Mental Math Video Clips
Annotations
Disc One, Grades 1−3. Five Segments:
Segment 1: Gr. 1−2, Reinforce Ten-Frame Strategy
In this segment, the grade 1 students are developing strategies to help them learn the addition and related subtraction facts to 18; while the grade 2 students are refining and recalling addition and subtractions facts to 18 with a three second response using the ten-frame. The Ten-Frame Strategy is introduced by using dot plates to help the children develop a mental visual of a number,and then ten-frame mats are introduced to help them not only to visualize a ten-frame, but also to use “ten-frame” talk. The teacher uses activities such as placing a large blank ten-frame on the board, putting single digit numbers beside the ten-frame and having ten-frame talk about what they see and explain your answer. The chant activity provides reinforcement for the ten-frame strategy for addition and related subtraction facts using “ten-frame” talk by asking the questions, “How many do you see?”, “How many more?”, and “What do you know?”. Discussion for adaptations for students and an assessment activity are found in the segment as well.
Segment 2: Gr. 1−2, Introduce Make-Ten Strategy
The children, in this segment, are asked to discuss with each other strategies to solve 9 + 5 two ways. Discussion helps the children develop strategies for solving this question as well as develop understanding centering on a collection of things that can be grouped into tens and ones thus developing the concept of place value as well. The teacher used 9 + 5 for the introduction question to enable the children to have more success as 9 is close to 10. The children suggest strategies and explain to the teacher what they are thinking and why. As a reinforcement activity for the Make-Ten Strategy, the teacher uses two ten-frame mats on the overhead, asking students to use the ten-frame to explain how they would see sums such as 9 + 8 as 10 + 7. This activity is also a wonderful assessment again using ten-frame talk to find out “How do they know?” and “What do you know?”. The segment also provides a time frame, expectations for grade 1 and grade 2 students as well how the introduction and reinforcementoverlap.
Segment 3: Gr. 1−2, Assess Strategy Selection
There are three activities highlighted in this segment to assess strategy selection. The work on the ten-frame, used as a one of the models for these activities, is planned for September. The teacher explains that it takes children a long time to make the ten-frame their own. Activity one is a sorting activity. The children sort different facts into three strategies, under the headings: Ten-Frame, Doubles, and Make-Ten. Fact cards depicting these strategies are posted on the board and the children choose a fact card, placing it on a pocket chart under the correct heading for their card. They then explain their thinking.
The second activity is called Loop and Underline. Children match the strategy to the fact. The facts are on the board and the children decide if the fact they chose is a Make-Ten Fact or a Ten-Frame Fact. Depending on their strategy selection, they will draw a loop around a Make-Ten Fact and underline a Ten-Frame Fact. After selecting their strategy, they are asked to solve the fact and explain their thinking.
Activity three is a flash card activity. The teacher uses this activity to assess for a three second response and to see what strategy the children would use to solve the fact – ten-frame, plus one, make-ten, doubles, etc. It also helps get at strategy selection in more than one-way because strategy selection connects for children differently.
Segment 4: Gr. 2−3, Reinforce One & Two Digit Addition Using theNear Doubles Strategy
In this grade 2-3 classroom, the teacher is using fact cards to reinforce the doubles strategy, learned in previous grades, to make a connection to the doubles plus one strategy or the near doubles (one aparts) strategy. The teacher realizes the importance of making strong pattern connections with numbersfor children by asking children in grade 2 to add4 + 5 and in grade 3 add 40 + 50 using the near doubles strategy. Wait time is a critical factor for mental math. When beginning mental math, wait time should be longer than a three second response. A three second response by the end of grade 2-3 is considered mastery. Assessment is done through day-to-day observation, samples of student work and pencil/paper tasks. Acquisition of basic facts is evident in a student’s work, when working with higher numbers, the children become more efficient and do not need to count on their fingers as much.
Segment 5: Gr. 2−3, Reinforce One & Two Digit Addition Using theMake 10 Strategy
The key to teaching mental math strategies is to teach the strategy, make sure the children are comfortable with the strategy and then go to practice and drill. Children in this classroom are very comfortable with the next number plus one (one aparts)strategy, the doubles strategy, and the doubles plus one strategy, and are now ready to use these strategies to help them reinforce their understanding of the Make 10 Strategy. This strategy helps children to eliminate counting on their fingers. Using fact cards, the teacher shows the class the fact card and asks each grade level for an answer with an explanation of their understanding of the make 10 strategy. Assessment is through observation of work in the classroom; pencil paper tasks; discussion and use of models; and using journal writing to show “what are you thinking when solving the problem” and “how it should look”. Journal writing solidifies the “thinking of the strategies” for the children.
