Lesson 1
Introduction to multiplication
Embedded Files
Key:
Assessment For Learning - (AFL)
Assessment Of Learning - (AOL)
Teacher Questioning - (TQ)
Working Mathematically - (WM)
Literacy Activity - (LIT)
Key ideas:
- Gauge prior knowledge of students
- Act as a revision tool as to what multiplication is
This introductory lesson is fostered around Stage 2 Syllabus dot points because these are essential that students understand prior to beginning this unit. Hence, this entire lesson will focus on revision of Stage 2 Multiplication & Division 2 concepts because I believe that this is a necessary way to start.
Syllabus dot points:
From Stage 2 Multiplication & Division 2
NOTE: These are only revised in the Introduction activity, as obviously all of these dot points cannot be covered in one lesson, and as they are Stage 2 they should have already been covered. I just think it is important to list them all to ensure that as a teacher you are aware of what the students have already learnt regarding this topic.
- Recall multiplication facts up to 10 × 10 (ACMNA075)
- Use the term 'product' to describe the result of multiplying two or more numbers, eg 'The product of 5 and 6 is 30' - links to Literacy
- Use mental strategies to build multiplication facts to at least 10 × 10, including:
- Using the commutative property of multiplication, eg 7 × 9 = 9 × 7
- Using known facts to work out unknown facts, eg 5 × 7 is 35, so 6 × 7 is 7 more, which is 42
- Using doubling and repeated doubling as a strategy to multiply by 2, 4 and 8, eg 7 × 8 is double 7, double again and then double again
- Using the relationship between multiplication facts, eg the multiplication facts for 6 are double the multiplication facts for 3
- Factorising one number, eg 5 × 8 is the same as 5 × 2 × 4, which becomes 10 × 4
- Recall multiplication facts up to 10 × 10, including zero facts, with automaticity
- Find 'multiples' for a given whole number, eg the multiples of 4 are 4, 8, 12, 16, …
- Relate multiplication facts to their inverse division facts, eg 6 × 4 = 24, so 24 ÷ 6 = 4 and 24 ÷ 4 = 6
- Determine 'factors' for a given whole number, eg the factors of 12 are 1, 2, 3, 4, 6, 12
- Use the equals sign to record equivalent number relationships involving multiplication, and to mean 'is the same as', rather than to mean to perform an operation, eg 4 × 3 = 6 × 2
- Connect number relationships involving multiplication to factors of a number, eg 'Since 4 × 3 = 6 × 2, then 4, 3, 2 and 6 are factors of 12' (Communicating, Reasoning)
- Check number sentences to determine if they are true or false and explain why, eg 'Is 7 × 5 = 8 × 4 true? Why or why not?' (Communicating, Reasoning)
From Stage 3 Multiplication & Division 1
- Use digital technologies to multiply numbers of
up to four digits(for this introductory lesson I will focus on multiplying single digit numbers)- Check answers to mental calculations using digital technologies (Problem Solving)
Relevant Working Mathematically indicators:
- Uses appropriate terminology to describe, and symbols to represent, mathematical ideas (Communicating, Fluency)
- Selects and uses appropriate mental or written strategies, or technology, to solve problems (Problem Solving)
Assumed prior learning:
- Recall multiplication facts up to 10 x 10 (Stage 2: Multiplication and Division 2) - this is explained in more depth in the above Syllabus Dot Points, because this lesson is focused on revising and fine-tuning student's prior knowledge
Learning goals:
By the conclusion of the lesson, students will be able to demonstrate and explain single-digit multiplication, and recall multiplication facts of up to 10x10 WM - Fluency, Reasoning, Communicating
Lesson length: 50 minutes
Resources:
- Projector or smart whiteboard
- Mini whiteboards (1 per student) & whiteboard pens
- Dice (enough for 1 per person)
- Access to device to view website
- Printed Ken Ken worksheets of varying difficulty
Orientation (5 minutes)
Orientation (5 minutes)
Watch this video about the relevance of multiplication:
TQ: What are some examples of multiplication in the real world that weren't in the video?
- Link to why multiplication is an important skill to learn
WM - Understanding
Outline classroom behavioural expectations and learning goal for the lesson and write on the whiteboard:
- Demonstrate and explain single-digit multiplication
- Recall multiplication facts of up to 10x10
WM - Fluency, Communicating
Introduction (10 minutes)
Introduction (10 minutes)
Brainstorm / mind-map
Students will have a mini-whiteboard each and be asked to create a mind-map to brainstorm everything that they remember about "Multiplication"
- e.g. 'product', order doesn't matter, factors, doubling, zero facts, multiplication facts
This activity is to be completed individually and after 3 minutes they will be asked to share their answers with a partner for 2 minutes. There will then be a class discussion AOL about what students have written, to get students brains activated regarding this new unit.
