Estimate...then Calculate

Math Practice Standard #5 includes estimation as an important skill our students should be using regularly.  “Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem.”  Students build number sense by estimating and it provides them with a way to check their answers for reasonableness (Cochran & Dugger, 2013).

The use of estimation is mentioned directly in several of our content standards.

• 3^rd Grade - Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [3-OA8]
• 4th Grade - Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  [4-OA3]
• 5th Grade - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5-NF2]

It is important that students develop the habit of estimating before calculating.  When they progress to more complex calculations such as 11.2 + 19.75 + 3, having the estimate of 33 (10 + 20 + 3) to reference will help them to quickly determine if an error was made when lining up the numbers. When students multiply and divide fractions and decimals, checking the estimate for reasonableness can eliminate many errors.   For example, in the calculation of 8.75 x 31.3, the ability to see that the answer should be around 270 (9 x 30) can help a student who may have placed the decimal point in the wrong place.  Students should even estimate when solving problems such as 7/8 x 3; 7/8 is close to a whole and 1 whole x 3 is 3.  The answer should be close to 3. 

Please continue to remind your students to estimate before they calculate, and to use the estimate to check answers for reasonableness.  If there is anything I can do to help you with this, please let me know.

Sources:

Cochran, J., & Dugger, M. H. (2013). Taking the Guesswork out of Computational Estimation. The Mathematics Educator, 60-73.

Number Talks - Refining our Practice

Mrs. Camara's class was highly engaged in this number talk emphasizing grouping strategies.

Number talks provide our students with opportunities to calculate with flexibility,  efficiency, and accuracy.  According to Sherry Parrish in her book Number Talks, mental math number talks are a “pivotal vehicle for developing efficient, flexible, and accurate computation strategies that build upon the key foundational ideas of mathematics such as composition and decomposition of numbers, our system of tens, and the application of properties".

Mrs. Bramlett captured students' division strategies by sketching open area models.

Refining our Number Talks

There are several strategies that can improve the effectiveness of number talks:

•  Designated Location - Parrish suggests that teachers have a designated location for number talks where the teacher is in close proximity to students, for observations and interactions.  She stated, “While many teachers wish to have their students remain at their desks, I have found that it is easier to build a cohesive community and a focused discussion when students shift away from their regular routines and are removed from typical desk distractions.”
• Wait Time – It is important to allow the appropriate wait time (until most students have an answer).  If students have a “thumbs up”, they should be thinking of other strategies while waiting.  If you have provided the wait time, and students are still pondering the problem, have students turn and talk to find a strategy together.
•  Student Communication – It is critical that all students be engaged in communication throughout the number talk.  Students can be engaged in these discussions through strategies such as restating strategies used by others, and participating in turn-and-talk to arrive at a strategy.
• Teacher Role – Since the goal is to have a classroom conversation, the teacher’s primary role is that of facilitator, as well as listener, questioner, and learner.  It is important that the teacher record each child’s thinking on the board as the child is talking.  Visual models such as area models, number lines, etc. can be used.   

Professional Development - 10/1/14

Thank you for your participation in our professional development today.  We learned about the importance of teaching academic vocabulary (Tier II words), and the impact it will have on student achievement in all content areas.  We discovered today that math and science problems contain many Tier II words.  If students do not know these words, it may prevent them from understanding many problems.  We also talked about how often these words are used in directions provided to students.

Reminder:  A new word will be introduced each A Day by the homeroom teacher (beginning October 6th). Brief activities (1-2 minutes) will also be facilitated by the homeroom teacher on days B-H.

We are all a critical piece of Academic Vocabulary Instruction.