Disc Two, Grades 4−6. Six Segments:
Segment 1: Gr. 4, Reinforce Addition & Subtraction Using Make100 Strategy
In this segment, the grade 4 students are using the Make 100Strategy to practice addition and subtraction of three digit numbers. The teacher gives 2 three digit numbers and asks the students to add them together using the make100 strategy. They use whiteboards to show their answers. Whiteboards are non-threatening and students can erase their answers quickly. Using the whiteboards for this reinforcement activity allows the teacher to observe very easily who might be struggling with the strategy. The teacher writes down 2-3 answers she observes on the boards and asks the students to explain how they used the make 100 strategy to arrive at their answer. The children discuss the idea of compensation and how they use it to help them determine the answer. They are encouraged to ask themselves …. “Did I add/subtract too much, not enough or just the right amount?” Whiteboards are also used for some of the assessment activities as they allow for quick observation for the teacher and help students explain how they calculated their answers.
Segment 2: Gr. 6, Reinforce Two-Digit Addition Using Compatible Numbers Strategy
The students, in this segment, are working with numbers that make 10, 100 and 1000. They are also using numbers that are easy to add together such as whole numbers and some decimal numbers. The teacher the overhead as a way to present the problem and students use whiteboards to display their answers. Discussion helps the children develop strategies for solving these questions using “friendly numbers” or compatible numbers. They use one strategy but give the teacher four different ways to use the same strategy. The strategy is reinforced through addition and subtraction of the numbers as well as shifting parts of the numbers around to make them compatible. Students need to have good number sense for this strategy especially when working with decimals. Assessment activities for this strategy can be done using pencil/paper timed questions as well as answers observed using the whiteboards.
Segment 3: Gr. 4, Reinforce Doubles & Double/Double Strategies
This segment features the Double/Double Strategy. It is the strategy for Doubles, or the two times table, and then building on this strategy, the four times table is added. This strategy gives practice to multiplication facts and quick recall of multiplication facts. The students in this segment have constant discussion with the teacher on this strategy and are very capable when asked to describe this strategy. For example: 6 x 4 = 24, explain your strategy: Double the 6 and you get 12, then double the 12 and you get 24. Children need to know their addition facts for doubles in order to be to be able to have concept attainment of the Double/Double strategy.
The children practice on a daily basis, and must have a quick recall of their multiplication facts (a 3 second response). An activity that the students do in this segment is called Wacky Webs. They are found in Celia Baron’s Thinking Strategies: Multiplication, aresource provided for all grade 4 teachers by the Department of Education. When using this activity, there is a great deal of math talk taking place. Assessment for this strategy can be pencil/paper, facts on a flip chart, or white boards. The teacher will ask for an answer or ask the students to verbalize the strategy.
Segment 4: Gr. 4, Assess Multiplication Facts
The children in this segment have been working on mental math from the first day of the year and continue to build on their mental math strategies throughout the year. By the end of the year these grade 4 students know mentally their multiplication facts up to 9x9 within a 3 second response; can use the make 100 strategy mentally; are able to add together a chain of 3 numbers in a row, and are able to multiply numbers by 10. The teacher uses mental math strategies found in the provincial Curriculum Document, as well as John Van De Walle’s book.
In order to give multiplication meaning, the teacher uses context for the facts. She will give a fact and asks the children to tell her a story about it or she will give a story problem and they must give her the multiplication fact to match the story.
Flash cards are used throughout this segment. Formal assessment for multiplication facts can be done with a whole class or one-on-one using flashcards, pencil/paper tasks and asking students to give you facts that use a certain strategy. Informal assessment can be done on whiteboards and by asking questions of the students throughout the day. The teacher is very consistent in always asking the children to discuss and explain their thinking to her, the class or a partner when doing any activities.
Segment 5: Gr. 6, Reinforce Multiplication Using Front-End Strategy
The key to using this strategy is to multiply the parts and then put them back together. One of the challenges with this strategy is previous experience with multiplication. When students multiply a 2-digit number by a one-digit number they begin to multiply from the left. Using the front-end strategy, the children begin with the first number in the 2-digit number and multiply the “parts” to the right. Knowledge of their multiplication facts, place value and regrouping is important in order for students to understand this strategy.
