OUR BELIEFS AT UWCT:
We believe that students need time at the beginning of an academic year to consider how exactly maths is learned. We are going to discuss just how we can stimulate brain growth. Before actually going into number work we will consider growth mindset messages with the students.
What are the growth mindset messages?
These mindset messages will be given continually. They are communicated at all times, through the ways that students are grouped together, the tasks they work on, the messages they hear, and the assessment and grading.
Mathematics lessons will allow students to:
One of the main ideas we intend to share with the students is that it is good to share and talk about their way of finding a solution. Time will be given to doodle and draw visuals to explain what is going on their heads. Students should feel comfortable using diagrams to show how they arrive at their solutions. Praising this process is important. It is probable that what one may find that what seems weird might be just what some kids need to understand an aspect of number. Our aim is essentially to support students in finding solutions/ methods that make sense for them.
We believe that students need time at the beginning of an academic year to consider how exactly maths is learned. We are going to discuss just how we can stimulate brain growth. Before actually going into number work we will consider growth mindset messages with the students.
What are the growth mindset messages?
- Everyone can do well in maths.
- Mathematics problems can be solved with many different insights and methods.
- Mistakes are valuable, they encourage brain growth and learning.
- Struggling and persisting with a problem is how the most valuable learning takes place.
These mindset messages will be given continually. They are communicated at all times, through the ways that students are grouped together, the tasks they work on, the messages they hear, and the assessment and grading.
Mathematics lessons will allow students to:
- Develop an inquiry relationship with mathematics, approaching maths with curiosity, courage, confidence..
- Talk to each other and the teacher about ideas – Why did I choose this method? Does it work in other cases? How is the method similar or different to methods other people used?
- Work on mathematics tasks that can be solved in different ways and/or with different solutions.
- Work on mathematics tasks with a low entry point but a very high ceiling – so that students are constantly challenged and working at the highest and most appropriate level for them.
- Work on mathematics tasks that are complex, involve more than one method or area of mathematics, and that often, but not always, represent real world problems and applications.
One of the main ideas we intend to share with the students is that it is good to share and talk about their way of finding a solution. Time will be given to doodle and draw visuals to explain what is going on their heads. Students should feel comfortable using diagrams to show how they arrive at their solutions. Praising this process is important. It is probable that what one may find that what seems weird might be just what some kids need to understand an aspect of number. Our aim is essentially to support students in finding solutions/ methods that make sense for them.
NUMBER TALKS:
Number Talks are short 5-10 minute class discussions done every day that are focused on increasing mental math fluency, flexibility and efficiency. Student are encouraged to share their thinking with the class and it is recorded so others may learn various ways of doing computations inside their heads. This helps students to build a deep understanding of number sense. Below are examples of what a Number Talk looks like.
Number Talks are short 5-10 minute class discussions done every day that are focused on increasing mental math fluency, flexibility and efficiency. Student are encouraged to share their thinking with the class and it is recorded so others may learn various ways of doing computations inside their heads. This helps students to build a deep understanding of number sense. Below are examples of what a Number Talk looks like.
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Unit 1- Place Value
Our central idea...
Number: Counting and Place Value
The value of a digit in a written number depends on its place in the number.
Explain that the two digits of a two-digit number represent amounts of tens and ones. (Acd.Mat.1.Num.CPV.4.1_G1) Elaborations
- Include the following special cases:
a. 10 can be thought of as a bundle of ten ones called a 'ten'
b. The numbers from 11 to 19 are composed of a ten and one, two, three four, five, six, seven, eight or none ones.
c. The numbers 10,20,30,40,50,60,70,80,90 refer to one, two, three, four five, six, seven, eight or nine tens (and 0 ones)
Compare two two-digit numbers based on meanings of the tens and ones digits and record the results of comparisons. (Acd.Mat.1.Num.CPV.4.2_G1)
Elaborations - Note: wait to introduce symbols >,<, = until student has demonstrated clear understanding of meaning (symbols are intentionally not part of benchmark)
Number: Counting and Place Value
The value of a digit in a written number depends on its place in the number.
