Operations and Algebraic Thinking

Understanding addition as putting together and adding to, and understanding subtraction as taking apart and taking from.

K.OA.1 : Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (claps), acting out situations, verbal explanations, expressions, or equations.

Day 1:

Understand the meaning of addition and recognize the plus sign.

Act it out: Have 4 students come to the front of the room.Ask: How many students are in the front of the room? (4write this on the board)Ask: What can I do to make it 5 students? (Have 1 more students go to the front write “and 2” on the board)

“4 and 1” makes 5

Pass out students sheet and have students record:

5 4 and 1

repeat with other pairs (decomposing 5) 1 and 4, 2 and 3, 3 and 2,

<<Challenge- ask: Can you think of any other ways to make 5? ( 5 and 0 or 0 and 5)>>

Introduce the word “ADD” as a word that meant to join. (put the word “add” up on the math word wall) Then model joining together or adding using your fingers. Hold up 4 fingers on one hand and 1 finger on the other hand (making sure your hands are a fair distance apart, then move them so they are touching and say “I just joined, or added, 4 and 1” (now put joining together on the word wall next to add)

<<Real Life connection- have a discussion about what objects you might want to join, You can have students look around the classroom or they can use examples from outside of school that they can think of)

Another way I can talk about adding or addition, is by using the word “plus” (add plus to the word wall)

See how I wrote 4 and 1 on the board? Instead of saying “and” I can say “plus” Let’s try this together:

4 and 14 plus 1

Now let’s re-write these

3 and 2

2 and 3

1 and 4

<<define plus on word wall>>

Say: Do you want to know an even EASIER way of writing these than 4 and 1, or 4 plus 1?

We can use a SYMBOL (might have to define and go over some examples of symbols) instead of the word “and” or the word “plus”. We can use +

On the same worksheet, underneath 4 and 14 plus 1

write: 4 + 1

(after you write 4 + 1, repeat the motion of joining 4 fingers and 1 finger)

then have students work on the remaining fact families1 and 42 and 3,3 and 2,

Do these one at a time and after each, have the students show you how they join their fingers, this will let you know if they are understanding the joining of two numbers (for example- are they joining 1 finger and 4 fingers for 3 +2?)

Possible additional support during this part of the lesson is to use a frame and counters for students to drag into frame

Day 2: Draw a Picture (modeled instruction)

Give students a piece of paper with 2 +1 on it

Before starting the activity do a quick review of the previous day.

Putting together/joining is “adding” and we can use the symbol + (Reference the word wall so students automatically look there) Show an example on your hands of joining, for example , 3 fingers and 2 fingers.

Today we are going to be drawing pictures of things we might join to show what we’ve learned about adding.

Take a look at your paper:Ask: What does it say? (students may say 2 and 1, or 2 plus 1)

Watch me as I show you how I would draw a picture that shows 2 + 1

(look around the room briefly…walk over to the pencil jar)

take 2 pencils out and say “I have 2 pencils” I am going to draw 2 pencils on my paper. (draw two pencils on the paper) now I know that (+) means to join or add, so I am going to add another pencil to my drawing. (put the + symbol between the drawing of the 2 pencils and the 1 pencil)

Say: So if I have 2 pencils and I add 1 pencil, I have 3 pencils altogether.

Now I want you to take a look around the room or think about some things that you might want to join to show 2 + 1 and then draw the picture like I did with the + sign between the two groups. I will leave my example on the board.

<<Circulate the room and meet with small groups, make sure to have sets of objects ready to go for students who may be struggling to find an example>>

Whole Class discussion:

What are some ways we can describe these pictures? ( 2 and 1, 2 plus 1, 2 and 1 more is 3, 2 plus 1 is 3)

Try to come up with a story about why you might want to add the objects in your drawing. (have a few students share)

Hands-On Activity: Tiered Station Work

(Always begin with modeling task)

If there is a smartboard, use interactive teacher created file (Clone the fish so students may pull from the fish bucket to add more fish to the group)

If no smartboard is available, use toys.

Say: There are 2 blue fish and 3 red fish. (Write 2+3 on the board) while saying two blue fish plus three red fish.

Let’s try showing this on our fingers (hold up 2 fingers to show blue fish on one hand, and three fingers on the other hand to show red fish- move them together to join them)

Ask: How many fish are there?

