OA-Understand+addition+as+putting+together+and+adding+to,+and+understand+subtraction+as+taking+apart+and+taking+from

K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings*, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. K.OA.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.OA.4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. K.OA.5. Fluently add and subtract within 5. || ===**Anchor Standard/Mathematical Practice(s)**=== K.MP.1. Make sense of problems and persevere in solving them. K.MP.2. Reason abstractly and quantitatively. K.MP.3. Construct viable arguments and critique the reasoning of others. K.MP.4. Model with mathematics. K.MP.5. Use appropriate tools strategically. K.MP.7. Look for and make use of structure. K.MP.8. Look for and express regularity in repeated reasoning. || K.TT.1 Use technology tools and skills to reinforce classroom concepts and activities. || ===**Revised Bloom's Level of thinking**=== **Remembering** **:** can the student recall or remember the information? define, list, recall **Understanding:** can the student explain ideas or concepts? sort, classify, describe, discuss, explain, identify, locate, recognize, select **Applying** : can the student use the information in a new way? demonstrate, illustrate, sketch, write. **Analyzing** : can the student distinguish between the different parts? compare, distinguish, examine, **Evaluating** : can the student justify a stand or decision? appraise, argue, defend, judge, select, support, value, evaluate **Creating** : can the student create new product or point of view? create, design, write. ||
 * ===**Common Core Standard**===
 * Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)
 * ===**Information Technology Standard**===

I can...

 * make a group smaller or larger by adding or subtracting objects.
 * solve addition and subtraction word problems.
 * take a number and break it apart in different ways.
 * When given a number, I can find the missing part to make 10.
 * add and subtract using numbers 0-5.

Essential Vocabulary

 * ===addition, subtraction, plus, minus, equals, sum, difference, solve, equation, decompose ===

Sample Assessments

 * <span style="font-family: Arial,Helvetica,sans-serif;">Join and seperate objects or people to model addition and subtraction.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Create story problems for given addition and subtraction situations.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Count to find the sum.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Seperate a set and count seperated amount to find the difference.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Decompose sets of objects into two or more sets and record with pictures or with numbers.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Find a missing quanity needed to make ten using objects, drawings, and ten frames.

<span style="font-family: Arial,Helvetica,sans-serif;">Differentiation

 * <span style="font-family: Arial,Helvetica,sans-serif;">Students can make up their own addition and subtraction stories and have the class record the answers.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Students use counters and manipulatives to solve addition and subtraction problems.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Students can use graphic organizer (part-part- whole mat) to solve addtion problems.

<span style="font-family: Arial,Helvetica,sans-serif;">Intervention:
<span style="font-family: Arial,Helvetica,sans-serif;">Addition <span style="font-family: Arial,Helvetica,sans-serif;">Subtraction
 * <span style="font-family: Arial,Helvetica,sans-serif;">If student's numbers in the number sentence do not match the pictures, then have students use counters to show the groups.
 * <span style="font-family: Arial,Helvetica,sans-serif;">If student makes errors when writing sums, then have them touch the pictures as they count the first group and conunt on to add the second group.
 * <span style="font-family: Arial,Helvetica,sans-serif;">If students are confused by the plus sign (+), then have them write the symbol (+) between two groups of pictures or counters.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Have students place counters or draw pictures on top of the numbers when finding the sum.
 * <span style="font-family: Arial,Helvetica,sans-serif;">If students are confused about subtraction in word problems is that sometimes we are "taking away," but sometimes we are comparing to see which group is larger. Use lots of manipulative activities to build these concepts, you should keep in mind that you need to model both types of subtraction.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Keep it simple and have it match their world: stories and manipulatives.

<span style="font-family: Arial,Helvetica,sans-serif;">Enrichment:

 * <span style="font-family: Arial,Helvetica,sans-serif;">Students can create an addition or subtraction game using pictures or numbers.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Compose a song or write a poem about adding or subtracting.