Explain that the two digits of a two-digit number represent amounts of tens and ones. (Acd.Mat.1.Num.CPV.4.1_G1) Elaborations
- Include the following special cases:
a. 10 can be thought of as a bundle of ten ones called a 'ten'
b. The numbers from 11 to 19 are composed of a ten and one, two, three four, five, six, seven, eight or none ones.
c. The numbers 10,20,30,40,50,60,70,80,90 refer to one, two, three, four five, six, seven, eight or nine tens (and 0 ones)
Compare two two-digit numbers based on meanings of the tens and ones digits and record the results of comparisons. (Acd.Mat.1.Num.CPV.4.2_G1)
Elaborations - Note: wait to introduce symbols >,<, = until student has demonstrated clear understanding of meaning (symbols are intentionally not part of benchmark)
The students played many games that helped them to practice reading 2 and 3 digit numbers as well as building them using base ten blocks.
Unit 2- Addition and subtraction
Addition and Subtraction
Grade 1 has been investigating several strategies for addition and subtraction. We started by practicing Counting on. We do this by starting with the big number, holding it in our head, and counting up the small number. We then practiced so we know the number bonds that add together to make 10. We have also been practicing to learn our doubles facts. All of these strategies will be powerful tools to use when adding and subtracting larger numbers later on.
Grade 1 has been investigating several strategies for addition and subtraction. We started by practicing Counting on. We do this by starting with the big number, holding it in our head, and counting up the small number. We then practiced so we know the number bonds that add together to make 10. We have also been practicing to learn our doubles facts. All of these strategies will be powerful tools to use when adding and subtracting larger numbers later on.
Knowing our doubles facts helps us with addition and subtraction. If we know 6+6 = 12, then we know 6+7 is one more... 13! We also know that 6+5 is one less... 11! Doubles facts also help us with early multiplication and division (doubling and halving). Let's learn those doubles!
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Subtraction
In Grade 1 we are learning to use 3 different strategies to subtract. First we learn that subtraction means "take away" and we practice using the "Counting Back" strategy. Students use number lines in the form of a ruler and count backwards to find the difference. This works really well when the number we are subtracting is small, like 17-3, we could count back three, "16, 15, 14". From there, we look at number triangles and look at the connection between addition and subtraction. For example, if we know that 3+4=7, then know we can switch the order and 4+3= 7. Connecting it to subtraction, we find that 7-3=4 and 7-4=3. Finally we learn the strategy of "Counting up". If we are subtracting a large number, it can be easier to start with that number and count up. For example if we have 17-15, it would take a long time to count back 15 spaces on the number line, on our fingers or in our head. It is much easier to start at 15 and count up, "16, 17" to find that the difference is 2.
Patterns in Number
Skip Counting
Our current Unit of Inquiry is about noticing, analysing and extending patterns in the whole around us. To do this in math, students have been exploring and practicing skip counting by 2's, 5's and 10's starting at a random 2-digit number and counting up to 120. They have also been skip counting backwards by 2's, 5's and 10's. Some of us who are ready for an extension are even practicing how to count by 3's, 4's, 6's, 7's, 8's and 9's. We have been searching for various patterns in the 100's chart that will help us to remember which numbers come next when skip counting. Skip counting will prepare us for pre-multiplication with repeated addition (5+5+5+5=20, 5X4=20)
Adding 2-digit numbers using skip counting by 10's
Students have been able to find patterns in the 100's chart to add by multiples of 10. They have been learning to count by 10's starting at a 2 digit number. For example, if we added 56+10, we could look on the hundred's chart to 56 and then skip count 10 more to 66. If we added 47+30, we could skip count 57, 67, 77 to find the total. Some of us who are ready for an extension practiced skip counting by tens and then counting up by ones. So for example 34+22, students would start at 34, then skip count by 10's twice to add 20 and then count 2 more ones to 56.
Creating, Analyzing and Extending Patterns
Grade 1 has had a lot of fun playing with different types of patterns in Mathematics. We have built ABAB, AAB, ABB, ABCD, and growing patterns. With a partner, we are extending their patterns that they made. We have also played some games with a partner to figure out which part of their pattern is missing.
Our current Unit of Inquiry is about noticing, analysing and extending patterns in the whole around us. To do this in math, students have been exploring and practicing skip counting by 2's, 5's and 10's starting at a random 2-digit number and counting up to 120. They have also been skip counting backwards by 2's, 5's and 10's. Some of us who are ready for an extension are even practicing how to count by 3's, 4's, 6's, 7's, 8's and 9's. We have been searching for various patterns in the 100's chart that will help us to remember which numbers come next when skip counting. Skip counting will prepare us for pre-multiplication with repeated addition (5+5+5+5=20, 5X4=20)
Adding 2-digit numbers using skip counting by 10's
Students have been able to find patterns in the 100's chart to add by multiples of 10. They have been learning to count by 10's starting at a 2 digit number. For example, if we added 56+10, we could look on the hundred's chart to 56 and then skip count 10 more to 66. If we added 47+30, we could skip count 57, 67, 77 to find the total. Some of us who are ready for an extension practiced skip counting by tens and then counting up by ones. So for example 34+22, students would start at 34, then skip count by 10's twice to add 20 and then count 2 more ones to 56.
