Lesson+Plan+-+Math+Unit+Plan

Michelle Lapointe Unit Plan- Multiplication Dr. Bulgar toc =__Overview__= Objective: SWBAT pull from previous information to help them solve the problems, ex. addition and subtraction. SWBAT identify multiplication as repeated addition. SWBAT construct arrays, understand arrays and make mathematical sentences out of arrays. SWBAT use the information gained to solve problem solving activities. (SWBAT use multiplication to compare, write multiplication stories, and write to explain [in the lessons that are not explained here])

The objective of this unit is to teach the children multiplication in small steps. Students will be able to understand that multiplication is repeated addition and that multiplication is a quicker and easier way of getting to a solution. Students will be able to understand, create, read and relate arrays to multiplication by the end of this unit. Students will also be able to use this information to solve multi step problems that require the use of all the strategies that they have learned to show their mastery. Students will also be able to use this information to build on for future units including division for one. In addition to teaching these three lessons, this comprehensive unit will also include using multiplication to compare, writing multiplication stories, and writing to explain. It is important in math that students understand why something makes sense. Adding lessons such as writing multiplication stories allows them the deeper thinking in creating a problem, opening their eyes to why it works. Because they have to think about the math behind the problem for the answer, they understand why it works. I also think that adding a writing to explain lesson, reinforces this important aspect. It makes it a point to have children articulate the reasoning behind a problem, and how they reached their answer. Students will struggle later on if they fail to realize the reasoning behind mathematical procedures. Just doing it because that is what you memorized is only hurting the child in the future. Along these same lines, it is important that children complete inquiry based problems where they are challenged to think of solutions and strategies for the problem. In a study done in China, it showed that students presented with inquiry based tasks where more successful because the mathematical concepts behind it were more prominent. In classrooms where teachers ask prompting questions, instead of just giving answers, students are more successful. As a goal of any teacher it is to have your students be successful, using the instruction built in this unit plan will pave the pathway for student’s success in the future.

=Lesson One: Multiplication as Repeated Addition=

Standards: 3.OA.1.Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. //For example, describe a context in which a total number of objects can be expressed as 5 × 7.// Objectives: SWBAT recognize that multiplication is repeated addition, ex: 3 x 4 equals 4+4+4. (Multiplication is the process of adding equal sets together). They will be able to recognize a multiplication number sentence, and become acquainted with it. SWBAT recognize you can find the total number of items without having to individually count each one. To introduce the concept of multiplication.

Procedure: Give the students a do now problem that is easy and reinforces their addition skills. For example: Sara collects trinkets, she has 4 plastic elephants, and 4 plastic ducks, how many trinkets does she have in her collection?

Go over the problem. Then give out a problem solving question that will elicit repeated addition, which allows me to go over it is multiplication. Example Problem: Joey loves to collect coins. He has 5 groups of 6 coins. How many coins does Joey have all together?

Allow the children some time to work on the problem, about ten minutes. They will need to work individually, not in groups because I want them to each individually think about the problem. This is because we will be building upon this knowledge in the next two lessons, so they need a firm grasp on it. This is where I would allow the students to come to the board/document camera in order to discuss their strategies that they used to solve the problem.

Allow three strategies to be discussed briefly, or continue until repeated addition was brought up. After they are all explained, go back to the repeated addition one. State “I want to talk about this a little bit more.” I will explain that multiplication is repeated addition so when you add six five times (because there are five groups) it is 5 time 6 or 5x6. It is very important at this point that I write 5x6 and explain it means 5 groups of six.

At this point I will give other examples of this. 7x3 is seven groups of 3, and students can solve it by adding 3 seven times. Give several other examples of this to be sure that students understand the concept.

Hand out a worksheet with guided practice and independent practice on it. Due the first have of the worksheet with my students to concrete understanding. Then allow students to work on the independent practice part of the worksheet.

After allowing students to complete the second half of the worksheet go over it together, checking for understanding.

Wrap Up: Repeat what multiplication is and how we can find it. The different ways we can write multiplication sentences.

Assessment: The assessment will be how well children do on the independent practice. This will be an informal assessment based on observation. The second assessment will be of hands. As the children for thumbs up or down if they understand what they learned today. The third form of assessment will be in their homework. They will have a worksheet and based on their answers from that the next day, I will be able to see if they understand that multiplication is repeated addition and the different ways you can write it.

