The Common Core Standards focus on rigor as conceptual understanding, procedural fluency, and application of concepts. Fluency described by the NCTM Principle and Standards of School Mathematics (2000) defines computational fluency as having efficient, flexible and accurate methods for computing. Here is a list of the fluency expectations in grades K-8.
Many people still confuse fluency with speed. Students are drilled with timed tests to memorize facts. This is not the same as developing fluency. Jo Boaler has updated her article "Fluency without Fear". This article provides an explanation of what fluency is and how we can help students build fluency. NCTM has published a couple articles that give ideas on how to assess fluency. Assessing Basic Fact Fluency_ by Gina Kling and Jennifer Bay-Williams provide great fluency assessment ideas.
The Common Core Standards require fluency with mental computation, not just pencil paper computation. One strategy to help students practice mental computation is Number Talks. Check out a few videos from Math Solutions.
Smart notebook file for ten frame. Smart notebook file for dot patterns.
K-2
Comparing and Ordering Number - No more alligator teeth. The Standards require letting go of mnemonics and "tricks" to get students to an answer. Sticking with mathematics and the language of the discipline will help build understanding in students. One of those mnemonics is alligator teeth. What can we do to get away from these tricks?
We have discussed that this method of alligator teeth does not really help students understand the math. Sticking with appropriate math vocabulary and math tools will help students remember. Keeping the strategies consistent across the grade levels. The tool to use is a number line!
Students need lots of practice with counting and hands-on activities. This link provides hands-on activities with dot patterns and ten-frames to build fluency. http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf
Many people still confuse fluency with speed. Students are drilled with timed tests to memorize facts. This is not the same as developing fluency. Jo Boaler has updated her article "Fluency without Fear". This article provides an explanation of what fluency is and how we can help students build fluency. NCTM has published a couple articles that give ideas on how to assess fluency. Assessing Basic Fact Fluency_ by Gina Kling and Jennifer Bay-Williams provide great fluency assessment ideas.
The Common Core Standards require fluency with mental computation, not just pencil paper computation. One strategy to help students practice mental computation is Number Talks. Check out a few videos from Math Solutions.
Smart notebook file for ten frame. Smart notebook file for dot patterns.
K-2
Comparing and Ordering Number - No more alligator teeth. The Standards require letting go of mnemonics and "tricks" to get students to an answer. Sticking with mathematics and the language of the discipline will help build understanding in students. One of those mnemonics is alligator teeth. What can we do to get away from these tricks?
We have discussed that this method of alligator teeth does not really help students understand the math. Sticking with appropriate math vocabulary and math tools will help students remember. Keeping the strategies consistent across the grade levels. The tool to use is a number line!
Students need lots of practice with counting and hands-on activities. This link provides hands-on activities with dot patterns and ten-frames to build fluency. http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf
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Addition Strategies
Students should develop understanding and strategies to learn their facts. The progression of strategies can involve one more and one less, making ten's, and doubles. Once students understand single digit addition, then using place value strategies build the understanding to lead to fluency for multi-digit addition. The strategies can be practiced during the Number Talks with two and three digit addends. Along with making tens, doubles, decomposing into place value components, compensation can be integrated. Remember to practice these strategies daily. Algorithms call for a set of procedures to be followed. We will focus on moving left to right and right to left. Partial Sums - left to right Traditional - right to left Strategies for Adding 798 + 697 |
Multiplication Strategies
Again, students should develop understanding and strategies. The strategies for multiplication are related to addition strategies.
Division Strategies
Partial Quotients - two digits divided by two digits Here is an example showing partial quotients. I have compared this to the Math in Focus, 5th grade, page 83. Once the page opens, just click on the play button. Here is another video building the area model and showing the partial quotients to the side - Division using area model and partial quotients. This is 3 digit divided by 2 digit. This problems is a 4 digit divided by a 2 digit. |
Subtraction Strategies
