Mental Math

1. Mental Math A Life Long Skill A program developed by: Lynn Sinclair Grade 7 Teacher EPEC, Dartmouth, NS lsinclai@staff.ednet.ns.ca 462-8401 Ext: 143

2. The following power point is designed to assist teachers with the presentation and delivery of Mental Math at the Junior High/Middle School level. Please realize the Mental Math program is a work in progress. Not all topics related to outcomes are represented in the tests. Most tests have been student tested; however, I will apologize in advance for any errors or omissions you may encounter. Lynn

3. MENTAL MATHAN OUTLINE OF THIS RESOURCE • The program itself consists of 140+ mental math tests. • The program was created for a grade seven classroom, but can easily be adapted for other grade levels. • It is important to note that this program is meant to be a resource for teachers; however, classroom teachers need to plan and prepare in order to establish daily mental math routines for their students that will effectively promote the development and use of Mental Math strategies.

4. MENTAL MATHAN OUTLINE OF THIS RESOURCE • The following are guidelines and suggestions established by the Department of Education for implementation of a Mental Math program. • As well, an explanation and guidelines of how the mental math program I developed is utilized in my classroom. • This includes the preparation, lead-up and ground work required to administer the designed mental math tests.

5. WHY MENTAL MATH? • Calculating in you head is a practical life skill. • Mental math can make written computation easier or quicker • Proficiency in mental math contributes to increased skill in estimation • Mental calculation can lead to a better understanding of place value, mathematical operations, and basic number sense. • Mental math can be challenging and rewarding life-long skill. • OUR BRAIN IS WITH US WHEREVER WE GO, OUR CALCULATOR IS NOT!!!

6. MENTAL MATHOVERVIEW OF THE DEPARTMENT • Mental Math is an integral component of our mathematics program. • All students are to engage in 5 minutes of mental math per day. • Mental math strategies develop and improve over years of regular practice, therefore… • Mental math should be a planned program of instruction.

7. MENTAL MATHOVERVIEW OF THE DEPARTMENT • A variety of mental math resources have been provided by the Department to assist with planning for classroom teachers. • In particular, the mental math text resource entitled Mental Math in Junior High (Dale Seymour Publications) has been provided. • In addition, Mental Math in the Middle Grades (Dale Seymour Publications) is another excellent resource.

8. MENTAL MATHOVERVIEW OF THE DEPARTMENT • In order for students to complete mental math activities as suggested by the curriculum document and the Mental Math text resources, students must be proficient with the following key concepts: Numbers Sense, Estimation, Basic Fact Recall. • It may be necessary to review/teach if students do not have these essential understandings. • When completing an assessment of learning at the end of a strategy development, a three to five second response time is expected

9. MENTAL MATHOVERVIEW OF THE DEPARTMENT • Students must have multiple representations of numbers if they are to complete mental math activities. • They should be able to visualize manipulative materials in order to help them solve mental math questions. • Therefore, the use of manipulatives in your math classroom is critical to the development of mental math skills.

10. MENTAL MATHOVERVIEW OF THE DEPARTMENT • Strong mental math skills rely on students being able to see the mathematics in all five representations. • Connecting concrete, pictorial, verbal, symbolic and contextual representations is key to helping students develop strong mental math skills. • Mental math strategies can be taught, as well as, be developed and shared by students.

11. MENTAL MATHOVERVIEW OF THE DEPARTMENT • Students can often suggest a variety of mental math and estimation strategies. • As an alternative to teaching the strategies, have students attempt to solve problems independently to see what strategies they may develop on their own. • Sharing these strategies improves the development of thinking it through in other ways, and establishes that there is more than one way to attack a mental math problem.

12. MENTAL MATHOVERVIEW OF THE DEPARTMENT • Class discussion is a crucial component of teaching mental math. • By students developing and sharing strategies they are more likely to take ownership of the strategy. • Talking about the thought processes is the only way to know if students understand and can apply strategies.

13. GUIDELINES FOR MENTAL MATH IN MY CLASSROOM • The Mental Math program developed centers on a series of tests I have created. • Tests are based on class lessons and activities related to the achievement of curriculum outcomes and/or specific strategies developed from the text resource Mental Math in Junior High. • Mental math is DAILY, however, students do not necessarily complete a test daily. • Alternatively, students engage in activities to promote development and sharing of strategies that encourage success during testing.

14. GUIDELINES FOR MENTAL MATH IN MY CLASSROOM • The test themselves each consist of 10 questions • Students have 5 seconds to answer each question • Test questions are not on a timer for entrance, but can be if users desire. • Tests are self corrected by students and results are recorded by students.

15. GUIDELINES FOR MENTAL MATH IN MY CLASSROOM • Names go in for bi-weekly draws (1, 2 or 3 chances each test) • If students correct incorrectly, no chance to win during the next draw. • Any talking during the test, result in tickets for the day being eliminated. • If students have no red pen for correcting, then, no tickets for that day. • Unprepared for three classes (homework or materials) eliminates you from that weeks draw.

16. GUIDELINES FOR MENTAL MATH IN MY CLASSROOM • Strategies used are shared, discussed and reinforced after test completion. • Mental math lessons are consistently delivered during the first period of the day that I see each group of students. • Lessons last from approximately 5 to 15 minutes. • This establishes a classroom routine that the students become accustomed to.

17. GUIDELINES FOR MENTAL MATH IN MY CLASSROOM • The procedures I use for delivery of Mental Math in my classroom, work for me! • If interested feel free to use my ideas, or make adjustments based on what would work best for you. • Key to remember is that Mental Math MUST be a planned program of instruction, focusing on strategy development with connections to the outcomes • The designed tests are meant to be a complement to your mental math program, not your program itself.

