ALEX Learning Activity

  

Slides & Pies - Multiplicative Comparison Lesson

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

You may save this Learning Activity to your hard drive as an .html file by selecting “File”,then “Save As” from your browser’s pull down menu. The file name extension must be .html.
  This learning activity provided by:  
Author: Samantha Wallace
System:Limestone County
School:Cedar Hill Elementary School
  General Activity Information  
Activity ID: 2901
Title:
Slides & Pies - Multiplicative Comparison Lesson
Digital Tool/Resource:
Slides & Pies Slideshow
Web Address – URL:
Overview:

Students will take a deeper dive into word problems to gain a firm understanding of multiplicative comparison.  They will compare problems using additive vs. multiplicative comparisons and problems where either the set or the product is unknown.  The activity also includes a matching game for students to match equations, models, and comparison statements. 
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 4
1. Interpret and write equations for multiplicative comparisons.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • When given a multiplication equation, create and explain a corresponding verbal multiplicative comparison statement.
    Example: interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 35 is 7 times as many as 5.
  • When given a verbal (written or oral) representation of a multiplicative comparison, write and solve the related multiplication equation.

    • Example: Sue has 7 cards and Joe has 5 times as many cards as Sue. The student will write 5 x 7 and accurately find the number of cards Joe has to be 35.
Teacher Vocabulary:
  • Multiplicative comparison
  • Multiplier
  • Equation
  • Times as many
  • Times as much
  • Verbal statement
  • Factor
  • Product
  • Quantity
  • Multiple
  • Scale factor
Knowledge:
Students know:
  • How to write an equation to represent a word situation.
  • Which quantity is being multiplied and which factor is telling how many times.
  • Varied language that describes multiplicative comparisons.
Skills:
Students are able to:
  • Interpret equations for multiplicative comparisons.
  • Write equations for multiplicative comparisons.
Understanding:
Students understand that:
  • Multiplicative comparisons relate the size of two quantities and a scale factor.
  • Factors in multiplication problems have different roles from each other in the context of comparison problems.
  • Explanations and drawings show ways multiplicative comparisons are similar to and different from equal groups and arrays.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.4.1.1: Use arrays to show equal groups in multiplication.
M.4.1.2: Recall basic multiplication facts.
M.4.1.4: Demonstrate computational fluency, including quick recall of addition and subtraction facts.
M.4.1.5: Recognize multiplication as repeated addition.

Prior Knowledge Skills:
  • Identify and define the parts of a multiplication problem including factors, multiplier, multiplicand and product.
  • Use multiplication to find the total number of objects arranged in rectangular arrays based on columns and rows.
  • Write an equation to express the product of the multipliers (factors).
  • Relate multiplication to repeated addition and skip counting.
  • Apply concepts of multiplication through the use of manipulatives, number stories, skip-counting arrays, area of a rectangle, or repeated addition.
  • Apply basic multiplication facts through 9 x 9 using manipulatives, solving problems, and writing number stories.
  • Solve addition problems with multiple addends.
  • Represent addition using manipulatives.
  • Distinguish between rows and columns.
  • Use repeated addition to solve problems with multiple addends.
  • Count forward in multiples from a given number.
    Examples: 3, 6, 9, 12; 4, 8, 12, 16.
  • Recall doubles addition facts.
  • Model written method for composing equations.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.
Mathematics
MA2019 (2019)
Grade: 4
2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • When given word problems involving multiplicative comparison, will solve using concrete, pictorial representations, and write related equations involving a single unknown.

    • Example: There are 12 children and 3 adults at the playground. How many times as many children are at the playground than adults? Represent the situation with the equation 12 = n × 3 and a tape diagram with a total of 12 and groups of 3, repeating each group 4 times to solve.
Teacher Vocabulary:
  • Multiplicative comparison
  • Times as many
  • Product
  • Factor
  • Multiplication
  • Equation
  • Symbol
  • Additive comparison
  • Tape diagram
  • Unknown
Knowledge:
Students know:
  • how to find products and quotients.
  • Recognize situations represented by multiplicative comparison.
  • Distinguish between multiplicative comparison and additive comparison.
Skills:
Students are able to:
  • Solve word problems involving multiplicative comparison.
  • Write equations using a symbol for the unknown to represent word problems involving multiplicative comparison.
  • Use drawings to represent the word situation involving multiplicative comparison.
Understanding:
Students understand that:
  • additive comparison focuses on the difference between two quantities and multiplicative comparison focuses on one quantity being some number times larger than another.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.4.2.1: 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.
M.4.2.2: Recognize key terms to solve word problems.
Examples: in all, how much, how many, in each.
M.4.2.3: Apply properties of operations as strategies to add.
M.4.2.4: Recall basic multiplication facts.
M.4.2.5: Demonstrate computational fluency, including quick recall of addition and subtraction facts.

Prior Knowledge Skills:
  • Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.
  • Identify key vocabulary words to solve multiplication and division word problems.
    Examples: times, every, at this rate, each, per, equal/equally, in all, total.
  • Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • Recall basic multiplication facts.
  • Add and subtract within 20.
  • Represent repeated addition, subtraction, and equal groups using manipulatives.
  • Distinguish between rows and columns.
  • Use repeated addition to solve problems with multiple addends.
  • Count forward in multiples from a given number.
    Examples: 3, 6, 9, 12; 4, 8, 12, 16.
  • Recall doubles addition facts.
  • Model written method for composing equations.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.
Learning Objectives:

Students will be able to interpret and write equations for multiplicative comparisons.

Students will be able to solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.
  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

  • Present the slideshow to the students.

  • Read the first water slide problem to the students and give them time to solve it.  Students should share equations and models with the class.

  • Read the next water slide problem and tell students they must look closely to see how this problem is different.  Give students time to work and share their solutions with the class. 

  • After students have had time to solve and share both problems, show the solution slide and ask students, "How are these two problems alike?  How are they different?"  Students should notice the difference in phrasing between problems -- "four meters longer" (additive) vs. "four times as long" (multiplicative). 

  • On the next slide, students must choose whether the phrase is additive or multiplicative.  They should pick a phrase from the list and write an equation with a variable (ex: 6 x ? or 2 + d)

  • The next slide has students compare two different multiplicative comparison problems, one with the set unknown and one with the product unknown.  Follow the same procedure as with the water slide problems, allowing time to solve and share each problem before asking students how they are alike or different.  Show the solution slide so students can see the models for each type.

  • After the slideshow, put students into groups of 2-4 and hand out the matching game.  Students must match four cards for each set: word problem, equation, comparison statement, and model.
Assessment Strategies:

Use formative assessment strategies during the slideshow and game to determine if students can:

  • interpret and write equations for multiplicative comparisons

  • solve word problems involving multiplicative comparison using drawings and writing equations to represent the problem, using a symbol for the unknown number
Advanced Preparation:

  • Preview the slideshow and prepare a way to display it for the class

  • Make copies of the matching game, one for each set of 2-4 students.  You may want to laminate for durability.  Each set is color-coded, so color copies are preferred but not necessary.

  • Teachers will need to create a free account for Teachers Pay Teachers to access the matching game. It is a free download. 

 
Variation Tips (optional):

The matching game could be played as a whole class interactive activity.  Each student gets one card and has to find their three matching partners.
Notes or Recommendations (optional):

This activity can be used as a stand-alone activity or together with the following activities as a complete lesson:

Yummy M&Ms - Multiplicative Comparison Intro

Multiplicative Comparisons at the Giant's Door
  Keywords and Search Tags  
Keywords and Search Tags: comparison, equation, multiplicative, scale, unknown, word problem