2+3 is 5

<<Introduce the = sign>> Ask: How many fish are there TOTAL or ALTOGETHER? (5)

We can find the TOTAL number of fish by counting all of them together. We can write a number sentence (add to word wall- later you can add equation next to it)

(Write on board) 2+3 = 5 We can say 2+3 equals 5. This means what is on the left of the = sign is the same as what is on the right side. (Have a non math discussion of what equal means providing a concrete example for students) You can then use counters to show a group of 2 and a group of 3 underneath 2+3, and then 5 counters under the 5 so students can see there are 5 counters underneath each side of the equal sign, demonstrating what “Equals” means (Define on word wall)(depending on how the class is doing- possibly introduce sum-keeping in mind this can be tricky for ELL students confusing it with “some”)

Give students connecting counters (10 each, 5 in one color, 5 in another color)

Have them connect 3 red cubes with 1 blue cube. Model how you would write this number sentence (have this on board for students to reference ______+_______=)

3+1=4 (have students copy this on their whiteboards)

Do a few more examples together and discuss.

Activity: Match the picture to the addition sentence

If a smartboard is available, use the interactive notebook to draw a line from the picture to the number sentence. If not, provide students with a hard copy worksheet. Make sure there are two number sentences that are = to the same

number such as 4. Ask the students how they could figure out which picture matched each number sentence if they were both equal to 4. (Students should talk about the groups being joined).

Check for understanding:

Show a picture with a number sentence and students will need to determine if the sentence is correct or not.

+ =

3+1=3

3+1=______

Ask: How did you know that 3 + 1 did not equal 4? (if you start with three, and you need to bring another duck in, I know there has to be more than 3 ducks)

Station Work:

( I always include a fluency station- flashcards or XTRAMATH)

Samples:

On Level:

Students work in pairs.Students will have number cards from 0-9Partner 1: will use the cards to make a number sentence with the total missing and will tell a related story problemPartner 2: will model partner 1’s story problem with counters and use a number card to complete the sentence.

Both partners will check their answers and then switch roles.Repeat with different number sentences

Above Grade Level:

Find all the ways to make a 5

Students will be writing each fact family and drawing a picture to represent the sentence. (they can use circles or counters, they don’t have to draw objects)

If a student writes 1+4 and 4+1 as different sentences, have them explain why these are different- using an example and telling a story problem that relates to each of them.

Below grade level: Intervention:

Students will have number cards 0-9 and 5 counters.

Give students a + and = sign

Teacher will show 1 + 4 Students will read this as 1 and 4 and 1 plus 4Have students place 1 counter below the 1 card and 4 counters below the 4 card.Ask: How many counters are there altogether? (5)

Reintroduce the equal sign meaning “the same as”

Say: 1 and 4 is the same as 5

Or

1 plus 4 equals 5

repeat with other cards

Group 1 (Above Grade Level) Students will be responsible for reading their own story problems. Teacher

will provide scaffolding as needed. Students will use cotton balls to illustrate each problem. Unneeded information will be inserted into problems, so children have to

discriminate which information to use. This group will be adding two numbers to 20.

After cotton balls have been placed on mat, students will record the problem on their record sheets, writing a full number sentence. Their record sheets will be a blank piece of paper. They will be responsible for every element of the number sentence.

An extension activity for this group is to have them glue three cloud combinations to a blue piece of construction paper. Students will write an addition number sentence for their picture. Ex: 4+5+3=12

Groups 2 (On Grade Level) Teacher will recite a variety of addition story problems to the group.

Students will use cotton balls to illustrate each problem. Students will be adding two numbers to 15. The teacher will demonstrate how to write a simple number sentence to the

group. The students will be expected to write their own number sentences on their blank record sheet.

Group 3 (Below Grade Level) Teacher will demonstrate a few addition story problems on her own work

mat. Teacher will recite a variety of addition story problems to the group.

Students will use cotton balls to illustrate each problem. Story problems will contain only pertinent information.

These students will be adding two numbers to 10. The record sheet will be formatted as follows: ____+_____=______. The students will have a number line to refer to for number writing. A

variety of manipulatives will also be provided.

Independent Practice- End of Unit assessment

Draw _______+_________=5

(provide supports for students below grade level- cut outs students can paste instead of drawing) (For above level-students can write a sentence)

Planning Tiered Instruction

Planning Interventions:

Use various forms of assessment to choose interventions to move students in a targeted, strategic way.

Goal is to gain independent strategies Always link to larger ideas. Interventions should be linked to classroom

instruction so it does not seem isolated. Math builds… Interventions should take students’ strengths into consideration and use their

prior knowledge (fractions/decimals) Use a multi-modal approach to meet various learning styles and preferences. Should be thoughtfully planned using scaffolding to close the gap and build up

to and beyond grade level expectations. Progress Monitoring!!

Objective-What do you want students to

understand as a result of the lesson?

Tier 1-Below Grade Level

If the task is too easy- students will become bored

Tier 2- On Grade Level

Should be engaging, not too easy, not too challenging. Students should be

working within their zone of proximal development

Tier 3- Above Grade Level

If the task is too challenging, students will become frustrated

Preassessment- collect data to determine

where to start whole group instruction