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Mental Math Grade 2

Mental Math Grade 2

Product Summery

Introducing Thinking Strategies to Students
Understanding our base ten system of numeration is key to developing computational fluency. At all grades, beginning with single digit addition,the special place of the number 10 and its multiples is stressed. In addition,students are encouraged to add to make 10 first, and  then add beyond the ten. Addition of ten and multiples of ten is emphasized, as well as multiplication by 10 and its multiples.
Relationships that exist between numbers and among number facts should be used to facilitate learning. The more connections that are established,and the greater the understanding, the easier it is to master facts. For example, students learn that they can get to 3 + 4 if  they know 3 + 3,because 3 + 4 is one more than double 3.

When introducing and explaining a thinking strategy,include anything that will help students see its pattern,logic, and simplicity. The more senses you can involve when introducing the facts, the greater the likelihood of success for all students.

When introducing and explaining a thinking strategy, include anything that will help students see its pattern, logic, and simplicity. The more senses you can involve when introducing the facts, the greater the likelihood of success for all students. Many of the thinking  strategies, supported by research and outlined in the mathematics curriculum, advocate for a variety of learning modalities. For example:
• Visual (images for the addition doubles)
• Auditory (silly sayings and rhymes) “4 + 4, there’s a spider on my door.”
• Patterns in Number
• Tactile (ten-frames, base ten blocks)
• Helping Facts (3 + 3 = 6, so 3 + 4 or 4 + 3 is one more. 3 + 4 = 7)
Teachers should also “think aloud” to model the mental processes used to apply the strategy and discuss situations where it is most appropriate and efficient as well as those in which it would not be appropriate at all.In any classroom, there may be several students who have already mastered some or all of the single-digit number facts. Perhaps they have acquired them through drill and practice, or through songs and rhymes, or perhaps they “just know them”. Whatever the case, once a student has mastered these facts, there is  no need to learn new strategies for them. In other words, it is not necessary to teach a strategy for a fact that has been learned in a different way. On the other hand, all students can benefit from activities and discussions that help them understand how and why a particular strategy works. This kind of understanding is key to number sense development.
Practice and Reinforcement
While the words drill and practice are often used interchangeably, it is important to consider the useful distinction offered by John Van DeWalle in his book, Teaching Student-Centered Mathematics Grades K-3 (Pearson Education Inc. 2006).
In his view, practice refers to problem-based activities (simple story problems) where students are encouraged to develop their own solution strategies. They invent and try ideas that are meaningful to them, but they do not master these skills.
Drill, on the other hand, refers to repetitive non-problem-based activities appropriate for children who have a strategy that they understand, like, and know how to use, but are not yet fluent in applying. Drill with a particular strategy for a group of facts focuses students’  attention on that strategy and helps to make it more automatic.
However, not all children will be ready for drill exercises at the same time and it is critical that it not be introduced too soon. For example, suppose a child does not know the fact 9+5, and has no way to deal with it other than to employ inefficient methods such as counting  on fingers or number lines.To give this child a drill exercise which offers no new information or encourages no new connections is both a waste of time and a frustration for the child. Many children will simply not be ready to use an idea the first few days and will need lots of  opportunities to make the strategy their own.

It is important to remember that drill exercises should only be provided when an efficient strategy is in place.

Once a strategy has been taught, it is important to reinforce it. The reinforcement or practice exercises should be varied in type, and focus as much on the discussion of how students obtained their answers as on the answers themselves.
The selection of appropriate exercises for the reinforcement of each strategy is critical. The numbers should be ones for which the strategy being practiced most aptly applies and, in addition to lists of number expressions, the practice items should often include  applications in contexts.
Drill exercises should be presented with both visual and oral prompts and the oral prompts that you give should expose students to a variety of linguistic descriptions for the operations. For example, 5 + 4 could be described as:
 the sum of 5 and 4
 4 added to 5
 5 add 4
 5 plus 4
 4 more than 5
 5 and 4 etc

Response Time
 Number Facts
In the curriculum guide, fact mastery is described as a correct response in 3 seconds or less and is an indication that the student has committed the facts to memory. This 3-second-response goal is merely a guideline for teachers and does not need to be shared with  students if it will cause undue anxiety. Initially, you would allow students more time than this as they learn to apply new strategies, and reduce the time as they become more proficient.