Creating, Analyzing and Extending Patterns
Grade 1 has had a lot of fun playing with different types of patterns in Mathematics. We have built ABAB, AAB, ABB, ABCD, and growing patterns. With a partner, we are extending their patterns that they made. We have also played some games with a partner to figure out which part of their pattern is missing.
Multiplication
Through our investigation into various patterns in the 100's board and practicing how to skip count, the students showed they were ready to learn repeated addition. This is the beginning stage of multiplication. It is essential that students have a very strong concept of what multiplication means before beginning to memorize multiplication facts. In class, we have been showing that multiplication means "equal groups of", using manipulatives to makes equal groups of objects and then skip counting, or using repeated addition to find the total. We also explore how to use an array to represent the multiplication sentence, always linking it to repeated addition so that students understand that multiplication means "equal groups of".
Number Talks
Number Talks are short 5-10 minute class discussions done every day that are focused on increasing mental math fluency, flexibility and efficiency. Student are encouraged to share their thinking with the class and it is recorded so others may learn various ways of doing computations inside their heads. This helps students to build a deep understanding of number sense.
Currently, we are working on using the doubles plus one and doubles minus one strategy to add in our heads, as well as making friendly numbers (10, 20, etc.) To do this students are often required to mentally split and combine numbers to make the nearest 10, so that the remainder can be added.
One tool we use is the rekenrek. Barbara Blanke of the Math Learning Centre, offers a comprehensive description of how this tool is used to help students develop number sense,
"What is a Rekenrek? Directly translated, rekenrek means calculating frame, or arithmetic rack. Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in Holland, designed it to support the natural mathematical development of children and to help them generate a variety of addition and subtraction strategies, including doubles plus or minus 1, making 10’s, and compensation. Students can use the rekenrek to develop computation skills or solve contextual problems. Once children understand the operations of addition and subtraction, and can model various situations, it is important that they automatize the basic facts by finding and using patterns and relationships. Unlike drill and practice worksheets and flashcards, the rekenrek supports even the youngest learners with the visual models they need to discover number relationships and develop automaticity. The rekenrek looks like an abacus, but it is not based on place value columns or used like an abacus. Instead, it features two rows of 10 beads, each broken into two sets of five, much like the ten frames used in Bridges in Mathematics. The rekenrek Like ten frames, this tool helps students see the quantity of five as a whole and develop strategies to solve equations like 5 + 2, 5 + 3, etc. The figure below shows how 7 + 8 would be set up on the rekenrek. In working with this model, children might find the total by adding 7 + 7 + 1, or 5 + 5 + 2 + 3, or 10 + 5. They could also choose to count on, but the rekenrek is likely to stretch children to see groups of five."
http://bridges1.mathlearningcenter.org/media/Rekenrek_0308.pdf
Currently, we are working on using the doubles plus one and doubles minus one strategy to add in our heads, as well as making friendly numbers (10, 20, etc.) To do this students are often required to mentally split and combine numbers to make the nearest 10, so that the remainder can be added.
One tool we use is the rekenrek. Barbara Blanke of the Math Learning Centre, offers a comprehensive description of how this tool is used to help students develop number sense,
"What is a Rekenrek? Directly translated, rekenrek means calculating frame, or arithmetic rack. Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in Holland, designed it to support the natural mathematical development of children and to help them generate a variety of addition and subtraction strategies, including doubles plus or minus 1, making 10’s, and compensation. Students can use the rekenrek to develop computation skills or solve contextual problems. Once children understand the operations of addition and subtraction, and can model various situations, it is important that they automatize the basic facts by finding and using patterns and relationships. Unlike drill and practice worksheets and flashcards, the rekenrek supports even the youngest learners with the visual models they need to discover number relationships and develop automaticity. The rekenrek looks like an abacus, but it is not based on place value columns or used like an abacus. Instead, it features two rows of 10 beads, each broken into two sets of five, much like the ten frames used in Bridges in Mathematics. The rekenrek Like ten frames, this tool helps students see the quantity of five as a whole and develop strategies to solve equations like 5 + 2, 5 + 3, etc. The figure below shows how 7 + 8 would be set up on the rekenrek. In working with this model, children might find the total by adding 7 + 7 + 1, or 5 + 5 + 2 + 3, or 10 + 5. They could also choose to count on, but the rekenrek is likely to stretch children to see groups of five."
http://bridges1.mathlearningcenter.org/media/Rekenrek_0308.pdf
We Made a Number Line!
Grade 1 J was deeply engaged in a hands on math project to improve the playground. We decided it would be great to have a large number line to practice our addition, subtraction, skip counting, repeated addition and multiplication on outside.
Using our measuring skills we carefully used tools such as a ruler and measuring tape to try and evenly space our numbers. We looked at geometry and shape to design the pattern of our number lines. We also needed to use our self-management skills and social skills to work together to finish the project.
The students really enjoyed working on such a large project. They were heard to say, "This is fun because it feels like a real grown up job!"
Using our measuring skills we carefully used tools such as a ruler and measuring tape to try and evenly space our numbers. We looked at geometry and shape to design the pattern of our number lines. We also needed to use our self-management skills and social skills to work together to finish the project.
The students really enjoyed working on such a large project. They were heard to say, "This is fun because it feels like a real grown up job!"
2D shapes + games
We examined the properties of various 2D shapes by making a class anchor chart. Some of the language about shape, such as vertices, and some shape names, was new, so we played some games to become familiar with the words. We played two games, called Back to Back and Secret Bag, where students had to ask questions and use their knowledge of the properties of the shapes in order to identify the mystery shape.
shape hunt
I asked the students this question.... "What makes a shape a shape?" The students identified traits such as, "It has to be closed." They built their conceptual understanding through looking at examples and non-examples, realizing that not all shapes have straight sides or vertices.
Next, we went on a hunt to find out where these 2-D shapes exist in the real world. The students recorded their findings and made a Seesaw video explaining the properties of the shape they found.
Next, we went on a hunt to find out where these 2-D shapes exist in the real world. The students recorded their findings and made a Seesaw video explaining the properties of the shape they found.
geometric board
Triangles are a difficult concept for children to understand initially because they typically only see equilateral triangles with the tip pointing up. To broaden their conceptual understanding of a triangle, the students were challenged to make the most interesting or creative triangle they could using the geo-boards. This stretched their thinking to realize that the property of a triangle is 3 vertices and 3 sides, and that the orientation, length of side or size does not matter when it comes to being classified as a triangle.
3D shapes
To identify the properties of 3-D shapes we explored different examples of 3D shapes within the classroom. Through sharing our findings, we were able to learn more about how many edges, vertices, and faces these shapes have.
Composite Shapes
The Grade 1 students have had a lot of fun exploring different ways to combine two-dimensional (2D) shapes to create a composite shape. We shared our composite shapes with the class and then played a game where we had to orally describe how to make our design to a partner. The partner then needed to use their listening skills and knowledge of the shape properties to recreate that particular design.
Build and Draw shapes
A big part of our unit on Shape has been to build and draw shapes to possess defining attributes. We looked at puzzles that only had part of a shape and worked to draw the rest of the shape using visualization and our knowledge of shape properties. We also built 3D shapes from paper using nets. We used these to build robots as a summative task.
2D and 3D Robot Building Summative Task
As a cumulative task, we used all our knowledge of shapes to build a robot made of 2D and 3D shapes. In order to be sure we share all of our learning on Seesaw, the class made up a checklist of criteria to include in our descriptions together. When we built our robots we were sure that we knew how we were going to describe our learning.
Measurement
How do we measure accurately?
What tools can we use to measure?
These are some of the inquiries we have when it comes to measurement. Through hands on group and individual problem solving, we will try to find the answers to during this unit.
What tools can we use to measure?
These are some of the inquiries we have when it comes to measurement. Through hands on group and individual problem solving, we will try to find the answers to during this unit.
I can booklet
As a summative assessment task for our unit on measurement, the students provided examples of how they completed measurements tasks.
Place Value and Money
To compliment our unit of inquiry on workplaces, the students are learning how to recognise money, count money, make certain amounts and make change. Within this unit, we are also reviewing place value. The students are inquiring into the meaning of each digit in 2 and 3 digit numbers. as well as adding and subtracting multiples of ten. Students have also been learning how to regroup groups of ten and hundreds through different games using coins and base ten blocks.