Math unit 1
Arranging a group of people
Margaret Frame
Math-Arrays and sharing
Grade: 4th
Estimated length: 1 hour
Standards:
Algebra: Model problem situations with representations such as an array to draw conclusions.
Connections: Recognize and use connections among mathematical ideas.
Communication: Communicate their mathematical thinking coherently and clearly. Use the language of mathematics to express mathematical ideas precisely.
Outcomes/Objectives:
Students will understand that arranging a number can be done in a number of ways. They will use graph paper to make all the possible arrays for a number of people, then turn those arrays into shares and a multiplication factor.
Students will connect an algebra problem to a different representation such as an array, shares and multiplication factors.
Students will learn how to count arrays, write the dimensions of that array and turn that array into shares.
Vocabulary:
Array, shares,
Materials:
Graph paper, glue, scissors, poster board, marker, pencil.
Procedure:
Students will work in groups of 2-4 to come up with ways to arrange the group of people.
Engage:
If you take a group of 24 people, how many different ways can you arrange them? Can you use this graph paper to represent a multiplication problem?
Explore:
One student from each group gathers materials from the materials table.
They work until they have identified all the arrangements they can think of for that group of people.
Teacher will assess prior knowledge by observing first attempts.
The students will record which arrangements work and don’t work.
Possible teacher questions:
What have we tried?
How many different arrays did you come up with?
Are any two arrays similar?
Explain:
Students will cut graph paper into arrays and glue onto poster board to explain how that array represents that amount of people.
As the poster board explanations are reviewed, students are can improve their work by adding the arrays and dimensions they missed.
Teacher will emphasize the words they have used to describe the array, e.g. arrangement, groups and introduce shares.
Possible teacher questions:
Are all the arrangements with that number on the board?
How do you know it is all the arrangements?
How are these arrays different? (point at a n x s and a s x n)
Can you check your arrangements by turning them into shares?
Does anyone know what the difference between an array and a share?
Expand:
Students will complete their poster board by turning all the arrays into shares.
Students will then explain how they counted the arrays or shares. ( by 1’s, 2’s, 3’s)
Evaluation:
Given a worksheet they will label the array in multiplication terms and turn the array into shares, and write one way to count those arrays or shares.
Extend (2):
The students will learn how to take a larger multiplication factors and connecting it with four small arrays then two bigger arrays. In this lesson they will be covering reasoning and proof.
References:
National Council of Teachers of Mathematics. (2002). Principles and standards for school mathematics. Reston, VA: Author.
Reflection:
This is great way to become more familiar with arrays, and also to connect arrays to shares and show how multiplication pairs are related. The lesson provides both pictorial and concrete observations. The lesson was prepared as a part of the Arrays and Shares Math unit for fourth graders but could easily be modified for third graders. This is the second lesson of the Math unit. The extend (2) is looking at using arrays with larger factors being turned into big arrays and then turning those into even smaller arrays.