Mastering Basic Facts (Early Operations)
Topic: ~Basic Number Operations
Lesson Plan – Mastering Basic Facts
Summary
Basic facts are problems that contain numbers which are less than ten. An example, in multiplication and addition, is 3+5 or 3X5, where both addends are less then ten. The same works for subtraction and division, for example 15-8=7. To master these basic facts means that a student can respond to an equation in less than three seconds, without using counting as a means to get the answer. Mastery then is to use a strategy, not counting, to quickly get the answer.
There are three steps involved in mastering basic facts, which are:
1) Help children develop a strong understanding of the operations and of number relationships. (a relationship, being, for example: 8+5=13 OR 8+2=10+the 3 left over from the five=13).
2) Develop efficient strategies for fact retrieval
3) Then provide practice in the use and selection of those strategies. A very effective form of practice is to use flash cards (p.140).
These strategies will give students an understanding for the math they are learning. This works better than the old fashioned rote learning model because students can make the math their own by coming up with strategies they understand.
This lesson plan, aimed at a grade 4 class, assumes that students can add and subtract and can do at least basic multiplication and division. The goal of this lesson plan is to advance students from helpful, but inefficient, methods such as counting to solve problems, to using fast strategies to solve problems. This will be done by explaining strategies and why they are important, then showing example strategies for each addition, subtraction and multiplication. Then the class will be given a division problem and be asked to get into groups of two and ask them to see what strategies they can come up with. They will share these strategies with the group, so all students can have different strategies to choose from to see if one works better for them than the others. The group then will be given dominoes with different basic facts on them and they can solve them using the strategies that work for them. The lesson will end with a debrief emphasizing the ease of using strategies over counting.
Title: Mastering Basic Facts
Content Standards: Numbers & Operations
Process Standards: Problem Solving & Reasoning
General Curriculum Outcomes [Atlantic Canada Mathematics Curriculum]:
B2 – Demonstrate an understanding of multiplication meanings and applications;
B3 – Demonstrate an understanding of the various meanings of division;
B9 – Demonstrate a knowledge of multiplication facts to 9X9;
B15 – Mentally solve appropriate addition and subtraction problems.
Grade Level – Subject: Grade 4 – Mathematics
Overview:
Children in grade 4 should be able to add and subtract, even if they count to do it. They should also be familiar with multiplication and division. They probably can not do these operations without counting or even understanding of how the operations work. This lesson will give students an understanding of how these facts work and strategies to make them easier to do. These strategies will eventually become automatic to students so they can focus on more complicated problems.
Purpose:
The purpose of this lesson is to reinforce multiplication and division and allow students to make solving these problems an internal, individual thought process. They will be able to make their own strategies or use ones that work for them.
Objectives:
As a result of this activity 80-100% of students will be able to:
1) Realize how strategies can make solving problems easier;
2) Create and apply strategies that work for them;
3) Have successfully applied strategies and mastered some basic facts.
Assessment:
1) Checklist (Appendix C) for individual assignment with dominoes
2) Quiz to check understanding
Resources and Materials:
Pens, pencils, dominoes, problems for board and quiz.
Activities and Procedures:
1) Introduction: I know you already know how to add, subtract and even probably know how to multiply and divide but I am going to show you how to make these problems even easier by creating strategies to solve the same problems. For example I know that you know the double problem 6+6=12. Well do you know what 6+9=?. Well to make this easy without resorting to counting we can use a strategy. For example 6+6+3+15. The 3 comes for the leftovers after you take the 6 out of the 9. Another example is 3X7=21. You can double the 7 for 14 and then just add another 7 for 21. Or 6X8=48 or 6X6=36 + 6X2=12 so 36+12=48.
Or try14-9=5 (make the 9 a 10 so 14-10=4 then add 1 to make up for the extra one you subtracted to make 10).
(5 Minutes)
2) Put some problems up on the board (Appendix A) and allow the students to get into groups of two to come up with strategies that would work to solve them.
(5 Minutes)
3) Get group back together and have students share their strategies. They can use the board if they want to.
(5 Minutes)
4) Give the students a pile of dominoes with basic facts on them and allow them to individually practice using strategies to solve them. Have 1-2 minutes to use dominoes for each addition, subtraction, multiplication and division.
(5-7 Minutes)
5) Have a short oral quiz to assess understanding. See appendix B. Call out a basic fact problem and have students write down the answer in less than three seconds. Call out 5-10 problems depending on time and see how many the students get right.
(3 Minutes)
6) Debrief – get feedback from students so that they can reflect on the activity and see what they liked and what worked and what did not for them to solve the problems using strategies. (2 Minutes)
Appendix A
Problems for the board (how many strategies can you come up with?):
7+9=16
17-8=9
7X8=56 (7X7=49+7=56)
36?9=4 (9 times what =36)
Appendix B
Quiz: (questions to call out and remind group to use strategies to answer in less than three seconds)
9+8=17
7+6=13
14-9=5
13-8=5
14-6=8
6X8=48
4X9=36 (9X2 + 9X2)
4X8=32
81?9=9
56?8=7
Appendix C
Name: Not Yet OK Super Comments
Working on problems
Attempting strategies
Problem Solving
CONTRIBUTOR: Sherri C
Meanings for Operations
Topic: ~Basic Number Operations
Summary
In the traditional classroom, understanding the meanings for the operations was a foreign concept. While some manipulatives may have been used to explain how certain rules work, children were taught that addition, subtraction, multiplication and division were for distinct and narrowly-explained series of equations that “everybody needs to know”. This, more often than not, resulted in teacher’s relying heavily on rote memorization of mathematical “facts”, such as the times table. As a result, children were often able to recite their times tables, but only for a limited time because there was absolutely no understanding of how multiplication really works and how it related to their everyday lives. After writing a test, children promptly forgot what they had learned.