This 3-second-response goal is merely a guideline for teachers and does not need to be shared with students if it will cause undue anxiety.

 Mental Computation
In grade 1, children are introduced to one mental computation strategy,Adding 10 to a Single-Digit Number.
Even though students in kindergarten, first and second grade experience numbers up to 20 and beyond on a daily basis, it should not be assumed that they understand these numbers to the same extent that they understand numbers 0-10. The set of relationships that  they have developed on the smaller numbers is not easily extended to the numbers beyond 10. And yet, these numbers play a big part in many simple counting activities, in basic facts, and in much of what we do with mental computation.
Counting and grouping experiences should be developed to the point where a set of ten plays a major role in children’s initial understanding of the numbers between 10 and 20. This is not a simple relationship for many children to grasp and will take considerable time  to develop. However, the goal is that when they see a set of six with a set of ten, they should come to know, without counting, that the total is 16.
It should be remembered, however, that this is not an appropriate place to discuss place-value concepts. That is, children should not be asked to explain that the 1 in 16 represents "one ten" or that 16 is "one ten and six ones." These are confusing concepts for young  children and should not be formalized in Grade 1. Even in Grade 2 the curriculum reminds teachers that place-value concepts develop slowly and should initially center around counting activities involving different-sized groups (groups of five, groups of two, etc.) Eventually, children will be counting groups of ten, but standard column headings (Tens and Ones) should not be used too soon as these can be misleading to students.

The major objective here is helping the children make that important connection between all that they know about counting by ones and the concept of grouping by tens.

Your assessment of fact learning and mental computation should take a variety of forms. In addition to the traditional quizzes that involve students recording answers to questions that you provide one-at-a-time within a certain time frame, you should also record any  observations you make during practice sessions.
Oral responses and explanations from children, as well as individual interviews, can provide the teacher with many insights into a student’s thinking and help identify groups of students that can all benefit from the same kind of instruction and practice. 
Timed Tests of Basic Facts
The thinking strategy approach prescribed by our curriculum is to teach students strategies that can be applied to a group of facts with mastery being defined as a correct response in 3 seconds or less. The traditional timed test would have limited use in assessing this  goal. To be sure, if you gave your class 50 number facts to be answered in 3 minutes and some students completed all, or most, of them correctly, you would expect that these students know their facts. However, if other students only completed some of these facts  and got many of those correct, you wouldn’t know how long they spent on each question and you wouldn’t have the information you need to assess the outcome. You could use these sheets in alternative ways, however.
For example:
 Ask students to quickly answer the facts which they know right away and circle the facts they think are “hard” for them. This type of self assessment can provide teachers with valuable information about each student’s level of confidence and perceived mastery.
 Ask students to circle and complete only the facts for which a specific strategy would be useful. For example, circle and complete all the “double facts”.

Parents and Guardians:
Partners in Developing Mental Math Skills

Parents and guardians are valuable partners in reinforcing the strategies you are developing in school. You should help parents understand the importance of these strategies in the overall development of their children’s mathematical thinking, and encourage them to  have their children do mental computation in natural situations at home and out in the community.
You should also help parents understand that the methods and techniques that helped them learn basic facts as students may also work for their own children and are still valuable strategies to introduce. We can never be sure which ideas will make the most sense to  children, but we can always be certain that they will adopt the strategies that work best for them.
Our goal, for teachers and parents alike, is to help students broaden their repertoire of thinking strategies and become more flexible thinkers; it is not to prescribe what they must use.
Through various forms of communication, you should keep parents abreast of the strategies you are teaching and the types of mental computations they should expect their children to be able to do.

Our goal, for teachers and parents alike, is to help students broaden their repertoire of thinking strategies and become more flexible thinkers; it is not to prescribe what they must use.

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