=Lesson Two: Arrays and Multiplication=

Standards: 3.OA.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. //For example, determine the unknown number that makes the equation true in each of the equations, 6 × 6 = ?// 3.OA.7.Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Objective: SWBAT take the previous acquired knowledge and apply it to the current lesson. SWBAT to understand that you can represent multiplication problems in visual ways, one of them being an array. SWBAT recognize that an array is a multiplication problem. SWBAT to see an array and write the correct multiplication problem, or translate a multiplication problem into a correct array.

Procedure: Give a short do now worksheet reviewing the previous repeated multiplication lesson. For example: What is the sum of 4x4? Show your work, how many marbles are there if Mr. T has three bags of with 7 in each? Write all the number sentences that represent this problem.

Go over the Do Now worksheet making sure to review all of the strategies taught and learned the day before.

Next, hand out a problem solving worksheet to be completed. This worksheet will require the students to pull from previous taught strategies and their own strategies to complete. The worksheet will have a problem like: What is 5x6? How can you represent this by drawing a picture? How many different ways can you show 5x6 in pictures?

Manipulatives will be available to the children in this lesson Go over the worksheet after about ten to fifteen minutes. Give the students an opportunity to show all of their strategies to displaying visually their ideas. It is expected that since I taught them repeated addition that the children will put groups separated not arrays.

After the children share their ideas go back to arrays. Talk about how there is a systematic way to visually show multiplication problems that is universal. Write 5x6 on the board from the worksheet. Explain that the 5 is how many rows there are and the 6 represents the columns. Then the children can count them, before they have memorized their multiplication tables, or they can add in patterns. It also reinforces the repeated addition that was in the previous lesson.

Give out another worksheet with guided practice and independent practice on it. Manipulatives will still be available. Do the first half of the worksheet with the children creating arrays, then the second they will do on their own. When they are done they are to confer with the person sitting next to them.

We will go over the worksheet and use it as a wrap up. Go over homework directions.

Assessment: Like previously assessment will be informally during independent practice and also their performance on their homework worksheet.

=Lesson Three: Problem Solving= Standards: 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

Objective: SWBAT use the knowledge of repeated addition and arrays to solve a multi-step word problem. Students will use a specific strategy correctly. SWBAT to explain how they reached their answer and why that is the correct answer.

Procedure: Give the students a worksheet when math period starts. Read over the instructions and the questions on the worksheet. Have several problems on there to allow for different situations (the worksheet will have problems that elicits information and skills taught in previous lessons, including subtraction and addition, in conjunction with multiplication)

Allow the students to work on the worksheet for about 20 minutes. Then go over the worksheet a few problems at a time.

Explore all the options for students to use to solve the problem. Not limiting the strategies but trying to focus on the ones taught previously. (Some ways don’t always work for everyone)

Use this opportunity to clarify any questions that may arise about previous lessons that students did not ask them. Give extra examples if needed.

Spend the majority of the time going over the problems and stressing the reasoning behind the math.

Wrap Up: Go over all strategies used and generalize them so students can apply them to any situation. Go over homework. Homework will address problem solving as well.

Assessment: Assessment will be informal again. Taking notice while going over the worksheet after students complete it. Also I will collect this worksheet so that I can see student’s work when I review them to see what I need to go over. Instead of moving on if need be I can create small groups for extra help the next math lesson. Homework will also be collected and be a assessment of the skills taught.

=ASSESSMENT=

The assessment will be designed to be a couple word problems with multiple steps eliciting all the information that was taught in this unit. The word problems will cause students to take apart the problem and search for information that will make them to create an array. It will also ask the students to write the multiplication sentence in different ways, such as 4+4+4 or 4x3 or 3x4. A major part of this problem will ask the children why they know that is the correct answer, and how they found it. The reasoning behind shows understanding. Children will be responsible for showing all of their work through out the problem. After the basics of the problem have been addressed, children will have to adapt to a change in the problem. For example if Grandma baked cookies and one more tray of cookies came out of the oven, how would they need to adjust their array to show the additional cookies, what are the new number sentences that you would need to create, what is the new total and how much more is that from the original. The will also be expected to be able to compare the two problems. All in all, other than the correct answers I will be looking specifically for repeated addition, arrays, multiplication number sentences, and problem solving skills and how they all connect written out or clearly displayed. If students can correctly display these mathematical concepts on this assessment I know that they have met my objectives. They will be able to move without trouble to the next unit in their math curriculum, which would include looking into multiplication factors and their patterns or division depending on the school district and classroom teacher. In my classroom I would go over patterns in multiplication, as well as memorization then move on to division.