Standard KOA3 5=3+2 5=4+1. Sarah Krauss CCLM^2 Project Summer 2012

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Brice Turner
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Standard KOA3 Part 1: Standard Grade Level: Kindergarten Domain: Operations and Algebraic Thinking K.

1 Sarah Krauss CCLM^2 Project Summer 2012 DRAFT DOCUMENT. This material was developed as part of the Leadership for the Common Core in Mathematics (CCLM^2) project at the University of Wisconsin-Milwaukee. Standard KOA3 Part 1: Standard Grade Level: Kindergarten Domain: Operations and Algebraic Thinking K.OA Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Standard: KOA3. 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 drawing or equation (e.g. 5=2+3 and 5=4+1) Part 2: Explanation and Examples of the Standard Teacher Friendly Language: Break apart numbers up to and including 10 into pairs more than one way using objects or drawings and show representation of their thinking with a drawing or equation. What students should be able to do as a result of focusing on the standard: v Counting a set v Counting a given number of objects v Comparing sets or numerals v Model simple joining and separating situations with sets of objects Examples include: 5=1+4, 5=2+3, 5= 3+2, 5=4+1, 5=5+0. The two addends that make up the total can be called partners in Kindergarten (Progressions Document, p.10). This can help children understand that these are two numbers that go together to make the total. The Put Together/Take Apart situations with both addends unknown help facilitate the learning of these types of partner situations. So, if there were 5 balloons and some were red and some were blue, the student can find the different partners that come together to total 5. They could draw 3 red balloons and 2 blue balloons. They could draw 1 red balloon and 4 blue balloons. Or, they could draw 0 red balloons and 5 blue balloons. This is also an opportunity to discuss the fact that the partners could be switched but the total would still be 5. 5=3+2 5=4+1

2 Drawings would be used during at least the first semester of kindergarten to represent a student s thinking. Since the standard states that they may record each decomposition with a drawing or equation, it is my belief that not all students will leave Kindergarten writing equations. However, teachers should be constantly modeling equations after using drawings to illustrate thinking. Also in the progressions document (p.10), it is indicated that the total should be written to the left and the partners to the right of the equation (e.g. 5=0+5, 5=1+4 etc.) because this helps the children see a pattern in the partnerships. It also helps children see that the = sign is and equality of expressions, not just giving the total. Examples of Lessons in Kindergarten Dot Patterns Students need exposure to many different types of dot patterns so that they can begin to subitize small groups of things. According to the research, students ages 4-5 should be able to see in groups (subitize) 1-5 objects and children ages 5-6 should be working on subitizing 1-6 objects and patterns up to 10 objects. Using Dot patterns and asking children how did you see it? is a great way to focus in on subitizing. Start small with 1,2, and 3 dots. Ask children to quickly tell you how many they see. Once they have mastered the 2 s and 3 s (perceptual subitizing) they can move on to conceptual subitizing (compose and decompose numbers to 10).

3 Perceptual Subitizing Ideas 1. Dot Plate Flash start with smaller quantities (1,2,3 dots) and familiar dot arrangements. Flash the plate for 3 seconds and encourage a quick response counters under a box Hide 3 counters under a box. Uncover and ask how many counters are there? Encourage a quick response. 3. Making 2 s and 3 s Give each child 10 counters. Break their set apart by making two s. Repeat until they can make the sets quickly. 4. Rolling Dot Cubes Students roll the cubes with 1,2,3 dots on them. Ask, how may are there? and how did you see them? 5. Real World Examples of 2 s and 3 s - Have students look around the room and find examples of 2 s and 3 s (2 eyes, sides on a triangle) Conceptual Subitizing Ideas 1. Dot patterns up to 10 (can be color coordinated, i.e. 2 red and 3 blue) 2. Dot Plate Flash - how many dots did you see?, how did you see them?, How did you figure out the total amount?) 3. Make the Pattern - flash and students create the pattern using counters on their own mat 4. Hold Up - show with fingers that is the same as number of dots 5. Show the Numeral Students show the corresponding numeral to the number of dots on the flashed plate. 6. One More or One Less Flash the dot plates and ask children to say the number that is one more or less than the number of dots shown. Ask to explain reasoning. 10 Frames 1. Look Quick (p.4 It Makes Sense - Using 10 Frames to Build Number Sense) 2. Make the Number (p.9 It Makes Sense) 3. Ten Frame Memory (p.71 It Makes Sense) Show the students a 10 frame with 7 dots. Tell them you want them to figure out the number of dots by looking for groups instead of counting each dot. Ask the children what they see Model that there are several ways to see it. I see 4 dots and 3 more. Or, I see 5 dots and 2 more. Or 10 spaces with 3 missing etc. Teachers and students should be talking about these subitizing ideas by using the correct language. Teachers should focus on using the terms part-part whole or partners two numbers that go together to make a total.

