Overview:
During my practicum, I taught all daily math lessons. In total, I taught 14 math lessons over the course of three weeks. I developed a unit plan prior to beginning my practicum which helped me structure my lessons and design the assessment criteria in advance of instruction.
The unit I taught was focused on introducing multiplication and developing students’ understanding of multiplication using the “groups of” strategy. By the end of the unit, all students were able to demonstrate the steps to solve a multiplication problem using the “groups of” strategy and were proficient in their ability to identify the number of groups and the quantity in each group based on the multiplication sentence presented to them.
Summary:
I had three primary aims in mind as I structured this math unit. Firstly, I aimed to ensure students had plenty of time to practice their new skills and develop their understanding. Secondly, I aimed to ensure that all students progressed and developed their understanding of multiplication to the point where all students were proficient. Finally, I aimed to ensure that the assessment design was criterion-referenced and aligned with the instruction students received.
I prioritized the development of student understanding and proficiency in the “groups of” strategy over introducing multiple multiplication strategies like arrays and skip counting. I did so because I wanted to ensure that all students had the time and practice they needed to reach proficiency before they were introduced to a new approach to multiplication. This was their very first introduction to the concept of multiplication so I felt it was important to lay a solid foundation. My commitment to providing ample time to practice was demonstrated as I allowed students plenty of time to practice their skills and work through practice problems before moving on to learning how to solve realistic word problems. This approach also demonstrates an appreciation for the First Peoples Principle of Learning which states that learning takes patience and time.
To support students as they completed independent work, I created two different charts which were displayed in the classroom. These charts demonstrated some of the key concepts and procedures students were working toward understanding. I created both charts using the same colour-coding system I used during all guided practice on the board. The colour-coding system was used in hopes that it could help all students but especially those who found these new concepts particularly challenging. The colour-coding system made it easier to digest the information in each multiplication sentence. Green indicated the number of groups. Blue indicated the number in each group and was used when writing out the repeated addition sentence. Red indicated the total quantity and identified the product. Black was used for math symbols and sentences. I left the charts up during all lessons, including the summative assessment so students had a clear indication of what was expected of them.
Up until the day of the test, I used observational and formative assessments to gauge student progress and depth of understanding. I would assess their work as they completed it and work with students to address any corrections. This approach allowed me to see in real-time where students were at and provide targeted support to those who needed it. At the end of the unit, students completed a summative assessment which was made up of questions from the beginning, middle, and end of the unit. Students had been exposed to and practiced each type of question that was presented on the summative assessment so they were well-prepared to demonstrate their understanding.
Here you can view a copy of the summative assessment students completed and two examples of how students completed the assessment.
Overall, I was very pleased with how this unit unfolded. I had to make some adjustments to the pace along the way to respond to the needs of my students. In the end, all students were successful in their understanding of how to solve a multiplication practice problem using the “groups of” strategy. In the future, I would begin the unit with an even more basic introduction to the concept of multiplication and slowly introduce the vocabulary in the first few lessons rather than presenting so much new information at once during the first lesson. If I were to teach this unit again, I would maintain my focus on ample practice time but I would extend the unit by a few weeks and introduce other multiplication strategies like arrays and skip counting as well.
Here is the timeline I followed as I taught this unit:
Week 1:
| Day 1 | Introduction to multiplication and the “groups of” strategy using blocks to understand that the first number in a multiplication sentence tells us “how many groups” and the second number tells us “how many in each group” and the total quantity is called the “product” |
| Day 2 | Continued practice of the “groups of” strategy focused on understanding that the first number in a multiplication sentence tells us “how many groups” and the second number tells us “how many in each group” and the total quantity is called the “product”. Students completed work booklets. |
| Day 3 | Continued practice of the “groups of” strategy focused on learning the basics of multiplication by circling the groups presented, doing the repeated addition, and then writing out the multiplication sentence that would represent the pictures presented. Students began working on new work booklets. |
| Day 4 | Additional time to work on and complete the previous day’s work booklet. |
| Day 5 | Continued practice of the “groups of” strategy focused on whiteboard practice where students practiced drawing out the steps and solutions to multiplication practice problems. |
Week 2:
| Day 1 | Continued whiteboard practice solving multiplication practice problems using the “groups of” strategy. At the end of the lesson, students solved four practice problems on a worksheet using the steps they had been practicing on the whiteboards so their understanding could be thoroughly assessed. |
| Day 2 | Students were given this time to work through a booklet filled with multiplication practice problems. For each question, students were asked to draw out the groups, dot them in, write out the repeated addition, and solve for the product. |
| Day 3 | Multiplication word problems were introduced in this lesson. The majority of the lesson was spent focused on interactive guided practice at the board. At the end of the lesson, students solved one word problem independently. |
| Day 4 | Continued practice with word problems. The entire lesson was focused on interactive guided practice. For each question, I read the word problem out to the students and asked, “Who can tell me what the product is and explain their thinking?” Students then had the opportunity to share their thinking with the class. |
| Day 5 | Continued practice with word problems. The lesson began with some brief interactive guided at the board and then students were released to independent practice. |
Week 3:
| Day 1 | The review phase of the unit began on this day. The lesson began with interactive guided practice on the board. The guided practice focused on what was introduced during the first half of the unit. Students began working on a review booklet which had questions from each stage of the unit. |
| Day 2 | After some guided review focused on solving practice problems and word problems at the board, students were released to independent work. They continued working and completed their review booklets. |
| Day 3 | Students completed their summative assessment. |
| Day 4 | The students and I worked through each of the problems on the summative assessment as a class to review the test. Then, students played a multiplication dice game called “Perfect Products” in pairs. |
Formal Lesson Plans:
I have attached two formal lesson plans from this multiplication unit here. The first lesson plan focuses on solving whiteboard practice problems and the second lesson plan focuses on solving multiplication word problems.
Here are some examples of student work completed during this unit.