<span style="font-family: Arial,Helvetica,sans-serif;">Instructional Resources

 * <span style="font-family: Arial,Helvetica,sans-serif;">Mouse Count by Ellen Stoll Walsh
 * <span style="font-family: Arial,Helvetica,sans-serif;">ten frames
 * <span style="font-family: Arial,Helvetica,sans-serif;">dry erase boards
 * <span style="font-family: Arial,Helvetica,sans-serif;">math journals
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<span style="font-family: Arial,Helvetica,sans-serif;">Notes and Additional Information
<span style="font-family: Arial,Helvetica,sans-serif;">Using addition and subtraction in a word problem context allows students to develop their understanding of what it means to add and subtract. <span style="font-family: Arial,Helvetica,sans-serif;">Students should use objects, fingers, mental images, drawing, sounds, acting out situations and verbal explanations in order to develop the concepts of addition and subtraction. Then, they should be introduced to writing expressions and equations using appropriate terminology and symbols which include “+,” “–,” and “=”. <span style="font-family: Arial,Helvetica,sans-serif;">Students may use document cameras or interactive whiteboards to represent the concept of addition or subtraction. This gives them the opportunity to communicate their thinking.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Addition terminology: add, join, put together, plus, combine, total
 * <span style="font-family: Arial,Helvetica,sans-serif;">Subtraction terminology: minus, take away, separate, difference, compare

<span style="font-family: Arial,Helvetica,sans-serif;">Using a word problem context allows students to develop their understanding about what it means to add and subtract. Addition is putting together and adding to. Subtraction is taking apart and taking from. Kindergarteners develop the concept of addition/subtraction by modeling the actions in word problem using objects, fingers, mental images, drawings, sounds, acting out situations, and/or verbal explanations. Students may use different representations based on their experiences, preferences, etc. They may connect their conceptual representations of the situation using symbols, expressions, and/or equations. Students should experience the following addition and subtraction problem types (see Table 1).


 * <span style="font-family: Arial,Helvetica,sans-serif;">Add To word problems, such as, “Mia had 3 apples. Her friend gave her 2 more. How many does she have now?”
 * A student’s “think aloud” of this problem might be, “I know that Mia has some apples and she’s getting some more. So she’s going to end up with more apples than she started with.”
 * Take From problems such as:
 * José had 8 markers and he gave 2 away. How many does he have now? When modeled, a student would begin with 8 objects and remove two to get the result.
 * Put Together/Take Apart problems with Total Unknown gives students opportunities to work with addition in another context such as:
 * There are 2 red apples on the counter and 3 green apples on the counter. How many apples are on the counter?
 * Solving Put Together/Take Apart problems with Both Addends Unknown provides students with experiences with finding all the decompositions of a number and investigating the patterns involved.
 * There are 10 apples on the counter. Some are red and some are green. How many apples could be green? How many apples could be red?

<span style="font-family: Arial,Helvetica,sans-serif;">Students may use a document camera or interactive whiteboard to demonstrate addition or subtraction strategies. This gives them the opportunity to communicate and justify their thinking.

<span style="font-family: Arial,Helvetica,sans-serif;">This standard focuses on number pairs which add to a specified total, 1-10. These number pairs may be examined either in or out of context.

<span style="font-family: Arial,Helvetica,sans-serif;">Students may use objects such as cubes, two-color counters, square tiles, etc. to show different number pairs for a given number. For example, for the number 5, students may split a set of 5 objects into 1 and 4, 2 and 3, etc.

<span style="font-family: Arial,Helvetica,sans-serif;">Students may also use drawings to show different number pairs for a given number. For example, students may draw 5 objects, showing how to decompose in several ways.