In the modern understanding of how children learn, mathematics has taken on exciting new meaning in the classroom. Rote memorization has faded in favour of word problems, and children are now taught the meanings for the operation through a three-pronged approach: through models or manipulatives, symbols (as in the traditional classroom), and words. There three methods combined ensure that students are thinking about what the four operations really mean, and can apply the concepts in novel situations. In the lesson plan that follows, children should be able to examine through the use of word problems, several meanings for multiplication and division, and to recognize the relationship between the two. They will then be using manipulatives to help them understand the concepts from the word problems. In addition, the children will work on cross-curricular skills as they will be expressing their work in writing, thus showing that math can apply outside of simply equation problems.
Title: Division and Multiplication Problems
Content Standards: Meaning for Operations
Process Standards: Communication within groups, problem solving, and verbal expression.
General Curriculum Outcomes: [Atlantic Canada Mathematics Curriculum]
B1 Recognize several meanings for multiplication; B2 recognizes several meanings for division; B3 recognize the relationship between multiplication and division.
GRADE LEVEL/SUBJECT: 3/mathematics
OVERVIEW: Children in grade 3 have had a fair amount of practice in adding and subtracting and should be relatively familiar with early number concepts and number sense. Building on this previous knowledge the concepts of multiplication and division are introduced in such a way that children truly understand the concepts and not simply the rules. The following activity is designed to teach children about multiplication and division in a meaningful way, and demonstrate the intimate relationship between the two.
PURPOSE: The introduction of multiplication and division into a mathematics program can intimidate children who otherwise have been performing quite well. As with any new concept, it is easy to confuse children and prematurely turn them off of mathematics. The purpose of this activity is to slowly introduce the concepts of multiplication and division through word-based problems that children can relate too and to carefully evaluation comprehension to ensure that all students are comfortable with these concepts.
OBJECTIVES: As a result of this activity, 100% of the students will be able to:
1. Identify when to use multiplication
2. Identify when to use division
3. Write symbolic problems and answers for multiplication and division
4. Create novel situations where multiplication and division apply
ASSESSMENT: Recording sheet to be used during the lesson to verify if students are meeting the required comprehension of multiplication and division.
RESOURCES/MATERIALS: Paper, Pencils, Cups and Marbles (manipulatives), calculators.
ACTIVITIES AND PROCEDURES:
1. Begin by explaining that today we will learn about multiplication and division.
2. Divide the children into groups of two or three.
3. Introduce word problem number one (see appendix A) and explain how manipulatives are to be used.
4. Give children approximately five minutes to answer the question and explain how they used the manipulatives.
5. Discuss the answers. Did everyone get the same answer? How do we know it’s right?
6. Show how to express symbolically what the students just did in their word problem. Make certain to explain that the symbols do not change the meaning of what they just did it simply allows them to express it easily to others.
7. Present part two of the problem. Allow the children to show their answers with the manipulatives. What do we notice? If the numbers are inverted, do we get the same answer? Why?
8. Explain that we are going to try something a little different. Present word problem number 2 (see appendix A), and allow the children to work on in the same way they did on problem number 1.
9. Once the children have finished, discuss their answers. How do we know they are right?
10. Show symbolically how we would express what the children did in problem number 2. How is division related to multiplication?
11. Introduce part two of the problem. This will introduce the concept of remainders, an aspect of division they will deal with later in the year or in grade 4.
12. Time for a game! The game is called “broken division key” and the groups must discover two ways of figuring out sixty divided by five without using the division key. (There are three: 5+5+5+5+5+5+5+5+5+5+5+5=60; 5x12=60; 60-5-5-5-5-5-5-5-5-5-5-5-5=0. These can be reasoned out or done through trial and error).
13. Discuss the game and how it shows that division is connected to addition, subtraction and multiplication.
14. Wrap-up. Have the students create an interesting story in their groups that shows a multiplication equation. Have the students share their story and show how it can be symbolically demonstrated. Field any questions.
Appendix A
Problem #1 –
Part 1: Sheri has three bouquets of flowers. Each bouquet has 6 Calla Lily’s. How many Calla Lily’s does Sheri have in total? (3X6=18)
Part 2: Sheri meets 6 of her friends. She decides to give them three flowers each. Using the manipulatives, show what Sheri did. Was it fair? (6X3=18)
Problem #2 –
Part 1: Chris has thirty apples. He wants to put them in three boxes and have the same number in each box. How many apples are in each box? (30 / 3=10)
Part 2: What if Chris changes his mind and puts them in 4 boxes? (30 / 4=28 R2)
Title: Division and Multiplication Problems
SUPERClear understanding. Communicates concept in multiple representations. Shows evidence of using the idea without prompting.
ON TARGETUnderstands or is developing well. Uses designated models.
NOT YETSome confusion or misunderstanding. Only models ideas with help.
CONTRIBUTOR: Paul Vidal
