COMMON MISCONCEPTIONS Students may over-generalize the vocabulary in word problems and think that certain words indicate solution strategies that must be used to find an answer. They might think that the word always means to add and the words or always means to subtract. When more take away left students use the words to refer to subtraction and its symbol, teachers need to repeat take away ideas using the words or For example, students use addition to solve minus subtract. students’ this Take from/Start Unknown problem: Seth took the 8 stickers he no longer wanted and gave them to Anna. Now Seth has 11 stickers How many stickers did Seth have to begin with? left. If students progress from working with manipulatives to writing numerical expressions and equations, they skip using pictorial thinking. Students will then be more likely to use finger counting and rote memorization for work with addition and subtraction. Counting forward builds to the concept of addition while counting back leads to the concept of subtraction. However, counting is an inefficient strategy. Teachers need to provide instructional experiences so that students progress from the concrete level, to the pictorial level, then to the abstract level when learning mathematics. TASKS The following tasks represent the level of depth, rigor, and complexity expected of all Kindergarteners. These tasks or a task of similar depth and rigor should be used to demonstrate evidence of learning. TASK DESCRIPTIONS Scaffolding Tasks that build up to the learning task. Task Constructing Constructing understanding through deep/rich contextualized problem solving tasks. Task Tasks that provide students opportunities to practice skills and concepts. Practice Task Designed to require students to use several concepts learned during the unit Culminating Task to answer a new or unique situation. Allows students to give evidence of their own understanding toward the mastery of the standard and requires them to extend their chain of mathematical reasoning. Formative Lessons that support teachers in formative assessment which both reveal and develop understanding of key mathematical ideas and applications. Assessment students’ Lesson (FAL) These lessons enable teachers and students to monitor in more detail their progress towards the targets of the standards.
COMMON MISCONCEPTIONS Students may over-generalize the vocabulary in word problems and think that certain words indicate solution strategies that must be used to find an answer. They might think that the word more always means to add and the words take away or left always means to subtract. When students use the words take away to refer to subtraction and its symbol, teachers need to repeat students’ ideas using the words minus or subtract. For example, students use addition to solve this Take from/Start Unknown problem: Seth took the 8 stickers he no longer wanted and gave them to Anna. Now Seth has 11 stickers left. How many stickers did Seth have to begin with? If students progress from working with manipulatives to writing numerical expressions and equations, they skip using pictorial thinking. Students will then be more likely to use finger counting and rote memorization for work with addition and subtraction. Counting forward builds to the concept of addition while counting back leads to the concept of subtraction. However, counting is an inefficient strategy. Teachers need to provide instructional experiences so that students progress from the concrete level, to the pictorial level, then to the abstract level when learning mathematics. TASKS The following tasks represent the level of depth, rigor, and complexity expected of all Kindergarteners. These tasks or a task of similar depth and rigor should be used to demonstrate evidence of learning. TASK DESCRIPTIONS Scaffolding Task Tasks that build up to the learning task. Constructing Task Constructing understanding through deep/rich contextualized problem solving tasks. Practice Task Tasks that provide students opportunities to practice skills and concepts. Culminating Task Designed to require students to use several concepts learned during the unit to answer a new or unique situation. Allows students to give evidence of their own understanding toward the mastery of the standard and requires them to extend their chain of mathematical reasoning. Formative Assessment Lesson (FAL) Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications. These lessons enable teachers and students to monitor in more detail their progress towards the targets of the standards.