a student, who offered up 20 as the solution.
Instead of saying correct or incorrect, Laura said, “Other solutions?” the air was void of hands, so Laura inquired, “What’s your reasoning for 20 being the solution?”
“I used proportional reasoning,” replied the student. “I knew that 160 was 10 times bigger than 16, so since 8 x 2 equals 16, then you would have to multiply 2 by 10 before multiplying it by 8 to get 160.”
Laura recorded the strategy in numbers on the board and asked if students agreed or disagreed. Then, she said, “Who has a different strategy?” Two more students shared before Laura wrote the next equation up on the board.
In less than 15 minutes, the students explained, discussed, and debated strategies for the following string:
160 ÷ 8
400 ÷ 8
80 ÷ 8
496 ÷ 8
After each problem, students talked about their solutions and methods for solving the problem. They also analyzed how the problems in the string were related, and how that could help them be more efficient mathematicians. Throughout this time, Laura recorded strategies on the whiteboard while calling on volunteers to share and asking open ended questions to guide the conversation. For most of the number talk, the students responded to each other by making conjectures, explaining strategies, with one another.
At the end of the discussion, students named many strategies for division: using multiplication to solve because it is the inverse of division, breaking apart the dividend, and using their knowledge of powers of ten and known multiplication facts.
Laura’s role in the number talk was not to walk students through one specific way to solve a division problem, but to encourage flexible problem solving and strategy sharing between students. Laura used questions to foster student interaction and participation. The discussion that Laura facilitated exposed students to multiple strategies which could potentially lead to a solution, and gave the kids opportunities to think critically about what was presented.
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Resources for Planning Number Talks:
Number Talks: Helping Children Build Mental Math and Computation Strategies
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