4 Part 3: School Mathematics Textbook Program a. Textbook Development: Everyday Mathematics Kindergarten Lessons that fit with KOA Getting to Know Numbers Create number posters with different representations of a number. 4 is 4 dots, 4 fingers, 4 stars, 4 unifix cubes 1.14 Finger Count Fun Using fingers to determine identify numbers 1.16 Ten Frames Combinations of counters to make 10 or less than Number Stories Acting out or using counters to solve stories. Project 2 Our bodies help us count Using fingers to see different combinations of numbers. 3.3 Graphing Dice Rolls Subitize dots on a die 3.5 Domino Concentration Count dots on dominos, conceptual subitizing 3.8 Pocket Problems Objects in a pocket, add more objects how many in all? 3.13 Train Games Adding and subtracting from Number Line Math Walking up and back on large floor number line. Example: start at 4, how many steps to get to The Addition Symbol Use counters and + symbol on a slate. Move counters to see different combinations to get to a total number. **4.8 Roll and Record 2 Dice Graph the total of 2 dice **4.15 Number Stories Relating + and to number stories 5.4 Guess my Number Figure out what is 2 less than 5 or 3 more than 6 **7.3 Class Number Story Book Draw a picture illustrating the context with an equation **7.6 Dice Addition Perceptual subitizing: 3 dots + 2 dots =5 dots **8.4 High Roller Roll 2 die, keep the higher one and reroll the 2 nd **8.9 Name Collection Poster Different ways to write each number Example:7=6+1, 7 in a ten-frame, 5+2= What s my Rule Students figure out the missing addend or partner when given the total die Missing # Problems Pocket with objects, add or subtract some from the pocket. Again, missing addend problem. **These lessons directly relate to KOA3 by decomposing numbers less than and equal to 10 in more than one way and use drawings or equations to illustrate thinking.

5 b. Conclusions: The conclusions that I am seeing after investigating the Everyday Mathematics program is that there is not enough time spent on the KOA3 standard. Different decompositions of numbers up to 10 are introduced throughout the year but there doesn t seem to be any continuation of the introductions. This standard seems to be touched on but not fully developed. Since students need to be able to add and subtract fluently within 5 by the end of Kindergarten (KOA5) the decompositions of numbers in more than one way is imperative throughout the year. I am also noticing that there is a lot of emphasis put on fingers and not as much emphasis put into counters or drawings. There are not as many lessons that have the students illustrate their thinking with pictures or equations. I m hoping to integrate a math journal with various types of word problems using the decomposition of numbers within 10 so that the students need to illustrate their thinking with drawings or equations. 1 st Grade Curriculum: The 1 st grade Everyday Math curriculum uses games to work on the facts up to 10 for the first part of the year. They then move on to facts up to 20 by exposing them to different games and situations. But, after looking through the curriculum, they also do not seem to have enough emphasis on teaching level 2 strategies, exposure to level 3 strategies, or illustrating thinking with pictures or equations. Again in 1 st grade they try to cover a lot of ground but do not focus one topic for an extended amount of time. It doesn t have as much understanding or meaning behind it as the core standards suggest. Suggestions: The Everyday Math Curriculum has many good lessons that are fun for kids to play and do but I feel that the curriculum is an inch deep and a mile wide. We need to narrow down the focus so that students are exposed to the partner pairs up to 10 and become fluent up to five. More time needs to be given to using the dot plates, five frames, ten frames, math racks on a weekly basis. Students need to be able to see that there are several different ways to decompose numbers under and equal to 10. By utilizing a math journal on a weekly basis with various types of problem situations, I can continuously model and have students create their own drawings and equations to solve different word problems.

1.2A: Subitize (0-10) Use dominoes (real tiles or domino pictures), dot cards, 10-frames cards, and/or other tools with structured arrangements.

1.2A: Subitize (0-10) Use dominoes (real tiles or domino pictures), dot cards, 10-frames cards, and/or other tools with structured arrangements. FIRST GRADE 1.2 NUMBER AND OPERATIONS. The student applies mathematical process standards to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships