419100-380999School Placement/ Socrúchán Scoile Progressional Scheme/Sceim Leanúnach 2018
Subject Area: Maths Class Level/s: 5th Class Time Period: 1 week
No. of Lessons: 3
Length of lessons: 40 minutes
Strand Unit / Element:
Rules and Properties
Theme / Enquiry Question / Key Idea:
The main ideas of this topic are
Develop the students’ understanding of how number operations behave.
Illustrate that there is a need for rules to guide us in the order in which we carry out these operations.
Interpret and apply these rules in problem solving situations.
Linkage and integration:
English: Procedural Writing
Science: Experiment Writing
PE: Games- Games with rules
Broad Learning Outcomes: (General and specific to topic)
The child should be enabled to explore and discuss simple properties and rules about brackets and priority of operation ( Curriculum)
The child should be enabled to apply mathematical concepts and processes, and plan and implement solutions to problems, in a variety of contexts
The child should be enabled to communicate and express mathematical ideas, processes and results in oral and written form
The child should be enabled to make mathematical connections within mathematics itself, throughout other subjects, and in applications of mathematics in practical everyday contexts.
Children should be enabled to:
Examine the importance of the order of operations matters.
Explain the relationship between addition and subtraction, and between multiplication and division in their own words.
Demonstrate their understanding of the order of operations through spoken number problems.
Explain the rules for the order of operations, including defining the acronym, BIMDAS.
Apply the order of operations to solve problems.
Children’s Previous Related Learning:
I will work with the classroom teacher to ascertain the children’s previous related learning and jointly plan the lessons and scheme of work accordingly.
Progressional Sequence (what?)
Teaching and Learning Content/skills/key concepts/language: Teaching and Learning Approaches (how?)
Activities / Classroom Organisation including Differentiation: Assessment Strategies and Methods (how do we know?) Resources (with what?):
Include digital technology
The children will focus on the concept of order.
The children will identify and explain why order is important in our daily lives.
Key Mathematical Language: Order, Number operations, inverse relationship
The focus of this lesson will be on BIMDAS and the importance of brackets.
The children will review the importance of order.
The students demonstrate how equations can be interpreted in multiple ways.
The children will discuss and evaluate the importance of brackets in mathematical equations.
Using BIMDAS the children learn to prioritize the number operations.
Key Mathematical Language: Order of Operations, acronym, mathematical punctuation, indices/exponentials, precede, repeated multiplication.
The focus of this lesson is applying BIMDAS to real life situations and problem solving.
The children will review the importance of order and BIMDAS.
The children construct equations that have an unknown value.
The children will create and solve their own equations/ word problems using BIMDAS.
Mathematical Language: Convention, Unknown, Order of Operations, BIMDAS
Firstly we will discuss what order is, asking for a simple definition and examples of order in our lives.
Then the group leaders will collect an Action Statement Pack with their assigned table colour on it.
The children will be seated according to their ability.
The children then have to put the statements in a sequence that seem logical to them.
After 5 minutes the groups will present their sequences in order.
I will then get some groups to read the sequence out of order to highlight the fact the nonsense of this, and that there is a sensible order to their actions and that some actions must be performed before others.
I will then ask the children to explain what the term number operation is- if they don’t know I will explain it to them.
I will then ask a students to record on the class chart the number operations.
The group leaders will distribute the chart paper and markers.
I will then get the students explain each of the operation symbols, + – x ÷.
I will then get the students to conduct a TPS about the relationship between the operations of addition and subtraction, and between multiplication and division.
I will then highlight the inverse relationship in each pair of operations. Have students explain this with equation and word examples.
I will pose: ‘In maths, the order that we carry out number operations does not change the outcome/result.’ to the children.
I will then get the students discuss this first in pairs and then share their agreement/disagreement and their reasons for their position with the class.
Write this equation on the class chart:
17 + 6x 7– 2= ?
I will get the students to work in pairs to solve the equation and explain their solution(s).
I will get the students read the equation aloud in three different ways.
I will write these, using words, emphasising the different punctuation.
I will get the students work in pairs to write each of these three interpretations as equations, inventing their own ‘mathematical punctuation’. I will get the children share these, writing these on the class chart for others to see. I will accept and explore all suggestions.
I will explain why brackets are helpful, and record the e. Explain that brackets are also known as parenthesis.
(17 + 6) x 7 – 2 = 159
17 + (6x 7) – 2 = 57
(17 + 6) x (7 – 2) = 115
We will review the importance of order of actions.
I will explain to students that mathematicians have agreed on an order of operations.
I will write BIMDAS on the board, explaining that this is an acronym for the agreed order of operations.
I will ask, ‘What is an acronym? What could BIMDAS stand for?
I will get the students to discuss each of these questions in their table groups , then they will record their ideas beside the acronym letters on their group charts
B :brackets. I: Indices or the power of, D: division, M: multiplication, A: addition, S: subtraction.
I will explain that the order of operations is sometimes known as operation precedence. It is a rule that we use to clarify what operation we do first. (to precede means to come (or go) before or first.)
If not well understood, I will explain Indices, demonstrating that it is repeated multiplication: ie 72 = 7 x 7 = 49,
I will then get the group leaders to distribute the worksheets to their tables.
The worksheets are colour coded with the tables colours, to cater for the different ability levels in the class.
The children will work in pairs to solve the equations and explain which operation comes first and why.
I will then correct the work with them and clarify any Muddy points.
Once the children understand the concept of the order of operations, we will then play Who wants to be a Millionaire? Order of Operations Edition to solidify the concept.
I will pose the following question to the class: Having the BIMDAS convention means that we will all agree on the value of an unknown amount in an equation and I will get them to do a TPS giving their reasons for agreeing or disagreeing with the statement.
I might have to clarify what the word convention means.
In the discussion I will clarify what the unknown in an equation such as (36 – 6) ÷ 5 = ?.
I will also clarify that sometimes an unknown (amount) is shown with a letter symbol, such as ‘n’.
I will pose the following problem to the class. “I’m thinking of a number. We’ll call this number ‘n’. I add five to it. I triple it. This is equal to forty six.”
I will ask for some students to record their equation on the mini whiteboards. We will discuss their ideas, highlighting the importance of using the convention of brackets to show the order of operations. The focus is on correctly recording the equation at this point, not finding the value of n.
The group leaders will distribute paper and pencils to their tables.
Each student write five of their own, “What number am I thinking of?” problems. They will write the words of each of the problems on one piece of paper, and on the second piece, their own solutions to the problems, with the number they are thinking of in the place of ‘n’.
The students will then swap their problems with someone at their table. The students will then record their solutions to their partner’s problems separately from the problem page. These problems can then be exchanged with another pair of students and discussed.
Coloured (felt) pens
Group Charts from Lesson 1
Who wants to be a Millionaire? Game
Group Charts from Lesson 1