Lesson 4

Method 3: Algorithm

Key:

Assessment For Learning - (AFL)

Assessment Of Learning - (AOL)

Teacher Questioning - (TQ)

Working Mathematically - (WM)

Literacy Activity - (LIT)

Key ideas:

Students learn and use the formal algorithm to demonstrate multiplication problems of a one digit number multiplied by another number of up to four digits
Students use the factorising method to break up difficult problems into simpler and smaller numbers that can be more easily multiplied

Syllabus dot points:

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental and written strategies and appropriate digital technologies (ACMNA100)

Use mental and written strategies to multiply two- and three-digit numbers by two-digit numbers, including:

Relevant Working Mathematically indicators:

Describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions (Communicating, Understanding)

Assumed prior learning:

Addition
Multiplication of rounded numbers such as tens, hundreds and thousands, as well as those below 10

Learning goals:

By the conclusion of the lesson, students will be able to demonstrate and explain the algorithm method of multiplication and identify when it should be used. Students will also be able to identify when factors can be used to simplify difficult problems, for example in 12 x 25, students could simply to 3 x 4 x 25, with 4 x 25 being 100, making this simpler to solve

WM - Fluency, Reasoning, Communicating

Lesson length: 50 minutes

Resources:

Mini whiteboards (1 per student) & whiteboard pens
Access to this website
Printed worksheets
Large whiteboard x 6 (enough for 1 per table group)

Introduction (10 minutes)

Outline classroom behavioural expectations and learning goal for the lesson and write on the whiteboard:

Demonstrate and explain the algorithm method of multiplication and identify when it should be used
Identify when factors can be used to simplify difficult problems, for example in 12 x 25, students could simply to 3 x 4 x 25, with 4 x 25 being 100, making this simpler to solve

To introduce the class to todays topic, the class will watch this video

WM - Understanding

To further explain the concept, the teacher should refer to the slides below.

LearnZillion. (2019).

Lesson slides.pdf

Body (30 minutes)

Activity 1: Be the teacher (20 minutes)

Working in TABLE-GROUPS, each group will have one large whiteboard as well as one mini-whiteboard for each group member. The teacher will write a list of 5 questions on the board, and within each group the students must each select 1 of the 5 questions to complete and teach to their group. These questions will vary in difficulty, allowing the students who feel more competent to select the more difficult questions. (The teacher should decide these questions depending on their class capabilities)

Students within the same group cannot select the same question so they must use their teamwork and communication skills to allocate the questions fairly. Students must then work independently to solve the problem on their mini-whiteboards before explaining how they solved the problem to their table group, where they can use the larger whiteboard to show their working.

WM - Communicating, Reasoning, Understanding, Problem Solving

TQ: What could be a simpler way of explaining that concept?

Why did you choose to use that step there?

Activity 2: Working backwards (10 minutes)

Working individually, or in pairs if necessary, students will be given a worksheet with multiple algorithms on it, some requiring an answer and some will already have an answer and may be missing other numbers. Students are to use their numeracy and problem solving skills to complete all of the problems, this may require working backwards or trial and error. Students will then compare their answers with a partner and discuss any differences in answer by going through their thinking process.

lesson 4 activity 2 worksheet

WM - Communicating, Reasoning

TQ: What is important to remember when solving this worksheet?

Conclusion (10 minutes)

Exit cards AFL

Students will be given exit cards with some multiplication questions on them, where they will be required to multiply a 3 or 4 digit number by a 1 digit number. The questions will vary in difficulty, and the teacher should ask students to complete as many of the questions as they are able to and hand them in prior to leaving the classroom.

WM - Communicating, Understanding, Reasoning

lesson 4 exit card

Conclude lesson by referring back to the learning goal for the lesson and collecting exit cards, as well as informing students of the required homework.

Homework

There will be no homework for this lesson unless students did not finish activity 2, in which they must complete activity 2 for homework.

Reflection and evaluation

1. Analysis of the lesson

Was the timing sufficient?
Was the difficulty challenging enough for the students?
Was the TQ appropriate?

2. Evidence of student learning

Was the learning goal achieved by the end of the lesson?
Were students able to work independently through class activities showing student direction?
Did the working environment foster social support for students that allowed them to communicate ideas and information relating to lesson content?

3. Implications for future lessons

What pedagogy needs to be changed for next time?
What structural change/resources/difficulty needs to be altered for next time?

References:

LearnZillion. (2019). Lesson slides. Retrieved from https://learnzillion.com/resources/16852/?card_id=71300

National Center on Intensive Intervention. (2017). Multiplying 23 x 19 using the traditional algorithm. Retrieved from https://www.youtube.com/watch?v=85xxAfNP_vM

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