ALEX Learning Activity

  

Multiplicative Comparisons at the Giant's Door

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  This learning activity provided by:  
Author: Samantha Wallace
System:Limestone County
School:Cedar Hill Elementary School
  General Activity Information  
Activity ID: 2903
Title:
Multiplicative Comparisons at the Giant's Door
Digital Tool/Resource:
Multiplicative Comparisons at the Giant's Door
Web Address – URL:
Overview:

In this resource from Bridges in Mathematics, students use a picture of a giant's doorway to solve multiplicative comparison problems.  They have to write an equation and find the answer using appropriate units.  A challenge problem includes a fractional scale factor.
  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.
  Strategies, Preparations and Variations  
Phase:
After/Explain/Elaborate
Activity:

  • Display a copy of the worksheet before handing it out to the students.  Show the image and ask students what they see or notice. Identify all of the tools to make sure students are familiar with the items.

  • Read the directions, pointing out that the giant's hammer is 48" tall.  They will need to use that information to solve the problems.

  • Pass out the worksheet and give students time to work independently.  Walk around and make sure students are following the directions; help students as needed.

  • Collect the worksheet.  Review by having students share their strategies for solving the problems.
Assessment Strategies:

Assess student work to determine if they were able to:

  • interpret and write equations for multiplicative comparisons.

  • solve word problems involving multiplicative comparison using drawings and write equations to represent the problem.
Advanced Preparation:

Preview the worksheet and prepare a way to display the image.

Make a copy of the worksheet for each student.
Variation Tips (optional):

This activity could be done with peer support or as a whole class.

The size of the hammer could be adjusted for easier calculations.
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

Slides & Pies - Multiplicative Comparison Lesson
  Keywords and Search Tags  
Keywords and Search Tags: comparison, equation, multiplicative, scale, unknown, word problem