Guided Lessons

# Animal Kingdom Comparisons

How much longer is a blue whale than an orca? Teach your students to use bar models and number sentences with variables as they solve these wild word problems!

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Students will be able to solve comparative word problems using bar models and number sentences with variables.

(5 minutes)
• Show students two identical items and six different identical items (i.e. two blue markers and six red markers). Explain that there are three times as many red markers as blue markers because six is two times three. Write 6 = 2 x 3 on the board.
• Explain that sometimes multiplication can be used to compare two numbers. When a multiplication equation is used to make a comparison, it is called a multiplicative comparison.
• Tell students, "Today we are going to solve comparative word problems using two strategies: bar models and equations with variables."
(15 minutes)
• Write a word problem on the board: An orca is 20 feet long. A blue whale is four times as long. How long is a blue whale?
• Draw a bar model to represent the problem. First, draw one bar and label it 20 feet. Write "orca" to the left of the bar. Below, draw four bars, each the size of the first bar. Label each of the four bars 20 feet. Write "blue whale" to the left of the four bars.
• Explain that if an orca is 20 feet long, we can use four bars to show that a blue whale is four times as long.
• Add (or multiply) the four bars to find the length of the blue whale (80 feet). Then, write 80 = 4 x 20 and explain that 80 is four times as much as 20.
• Solve the same problem again, this time using an algebraic equation to solve.
• Write a number sentence using variables (n = 4 x 20) and explain that n represents the length of the blue whale, which is the unknown number in the problem, and 20 is the length of the orca.
• Underline the number four in the equation and point out that, since we know a blue whale is four times the length of an orca, this equation will help us figure out the value of n, or the length of the blue whale.
• Solve for the value of n (n = 80).
• Write another word problem on the board that reads: A kangaroo can jump 30 feet and a bullfrog can jump five feet. The kangaroo can jump how many times farther than the bullfrog?
• Write an algebraic equation to represent the problem (30 = n x 5).
• Draw a small bar and label it "5 feet" to represent the bullfrog jump. Below, draw a longer bar and label it "30 feet" to represent the kangaroo jump. Explain that since we don’t know how many times farther a kangaroo can jump, we need to divide 30 by five to find the answer.
• Draw vertical lines in the larger bar to divide it into five equal parts (try to make each part equal to the size of the small bar that represents the bullfrog jump).
• Think aloud (i.e. if this bar, labeled 30, is divided into five parts, what is the value of each part?) Label each unknown part with the variable n.
• Explain that since we know five times six is 30, then the value of each part (n) must be six. Write 30 = 6 x 5 and repeat, "30 is six times as much as five."
• Revisit the algebraic equation (30 = n x 5) and compare it to the bar model you drew. Then, write n = 6.
(15 minutes)
• Write a word problem on the board that says, "Jenny’s cat weighs six pounds and her dog weighs 48 pounds. Her dog weighs how much times more than her cat?"
• Have students work in small groups to discuss and work through the problem. Remind students to draw bar models and write equations (i.e. 48 = 6 x n) to represent the numbers they are comparing.
• Have the class regroup and ask students to share reflections about their process and strategies with the class.
• Repeat with a second problem, "A deer eats seven pounds of vegetation each day. A giraffe eats ten times as much. How much does a giraffe eat each day?"
(10 minutes)
• Write a word problem on the board that reads: At the pet store, a goldfish costs \$4. An angelfish costs seven times as much. How much does one angelfish cost?
• Instruct students to solve the problem independently, showing work in a math notebook or scratch paper.
• Repeat with a second word problem: Paulo panda is 9 years old and Terry tortoise is 72 years old. How many times older is Terry?
• Instruct students to solve the problem independently, showing work in a math notebook or scratch paper.
• Circulate and offer support as needed.

Support:

• Have students solve only multiplication problems, and do not offer problems that involve division.
• Provide additional examples during guided practice.

Enrichment:

• Allow students to make their own multiplicative comparisons based on something in their own life (i.e. how much taller they are than a sibling).
• Allow your students to practice this skill by providing time to work through online exercises or games. See suggested media.
(10 minutes)
• Hand out pre-made cards that will match up to make multiplicative comparisons (i.e. one card might read n = 5 x 4 and its matching card would read n = 20. Or a card might read 35 = n x 7 and its match would read n = 5).
• Ensure that there are enough cards so that every student can make a match with a partner. Add a card for yourself if you have an odd number of students.
• Have students walk around the room looking for their match. When all students have matched their cards and made a number sentence, go around the class and have each pair read their sentence aloud.
(5 minutes)
• Show students 12 blue markers and four red markers and ask students, "How many times more blue markers are there than red?"
• Repeat with a few more combinations of numbers.