One Hundred Hungry Ants
Author: Elinor J. Pinczes
Publisher: Houghton Mifflin Company
Overall Curriculum Expectations:
-solve problems involving using a variety of strategies, and investigate multiplication
(Grade 2)
-solve problems and demonstrate an understanding of multiplication (Grade 3)
Specific Expectations
- represent and explain, through investigation using concrete materials and
drawings, multiplication as the combining of equal groups (Grade 2)
- relate multiplication of one-digit numbers to real life situations, using a variety of
tools and strategies (Grade 3)
Concept: I can recognize that there are several ways to partition a set of equal
groups by using different factors, and the shape of an array will change but the total
number within the set will remain the same.
The book One Hundred Hungry Ants is a story about a group of 100 ants that are
travelling in a hurry to a picnic. Under the direction of the smallest ant, they
reorganize into five different arrangements of equal groups. First they regroup into
two rows of fifty. Next they break into four rows of twenty-five. Then they form five
rows of twenty. Finally the group is arranged into ten rows of ten. Eventually all one
hundred of the hungry ants arrive at the picnic only to discover that there is not any
food left. In the end the smallest ant flees as the other ninety-nine disgruntled ants
go after their ousted leader.
This book provides an interesting context to help students think about multiplication
as the ants reorganize themselves into five different rectangular arrays. The story
could be used as a springboard for teaching both multiplication and/ or division. The
pictures demonstrated different factors of one hundred.
Introduce the Book: As I read the story, I have students model using manipulatives
or draw a mental picture of the 5 different ways the ants arrange themselves (1 x
100, 2 x 50, 4 x 25, 5 x 20 and 10 x 10) I pause at each point to allow the students
time to predict what other arrangements the ants will form and allow them time to
express their thinking in numbers pictures or words.
Math Features:
- rich context for problem solving that can be used in both primary and junior
- visual representation of a math concept
- presents math language
- address more that one math concepts
Lesson Plan - Grade 2 /3
Curriculum Expectations
Overall Curriculum Expectations:
- solve problems involving using a variety of strategies, and investigate multiplication
(Grade 2)
- solve problems and demonstrate an understanding of multiplication (Grade 3)
Specific Expectations
- represent and explain, through investigation using concrete materials and
drawings, multiplication as the combining of equal groups (Grade 2)
- relate multiplication of one-digit numbers to real life situations, using a variety of
tools and strategies (Grade 3)
Task/Problem
To demonstrate the concept of multiplication as equal groups represented in a
variety of ways.
Part 1 Minds On or Activate Prior Knowledge
Remind the students that you read One Hundred Hungry Ants earlier.
Ask them how the different arrangements of ants are the same but different (number
of rows change but the total number of ants stay the same) Ask about the strategies
they used to model the different arrangements of ants? List the strategies and tools
they used. Finally, tell the students that they are going to be like the smallest ant and
reorganize smaller groups of ants.
Problem :
Suppose there were smaller groups of ants going to the picnic.
A. How many different ways can you arrange 6 ants in equal rows?
How do you know you have found all the ways?
B. Arrange 7 ants into equal rows .
How many ways can you do this? Explain.
Questions:
How have you shown your thinking? (picture, model, number sentence)?
How can you show your thinking in numbers and symbols? (I can make a
multiplication sentence or show repeated addition)
How can you use math language to express my thinking? (I made equal groups…)
How do you know you have found all the possible solutions? (I rearrange the factors
to create a new multiplication sentence)
Part 2 - During, Hands On
Have the students work in pairs to answer the word problem:
You are going to make more equal groups as the leader of a marching band. How
many members will be in your band? How will you arrange the band members to
form equal rows? Use numbers pictures and word to explain your thinking.
Questions:
What strategy are you using?
Can you show your thinking another way? (picture, model, number sentence)?
How can you show your thinking in numbers and symbols? ( I can make a
multiplication sentence or show repeated addition)
How can you use math language to express your thinking? (I made equal groups…)
How do you know you have found all the possible solutions? (I rearrange the factors
to create a new multiplication sentence)
Part 3 - Consolidation
I would highlight three different pieces of students’ work that highlight a different
strategy to discuss for the consolidation.
Questions:
What strategy did you use? (e.g. repeated addition, groupings, skip counting)
How are the arrays the same or different? (the total remains the same but the
number of rows change)
How are the numbers sentences the same but different? (factors can be repositioned
and the product remains the same)
Have we found all the possible solutions? (fact families)
What other math does this remind you of?
What did we learn about multiplication?
Learning Goal:
I can multiply numbers by organizing objects into equal groups.
Success Criteria:
I know that multiplication is related to addition.
I can make equal groups.
I can draw an array.
I can count on by skip counting on a number line or hundreds chart.
I can use repeated addition.
I can use numbers and symbols to explain my thinking.
I can use math language to explain my thinking.
Strategies:
- use counters
- make a picture
- skip counting on a number line or hundreds chart
- equal groups
- make an array
- repeated addition
- multiplication sentence
Tools:
- paper/pencil
- manipulatives
- number line
- hundreds chart
Misconceptions:
- Students make arrangements that do not have equal groups
- Students may not be able to determine the number of rows and columns in an
array
- Students may not be able to make equal groups
- Students may not be able to express their thinking in numbers and symbols
(multiplication sentence)