<span style="font-family: Arial,Helvetica,sans-serif;">Sample unit sequence:


 * <span style="font-family: Arial,Helvetica,sans-serif;">A contextual problem (word problem) is presented to the students such as, “Mia goes to Nan’s house. Nan tells her she may have 5 pieces of fruit to take home. There are lots of apples and bananas. How many of each can she take?”
 * <span style="font-family: Arial,Helvetica,sans-serif;">Students find related number pairs using objects (such as cubes or two-color counters), drawings, and/or equations. Students may use different representations based on their experiences, preferences, etc.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Students may write equations that equal 5 such as:
 * 5=4+1
 * 3+2=5
 * 2+3=4+1

<span style="font-family: Arial,Helvetica,sans-serif;">This is a good opportunity for students to systematically list all the possible number pairs for a given number. For example, all the number pairs for 5 could be listed as 0+5, 1+4, 2+3, 3+2, 4+1, and 5+0. Students should describe the pattern that they see in the addends, e.g., each number is one less or one than the previous addend.

<span style="font-family: Arial,Helvetica,sans-serif;">The number pairs that total ten are foundational for students’ ability to work fluently within base-ten numbers and operations. Different models, such as ten-frames, cubes, two-color counters, etc., assist students in visualizing these number pairs for ten.

<span style="font-family: Arial,Helvetica,sans-serif;">Example 1:

<span style="font-family: Arial,Helvetica,sans-serif;">Students place three objects on a ten frame and then determine how many more are needed to “make a ten.”

<span style="font-family: Arial,Helvetica,sans-serif;">Students may use electronic versions of ten frames to develop this skill.

<span style="font-family: Arial,Helvetica,sans-serif;">Example 2:

<span style="font-family: Arial,Helvetica,sans-serif;">The student snaps ten cubes together to make a “train.”


 * <span style="font-family: Arial,Helvetica,sans-serif;">Student breaks the “train” into two parts. S/he counts how many are in each part and record the associated equation (10 = _ + _).
 * <span style="font-family: Arial,Helvetica,sans-serif;">Student breaks the “train into two parts. S/he counts how many are in one part and determines how many are in the other part without directly counting that part. Then s/he records the associated equation (if the counted part has 4 cubes, the equation would be 10 = 4 + _).
 * <span style="font-family: Arial,Helvetica,sans-serif;">Student covers up part of the train, without counting the covered part. S/he counts the cubes that are showing and determines how many are covered up. Then s/he records the associated equation (if the counted part has 7 cubes, the equation would be 10 = 7 + _).

<span style="font-family: Arial,Helvetica,sans-serif;">Example 3:

<span style="font-family: Arial,Helvetica,sans-serif;">The student tosses ten two-color counters on the table and records how many of each color are facing up.

<span style="font-family: Arial,Helvetica,sans-serif;">This standard focuses on students being able to add and subtract numbers within 5. Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.

<span style="font-family: Arial,Helvetica,sans-serif;">Strategies students may use to attain fluency include:


 * <span style="font-family: Arial,Helvetica,sans-serif;">Counting on (e.g., for 3+2, students will state, “3,” and then count on two more, “4, 5,” and state the solution is “5”)
 * <span style="font-family: Arial,Helvetica,sans-serif;">Counting back (e.g., for 4-3, students will state, “4,” and then count back three, “3, 2, 1” and state the solution is “1”)
 * <span style="font-family: Arial,Helvetica,sans-serif;">Counting up to subtract (e.g., for 5-3, students will say, “3,” and then count up until they get to 5, keeping track of how many they counted up, stating that the solution is “2”)
 * <span style="font-family: Arial,Helvetica,sans-serif;">Using doubles (e.g., for 2+3, students may say, “I know that 2+2 is 4, and 1 more is 5”)
 * <span style="font-family: Arial,Helvetica,sans-serif;">Using commutative property (e.g., students may say, “I know that 2+1=3, so 1+2=3”)
 * <span style="font-family: Arial,Helvetica,sans-serif;">Using fact families (e.g., students may say, “I know that 2+3=5, so 5-3=2”)

<span style="font-family: Arial,Helvetica,sans-serif;">Students may use electronic versions of five frames to develop fluency of these facts.

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