The students in this segment are using whiteboards. They find it a challenge to remember the question and break it up into parts. They are allowed to write down the pieces that they would see in their “heads” to help them. When introducing this strategy, it takes 15-20 minutes and then the students practice the strategy everyday for about a week for their 5 minutes of mental math per math class. Initially, they are given a 10 second response time and then gradually as they become more efficient with the strategy, it is a 5 second response time.
Assessment is observation using the whiteboards, oral conversations with explanations and pencil/paper timed activities.
Segment 6: Gr. 6, Introduce Halve/Double Strategy for Multiplication
The children in this segment are using whiteboards to display their answers for the Halve/Double strategy. They are given nice numbers at first to double, and then larger numbers and they have to regroup. The teacher asks the students to explain their thinking and discuss the strategy they used. Some students are using compensation strategies to arrive at their answers.
The strategy of Halve/Double is introduced by halving first. When given a question the students look for an even number first, halve it and then double the second number. For example: 4 x 15, half of 4 is 2 and double 15 is 30, so 2 x 30 is 60. The critical point in this strategy is to look for an even number!
Introducing this strategy to the class depends on the students’ previous knowledge of multiplication facts and uses the . The teacher introduces the strategy to the class, they practice it and revisit it throughout the year. Assessment is observation, using whiteboards to display answers, activities and listening to math talk in other parts of math class.
Disc Three, Grades 7−9, Six Segments
Please read the descriptions to help you determine the order in which you might like to preview or show these clips. For example it might be appropriate to show or preview Segment 2 before Segment 1.
Segment 1: Gr. 8 Reinforce Addition and Subtraction of Fractions by Rearrangement
This segment illustrates how students can be encourages to rearrange and/or decompose (take apart) fractions and then regroup them as an efficient way to find the sum or difference mentally. Upon regrouping, the students use the “Make One” strategy as a way to determine the answer. Prior to this activity students have worked with Fraction Factory to help determine the sum or difference but this segment works mainly with symbolic manipulation. Suggestions are given for various ways to reinforce or practice mental computation with fractions. Students are given the opportunity to orally explain their work.Connections are made to the curriculum guide and what is stated there as grade 8 expectations.In this segment it is interesting to note how the teacher addresses a common mistake student make of run on work using an equal sign.
Segment 2: Gr. 8 Introduce Addition of Fractions using the Make One Strategy
This segment introduces the mental addition of fractions using the make one strategy. A problem is introduced and students are asked how they might solve it before the teacher offers to show the solution. This reinforces the idea that given the opportunity students will usually come up with the strategy on their own. Students start from the concrete and pictorial before moving to the symbolic. They are seen working with Fraction Factory and are given many opportunities to explain their thinking. The teacher gives clear directions on how she proceeds from this point until the first assessment on this activity. An added strength of this segment is the teacher’s comments showing the progression of the make one strategy through the grades with video clips from other grades included.
Segment 3: Gr. 7 Assess Addition of Decimals using the Make One Strategy
In this segment the teacheruses Power Point as a way to present examples for students to solve and then gives further questions as an assessment task. Students are given the opportunity to explain their strategies for solution of a problem. Students are encouraged to make connections to money and to approach their solutions in various ways. There are good messages on assessment in this segment such as the teacher stating how compares a new assessment task to a previous one to determine each student’s progress and uses that to help her make instructional decisions. The teacher has color coded the questions in the assessment. This allows students of varying ability levels to be successful as they attempt questions that are a certain color. The benefits of using technology are explained. Connections are made to the curriculum guide and the grade 7 mental math outcomes that she is addressing.
Segment 4: Gr. 8 Assess Halve/Double Strategy for Percentage
In this segment the teacher explains the progression of the halve/double strategy throughout the grades as well as explains the criteria and judgment skills needed to use this strategy. Students are given the opportunity to verbally explain their solutions. There are many good messages on assessment in this segment such as
-using various forms of assessment
-including items from previous topics
-the importance of the proper structuring and progression of tasks
to name a few. Suggestions for assessment of students with specials needs are also given.
Segment 5: Gr. 7 Introduce Make Zero Strategy for Integers
The make zero strategy is an important concept for integers and subsequently for algebra. Students use two colored counters to represent zero and then other integers in various ways. Students are given the opportunity to verbally explain their thinking as well as use the overhead to demonstrate their work to the rest of the class. The make zero strategy is then incorporated into the addition of integers, again with the students using the two colored counters. The teacher gives various suggestions on how to assess the zero principle.