Courtney Britz Multiplication Unit Lesson 5 Objectives: Students will: • Express multiplication problems through multiple means • Solve multiplication problems to discover a missing variable • Record their process in solving multiplication problems Materials: • Mystery number power point • Multiplication record sheet • Computer • Smartboard if available • PowerPoint • Construction paper • Lined paper • Checklist for writing • Checklist for poster • Three multiplication problems per group Assessment: • Multiplication record sheet • Written explanation and description of multiplication • Multiplication poster Instructional Plan: • Who can tell me what we have been solving for in all of our previous multiplication problems? (the product) • Well today’s lesson is going to be a little different. Today we are going to be solving for mystery numbers. In some cases these mystery numbers are the factors in our multiplication problems. The numbers we are solving for will be represented in the problem by a star. • CREATIVE HOOK ABOUT MYSTERY NUMBERS • Bring up Mystery number power point. o Here is an example. 5 x ★ = 25.  In this problem what do we know? • We know that one of the factors is 5. • We also know that the product of the two factors is 25.  So how are we going to figure out what our mystery number is? • What do you guys think: Possible answers o Skip count o Set up an array o Draw a picture  Depending on the multiplication problem we are given any of these strategies can be useful. • To solve this problem lets start with skip counting. What number do we need to skip count by? •
•
o 5, 10, 15, 25 o How many times did we skip count by 5 to get to 25. o 5. So we now know that 5 x 5 is 25. For this problem our mystery number is 5. • Lets solve the same problem using the array method. (Pass out array grids and manipulatives and bring up the array slide on the PowerPoint) o We know that our first number is five. How should we display this number using our array grid? Call on students to answer and visually show answer on PowerPoint. o Now what do we have left. We know that our answer is 25 and we know that within our array each column has to have the same number. Talk to your partners and discuss the next step. Show your thinking on your array. o After students have answer shown on their arrays ask a student to share their thinking and the answer he or she came to.  Again show on the PowerPoint the correct display. • Lastly, we can solve this problem by thinking about equal groups. o Place your array grids aside but keep your manipulatives out. o Again lets work through the problem 5x★=25  This time, work in your pairs to discover how we can show 5x★=25, by thinking about 5 groups of our mystery number is equal to 25. o On the PowerPoint show the 5 groups as represented by circles. o Use the manipulatives to determine how many are needed in each circle to make 5 equal groups. o As student finish provide feedback and display the answer on the PowerPoint. As we have just proved any one of the strategies we have learned throughout this unit can be applied to solving multiplication problems. Including more complex problems where we are solving for mystery factors. Today you will be working though a variety of problems and solving for mystery numbers which will always be identified with a star ★. o Each groups will be solving three different multiplication problems. Groups will be differentiated. o You will be recording your work on a multiplication record sheet. o On this record sheet you will write the problem you have been given to solve, the repeated addition equation, a visual showing ___ groups of ___ , an array, and the mystery number. After solving for the mystery number, and displaying your understanding in the required ways, students will be given another multiplication problem to solve. They will use this problem to complete the summative assessment for this unit. The students are required to individually create a unique representation of their multiplication problem. Students must show multiplication problems in the visual and mathematical ways discussed on a poster board. • After creating their poster, students will write a small paragraph detailing how they worked to discover the mystery numbers. Furthermore students can reflect upon which strategy they benefit most from and identify any areas of difficulty. Standards Common Core: Operations and Algebraic Thinking Represent and solve problems involving multiplication and division 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 8x?=48, 5=__÷ 3, 6x6=? NCTM: Algebra Standard for Grades 3‐5 Represent and analyze mathematical situations and structures using algebraic symbols Represent the idea of a variable as an unknown quantity using a letter or symbol Express mathematical relationships using equations Use mathematical models to represent and understand quantitative relationships Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions •
Multiplication Record Sheet Multiplication
Problem
Repeated Addition
Groups
Array
Answer
Multiplication Problems for Group 1
1. 7x
2.
3. 5x
= 56
x4=36
= 30
Multiplication Problems for Group 2
1. 2x
2.
3. 6x
= 18
x4=24
= 30
Multiplication Problems for Group 3
1. 7x
2.
3. 6x
= 70
x9=81
=48
Multiplication Problems for Group 4
1. 5x
=25
2.
x 2= 12
3.
x6= 42
Checklist for Poster
Students’ Name: ________________
Student correctly displays multiplication problem as repeated addition _____/10
Student correctly displays multiplication problem as an array
_____/10
Student correctly displays multiplication problems using equal groups
_____/10
Student uses materials and manipulatives to show information
_____/5
Students’ work is organized and easy to interpret
_____/5
Likert Scale for Writing
Students’ Name: ________________
Writing contains few grammatical errors0 1 2 3
Writing contains few spelling errors0 1 2 3
Writing has two paragraphs0 1 2 3
Each paragraph has at least 5 sentences0 1 2 3
Students provide details about repeated addition0 1 2 3
Students provide detail about the array method0 1 2 3
Students provide detail about equal groups0 1 2 3
Student reflects about most helpful strategy0 1 2 3
Student reflects about mathematics0 1 2 3
Student uses complex and simple sentences 0 1 2 3