The teacher should write down some of the class' answers on the whiteboard.
TQ: When students answer questions, if it is incorrect or not clear, ensure that you ask them to explain themselves or ask why they suggest that answer?
Below are some beginner videos regarding multiplication that would be useful to show any student who is struggling to grasp or recall the concept of multiplication:
Body (30 minutes)
Body (30 minutes)
Activity 1: Greatest Product game (20 minutes)
Students will work in pairs and be given 2 dice between the pair. Taking turns, each person will roll both dice and write down both numbers, then multiply the numbers together AFL. Once both people have had a turn, the students must compare each roll and see who had the greatest product. Students are to keep track of points using tally marks. While students are playing the game the teacher should walk around the room to ensure that students understand and check progress, giving modifications to the groups who need it.
- The first player to 10 tallies wins (or set any goal you would like)!
- Variations: Play to find the lowest product; use 3 dice instead of 2, increase the dice to be 10-sided for example
Students can use the Array Display activity on the website http://www.ictgames.co.uk/ if they are having trouble with the multiplication, it will show this in a visual array and provide the answer.
There will then be a class discussion about the game and the trends.
WM - Fluency, Understanding
TQ: Which numbers were better to roll in order to win each round? i.e. higher numbers such as 6
Activity 2: Ken Ken game (10 minutes)
Students will work individually to complete Ken Ken puzzles ranging from 4x4 to 9x9 that focus on multiplication but include other operations. Students will use this as a revision tool AFL from their knowledge of up to 9x9, and there should be puzzles of varying difficulty so that students can choose if they want to start at an easier puzzle and work their way up, or if they want to try an expert level puzzle.
Teacher note: If not familiar with Ken Ken puzzles, students must place 1 number in each box e.g. if 4x4 puzzle the numbers range from 1-4, and they must sum to the small number in the box abiding by the given operation. The same number cannot be in the same row or column, i.e. each row and column must have 1, 2, 3 and 4.
- Variations: Varying levels of difficulty of the puzzles, and size of the puzzles e.g. 4x4 ranging up until 9x9
- Extension 'challenge': Give students a blank Ken Ken puzzle and ask them to design their own, check to see if it works, and then share with a partner.
WM - Fluency, Understanding, Problem Solving
TQ:
- What strategies worked well to solve the puzzle?
- What made the puzzle difficult?
- What skills made the puzzle easier to solve?
Conclusion (5 minutes)
Conclusion (5 minutes)
Exit cards AFL
Students will be given exit cards (see below) with some multiplication questions on them, ranging up to 10x10. The questions will vary in difficulty, and the teacher will instruct students to complete as many of the questions as they are able to and hand them in prior to leaving the classroom.
WM - Fluency, Understanding
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
Homework
Students are to write down on a blank A4 sheet of paper a 10x10 multiplication quiz comprising of 10 questions and bring it to class anonymously for next lesson.
Reflection and evaluation
Reflection and evaluation
1. Analysis of the lesson
- Was the timing sufficient?
- Was the difficulty challenging enough for the students?
- Was it too simple or difficult?
- How did you know?
- 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:
Barret, J. (2018). Array display. Retrieved from http://ictgames.co.uk/
Funza Academy. (2015). Why is multiplication important in our daily lives? Retrieved from https://www.youtube.com/watch?v=XFgXNUBBNMU&feature=youtu.be
Hogan, J. (2019). Maths games using dice. Retrieved from https://www.scholastic.com/parents/school-success/learning-toolkit-blog/math-games-using-dice-kids-aged-8-13.html
KenKen Puzzle. (2018). Ken ken. Retrieved from https://www.kenkenpuzzle.com/play_now
Math Salamanders. (2019). Multiplication worksheet. Retrieved from https://math-salamanders.s3-us-west-1.amazonaws.com/Multiplication/Fun-Multiplication-Worksheets/Fun-Multiplication-to-10x10/fun-multiplication-to-10x10-1.pdf
N/A. (2010). The multiplying multiplication song. Retrieved from https://www.youtube.com/watch?v=RexXVsSTfJg
N/A. (2015). Multiplication 3rd Grade - Learn Multiplication Educational Math Videos. Retrieved from https://www.youtube.com/watch?v=LD4zp8ruvaI
National Science Foundation. (N/A). Make your own ken ken. Retrieved from http://pi.math.cornell.edu/~mec/KenKen/Lecture_3.html
Oregon State University. (N/A). Reflection guidelines. Retrieved from http://blogs.oregonstate.edu/smehandbook/part-time-student-teaching/reflections-guidelines/
Answers to worksheet:
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