"building number sentences"

Big Idea:

There are many situations to which an operation is applied, and there are many procedures, or algorithms, for each operation.

Expectations:

Number

• B2. use knowledge of numbers and operations to solve mathematical problems encountered in everyday life

  • B2.4 use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of whole numbers that add up to no more than 100

Algebra

• C3. solve problems and create computational representations of mathematical situations using coding concepts and skills

  • C3.1 solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves sequential and concurrent events

  • C3.2 read and alter existing code, including code that involves sequential and concurrent events, and describe how changes to the code affect the outcomes

Social-Emotional Learning (SEL) Skills in Mathematics and the Mathematical Processes

• A1. Throughout this grade, in order to promote a positive identity as a math learner, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum.

In this lesson, to the best of their ability, students will learn to maintain positive motivation and perseverance, think critically and creatively, and build relationships and communicate effectively as they apply the mathematical processes problem solving (develop, select, and apply problem-solving strategies), reflecting (demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding (e.g., by comparing and adjusting strategies used, by explaining why they think their results are reasonable, by recording their thinking in a math journal), communicating (express and understand mathematical thinking, and engage in mathematical arguments using everyday language, language resources as necessary, appropriate mathematical terminology, a variety of representations, and mathematical conventions), and representing (select from and create a variety of representations of mathematical ideas (e.g., representations involving physical models, pictures, numbers, variables, graphs), and apply them to solve problems), so they can recognize that testing out different approaches to problems and learning from mistakes is an important part of the learning process, and is aided by a sense of optimism and hope, and make connections between math and everyday contexts to help them make informed judgements and decisions, and so they can work collaboratively on math problems – expressing their thinking, listening to the thinking of others, and practising inclusivity – and in that way fostering healthy relationships.

Have students gather around the perimeter of the 100 number carpet or the 10x10 grid.

• Have a student pick a number. The teacher can use guiding sentences such as, “Pick a two digit even or odd number.”

• Once a number is chosen (e.g., 49) place a counter on the number 49 to indicate that it is the chosen number.

• As a large group have a conversation around how we as a class can create a number sentence that equals 49 ( e.g., 50 -1 = 49)

• Have the students use the unplugged sticky notes to create a sequential coding to show that if you start at 50 and go back 1 square you will get to 49. OR if you put a sticky note at 50 and 49 there is a 1 square difference between these 2 numbers.

• Now explain to the class that you are going to use the coding device (ex Bee Bot) to code to make a number sentence to represent 49 using an addition or subtraction strategy.

• Co-create a list of number sentences to make 49 and have the class take turns modelling the coding using the plugged coding device.

(30 minutes)

• Divide students into groups.

• Give each group a 100’s chart.

• Have the students write the code on the 100’s chart for their number sentences and directional arrows using unplugged coding (doing the activities offline).

• Have the coding robots and iPads ready for the groups.

• Have the groups code using the coding devices to transfer their unplugged number sentences to plugged coding on the 100’s carpet or Grid using the coding device

For example if the chosen number is 25, students will demonstrate their number sentences, through coding the sequence of codes they have established to make 25.

• They will begin by placing a counter on 25

• The group will then work out the sequential code that they built for 25 such as 15 + 10 or 30 - 5 and move Dash or Dot around accordingly to the chosen numbers

If two devices are available per group, then one robot would move to 15 and the other to 25 and we would see the difference of 10 between 15 and 25, or move towards 30 and 25 and see the difference of 5 between 25 and 30.

The inverse relation can also be demonstrated such as if the numbers are 15 + 10 then how would they code Dash to get to 25. (15 + 10 = 25 or 25 - 10 = 15)

• Students can create a few number sentences and test their codes using addition or subtraction.

• Groups can record their moves using an iPad and share it with the class during consolidation.

• Groups can face off each other and call out numbers, have the other group use either addition or subtraction or both to create a number sentence.

For example, Group A can call out 67 and Group B has to create a coding sequence to show 65 using addition or subtraction.

• They can then compare their strategy with Group A’s strategy for the same total.

For example, “the numbers added in two different number sentences are equal to 65 but one number sentence has 45 + 15 and the other has 46 + 24. What do you notice about the 2 number sentences?”

• What do you notice about these two number sentences?

65 = 40 + 25

65 - 25 = 40

“The two number sentences use the same numbers but one is an addition and one is a subtraction.” (bring out the inverse relationship)

OR 44 + 37 = 81 and 37 + 44 = 81 (commutative property)»

Groups can have conversations and notice and name how their code differs from the other group. What is similar? What is different?

For example:

• Can we use a group of 10’s and add on to show my number sentence? Or subtract the same way using groups of 10?

• What are some other ways to show a number sentence? What would you have done differently? What did you learn?

• How can we check if we are correct?

Is there a strategy that I can use to code with the least number of moves to represent my number sentence?

• When Group B is on their challenge, Group A can record their moves and compare it with their own recording

• Gather as a large group and have students share their learning, and talk about challenges they have met and how they overcame them.

Conversations with the groups to gather anecdotal and written observations

Samples of the group and individual grids

Success criteria checklists with the columns such as “met”’, “yet to”

SEL Student Self-Assessment FRENCH / ENGLISH SEL Teacher Rubric