addends addition array bar graph columns data equal sharing/forming equal sized groups equation even odd pairing picture graph product rectangular rows scale sum total COMMON MISCONCEPTIONS (As stated in Teaching Student-Centered Mathematics Developmentally Appropriate Instruction for Grades K-2, Van de Walle, Lovin, Karp, Bay-Williams): “Children must come to understand that errors provide opportunities for growth as they are uncovered and explained. Trust must be established with an understanding that it is okay to make mistakes. Without this trust, many ideas will never be shared.” Regarding odd and even numbers, students may initially have difficulty “proving” how they know numbers are odd or even. Students may struggle with communicating their growing knowledge using precise mathematical language. Teachers should provide multiple opportunities for students manipulate numbers of objects and express their observations. With regard to an understanding of arrays, students may at first confuse rows and columns. Children should be provided with numerous chances to make real life connections to examples of rows and columns (some picture cards are provided in this unit). To further support an understanding, teachers may encourage students to use their hands to show the direction rows and columns go. As students move on to explore arrays, they may struggle with creating arrays. For example, students may not know where to begin as they attempt to create an array with 18 objects. Teachers should encourage students to look for equal groups (repeating number patterns) that can be added to make a total of 18. Multiple opportunities will increase student fluency with these tasks. When relating arrays to repeated addition equations, students who do not naturally make connections between the two may be guided towards discovery with questions such as “How many rows do you see in the array” “How many objects are in each row?” “Does each row have the same amount of objects?” “How can you add these numbers to find the total number of objects?” TASK TYPES Scaffolding Task Tasks that build up to the learning task.
Task Name Task Type/Grouping Strategy Content Addressed Standard(s) Task Description Students will: 3-Act Task Whole Group Arrays MGSE2.OA.4 Be presented with a problem and phot and asked to solve the problem. They will generate questions and be given additional information only upon realizing they haven’t been given enough information to solve the task. Scaffolding Task Large Group, Small Groups Odd and Even Numbers MGSE2.OA.3 Using square tiles explore the difference between odd and even numbers. Classify number into categories: odd or even. Scaffolding Task Large Group, Partners Odd and Even Numbers MGSE2.OA.3 Determine strategies to use to decide if a particular group of students are even or odd. Scaffolding Task Large Group, Small Group Odd and Even Numbers MGSE.2OA.3 Engage in experiences with repeated addition using real life objects and explore how even numbers can be split into two equal groups. Practice Task, Large Group, Individual Equal Addends MGSE2.OA.3 Continue to develop and apply the concept of equal addends to the mathematical problem solving opportunities. Scaffolding Task Large group, Small Group Odd and Even Numbers MGSE2.OA.3 Begin to understand that adding 2 equal addends produces an even sum; adding 2 odd addends produces an even sum; but combining an even and odd addend results in an odd sum. Constructing Task Large Group, Small Group Odd and Even Numbers MGSE2.OA.3 MGSE2.OA.4 Apply understanding of odd and even numbers to begin understanding arrays through exploration with manipulatives.