How can I plan my lessons using the Backwards Approach?Lesson #1

Identify the outcomes to be learned

N1.9 Demonstrate an understanding of addition of numbers with answers to 20 and the corresponding subtraction facts, concretely, pictorially, physically, and symbolically by:• using familiar and mathematical language to describe additive and subtractive actions from their experience• creating and solving problems in context that involve addition and subtraction• modeling addition and subtraction using a variety of concrete and visual representations, and recording the process symbolically.

Be aware of the processes that should be integrated into your string of lessons for this outcome.

Now that I have listed my outcome:

Determine how the learning will be observed

What will the children do to know that the learning has occurred?What should children do to demonstrate the understanding of the mathematical concepts, skills, and big ideas?What assessment tools will be the most suitable to provide evidence of student understanding?How can I document the children’s learning?

Create your assessment tools before you create your lesson task.

Name Models thinking using a ten frame

Uses counting strategies to find missing part

Is able to represent using part-part –whole

Is able to record number sentences+-

(counting forward or backward)

mat

Plan the learning environment and instruction

What learning opportunities and experiences should I provide to promote the learning outcomes?What will the learning environment look like?What strategies do children use to access prior knowledge and continually communicate and represent understanding?

What teaching strategies and resources will I use?How can I differentiate the lesson to challenge all students at their learning ability? How will I integrate technology, communication, mental math, reasoning, visualization, etc into this lesson? (7 Processes) Look at your outcomes to see which of the processes you should be including.

Plan your lesson here: What lesson format will you use? BEFORE-DURING-AFTER? Math PODS? ETC.

I will begin with an oral journal using the sentence starters: I see.. I think… This reminds me of…The photo that I have chosen is of a portion of the hundreds chart. Something that is very familiar to them and they discuss it every day. I will have copies of the photo for students to record their “thinking”, if they so wish to use it. This will keep the children that need to be challenged a bit, to record their thoughts but not in sentences. In a few days this journal idea will turn into labeling the photo and then students writing in their journal using the above sentence starters. This will be assessed using a rubric.

After the oral journal I will pull out the Power of Ten cards and students will tell/ share what they know. How have they used these cards? What are they learning? What does it look like/ sound like when you play games with a partner or small group or by yourself?(Reviewing expectations of behavior)

I will teach a new game called “Salute”. This game requires students to use either subtraction from ten or adding on in order to find their mystery number. Their partner says how many empty spaces or white spaces while the student needs to solve for the unknown. After, we will take this a step further and represent the number story in a few different ways (connections).

A ten- frame will be placed on partner “A”’s forehead.

Partner “B” will say how many empty spaces. Partner “A” will then think about how many red spaces. A discussion will follow in full group strategies how they solved for the unknown number.Once the students have had playing time and full group discussion, the activity will be taken one step further. Students will represent their work in 3 forms (ten frame, part-part whole and math sentences.

Show and share in full group.

Assess student learning and follow upWhat conclusions can be made from assessment information?How effective have instructional strategies been?What are the next steps for instruction?How will the gaps in the development of understanding be addressed?How will the children extend their learning?

Lesson 2How can I plan my lessons using the Backwards Approach?

Identify the outcomes to be learned

N1.9 Demonstrate an understanding of addition of numbers with answers to 20 and the corresponding subtraction facts, concretely, pictorially, physically, and symbolically by:• using familiar and mathematical language to describe additive and subtractive actions from their experience• creating and solving problems in context that involve addition and subtraction• modeling addition and subtraction using a variety of concrete and visual representations, and recording the process symbolically.

Be aware of the processes that should be integrated into your string of lessons for this outcome.

Lesson#2 will focus on the relationship between addition and subtraction FACT FAMILIES. We will also introduce representation on the number-line.

For students that you feel are still not ready to move on please have them practice virtually (illuminations) and concretely by playing the game below.Models and Connections

New mathematics is continuously developed by creating new models as well as combining and expanding existing models. Although the final products of mathematics are most frequently represented by symbolic models, their meaning and purpose is often found in the concrete, physical, pictorial, and oral models and the connections between them.

To develop a deep and meaningful understanding of mathematical concepts, students need to represent their ideas and strategies using a variety of models (concrete, physical, pictorial, oral, and symbolic). In addition, students need to make connections between the different representations. These connections are made by having the students try to move from one type of representation to another (how could you write what you’ve done here using mathematical symbols?) or by having students compare their representations with others around the class.

In making these connections, students should also be asked to reflect upon the mathematical ideas and concepts that students already know are being used in their new models (e.g., I know that addition means to put things together into a group, so I’m going to move the two sets of blocks together to determine the sum).

If I was not modeling a lesson you could have the two groups as listed above and the third as a small group to evaluate progress and understanding by watching, and asking questions.

Now that I have listed my outcome:

Determine how the learning will be observed

What will the children do to know that the learning has occurred?What should children do to demonstrate the understanding of the mathematical concepts, skills, and big ideas?What assessment tools will be the most suitable to provide evidence of student understanding?How can I document the children’s learning?

Continue using this assessment.

Lesson #2, I want to provide a connection of the representations for the addition and subtraction to ten. Introduce this rubric. Tell the students that they should think about all of the ways they are representing their work. How are they connected to each other?

Plan the learning environment and instruction

What learning opportunities and experiences should I provide to promote the learning outcomes?What will the learning environment look like?What strategies do children use to access prior knowledge and continually communicate and represent understanding?What teaching strategies and resources will I use?

How can I differentiate the lesson to challenge all students at their learning ability? How will I integrate technology, communication, mental math, reasoning, visualization, etc into this lesson? (7 Processes) Look at your outcomes to see which of the processes you should be including.

Plan your lesson here: What lesson format will you use? BEFORE-DURING-AFTER? Math PODS? ETC.

Before: Review learning from last lesson through a discussion.

I see… I think… This reminds me of…

Math vocabulary: commutative property, fact familyCan anyone tell a combining or separating story from this picture? 6+4=10 4+6=10 10-4=6 10-6=4Pass out the number line and two different colors of linking cubes (rods of ten in 2 colors).

How can we show this number story on a number-line?Pass out number-lines.

During: Work with a partner to solve.

After Show and share the different representations student s used to solve this problem.Discuss the connection. How is the pancake problem similar to this problem? How are the

different representations used in both stories? This is proving mathematically in a different way.Assess student learning and follow upWhat conclusions can be made from assessment information?How effective have instructional strategies been?What are the next steps for instruction?How will the gaps in the development of understanding be addressed?How will the children extend their learning?

Where do we go next?

Tomorrow students will solve a problem similar to the above problem. This problem will be done individually for assessment. The problem will be differentiated for levels in the classroom.Have a variety of ‘tools’ Photo copy of ten frames, part-part-whole, number-lines for students to uses as they solve the problem. These tools are ways for all students to be successful. Some children may not need the tools as they will be able to represent these graphic organizers themselves. The more they see and use these tools; eventually they will not need them as they will be able to draw them on their own.Use the NCTM rubric to evaluate.