18. GUIDELINES FOR MENTAL MATH IN MY CLASSROOM • Before administering any of the designed tests, students MUST have the opportunity to explore, practice and share skills that will promote confident mental math learners. • The following slides will provide an example of the ground work that leads to the testing of a mental math strategy in my classroom.

19. DEVELOPING A MENTAL MATH STRATEGY • The strategy “Searching For Compatible Decimals” (Lesson # 10 Mental Math in Junior High) encourages students to recognize pairs of decimal numbers whose sums equal a whole. • The leg work for this strategy begins early in September with a game played using a standard deck of cards. • The game modifies the Solitaire game where the player attempts to clear the playing field by making pairs of number with a sum of 13. The modification is using a sum of 10.

20. The playing field continues to a base of seven cards. The game is then played following the normal solitaire rules with the exception of using a sum of 10 as opposed to 13. The object of the game is to clear the playing field by making pairs of numbers that have a sum of 10, therefore, reinforces the mental math skill of making compatible numbers to 10.

21. DEVELOPING A MENTAL MATH STRATEGY • The game itself covers an early elementary mental math concept, but it is surprising the number of students that do not have this skill. • Students enjoy the game and it is a good ice breaker for the beginning of the year. • Once this game is played we talk about viewing the cards as 10, 20, 30 . . ., so making compatibles to 100, then, making compatibles to 1000 etc.

22. DEVELOPING A MENTAL MATH STRATEGY • This game sets the stage for several other games that are played using cards. • Another game is to have students (working in pairs) count out 10 cards and time each other to see how long it takes for them to find the sum. They soon realize, using compatibles makes the job quicker and easier. • The game can be extended to include more than ten cards or modified with sets of 10 cards pre-selected to make the task easier for students that may need modifications.

23. DEVELOPING A MENTAL MATH STRATEGY • Before introducing the strategy “Searching For Compatible Decimals”, it would also be necessary to ensure decimal understanding. • Prior to this strategy, students would engage in activities allowing them to build (using base ten blocks), recognize, illustrate, explain and express decimals in alternative forms. • Essentially, achievement of outcomes related to decimals, allow students to understand as well as visualize the decimals while trying to find compatibles.

24. DEVELOPING A MENTAL MATH STRATEGY • One activity used to reinforce multiple representation of decimal numbers is a card game created where students have to sort the cards based on the decimal they represent. • The cards can be used individually, with a partner or in small groups and various games can be played (limited only by the imagination of the user). • Students can simply sort the cards. • Play like 5 card rummy; the student who collects 5 cards that represent the same decimal wins • Concentration, Go Fish, etc. (examples of cards on next 2 slides)

25. One and three tenths 1 5.6 - 4.3 + 1 1 - 1

26. 3 • 10 130% 1 1.3 2.6  2 =

27. DEVELOPING A MENTAL MATH STRATEGY • Before covering the strategy of compatible decimals, we would cover Lesson # 6 of Mental Math in Junior High, which is “Searching For Compatibles”. • This strategy is a natural progression to compatible decimals, as it deals with identifying compatible numbers for multiples of 10 and 100. • As well, the strategy is easily extended to finding compatible money amounts, which tend to help students grasp the concept of compatible decimals easier.

28. DEVELOPING A MENTAL MATH STRATEGY • When presenting a strategy from Mental Math in the Junior High or Mental Math in the Middle Schools, I usually: • Present, review, discuss and practice the strategy using the information provided in the text. • Orally do the TRY THESE IN YOUR HEAD • Do a timed test using Power Builder A • Assign Power Builder B for homework or do a timed test using Power Builder B the following day

29. DEVELOPING A MENTAL MATH STRATEGY • Another activity to strengthen the concept of compatible decimals is a matching game. • Essentially, the game allows students to make pairs of compatible decimals. • Using the cards, student can simply find compatible decimals or use the cards to play a game of concentration with a partner(s) where they take turns turning over cards looking for a compatible pairs. • The slides that follow are examples of two sets of cards used.

30. 3.4 0.15 0.7 5.1 1.47 10.8 0.92 1.6 0.64 0.2 0.53 0.85 5.5 0.27 0.08 0.3 4.9 0.63 1.5 0.36

31. 3.4 0.15 0.7 5.1 1.47 10.8 0.92 1.6 0.64 0.2 0.53 0.85 5.5 0.27 0.08 0.3 4.9 0.63 1.5 0.36

32. 1.7 One and nine tenths 1.4 One and four tenths 1.2 One and two tenths 1.9 One and seven tenths

33. DEVELOPING A MENTAL MATH STRATEGY • Another option is printing Slide 30 as a game board and having students take turns placing two-sided counters on a pair of compatible decimals attempting to get four counters in a row. • Or, the slide can be presented via LCD/overhead and compatible pairs can be discussed • The cards can easily be adjusted to make more difficult or easier pairs of compatibles or to make cards reflect money amounts.

34. DEVELOPING A MENTAL MATH STRATEGY • Connecting concrete, pictorial, verbal, symbolic and contextual representations is key to helping students develop strong mental math skills. • Notice these card games do not have multiple representations, but . . . • With the previous work covered, students should be able to visualize manipulative materials and make connections that would allow them to solve the questions mentally.

35. Hopefully you will find this information beneficial. Feel free to make use of any or all of the resources provided. If you have any questions don’t hesitate to contact me and hopefully I’ll be able to help out. Happy Mental Mathing Lynn Sinclair