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Standard: Fluently add and subtract within 5.

Understanding the standard: Students are fluent when they display accuracy (correct answer), efficiency (a reasonable amount of steps in about 3 seconds without resorting to counting), and flexibility (using strategies such as the distributive property). Students develop fluency by understanding and internalizing the relationships that exist between and among numbers. Oftentimes, when children think of each “fact” as an individual item that does not relate to any other “fact”, they are attempting to memorize separate bits of information that can be easily forgotten. Instead, in order to fluently add and subtract, children must first be able to see sub-parts within a number (inclusion, K.CC.4.c). Once they have reached this milestone, children need repeated experiences with many different types of concrete materials (such as cubes, chips, and buttons) over an extended amount of time in order to recognize that there are only particular sub-parts for each number. Therefore, children will realize that if 3 and 2 is a combination of 5, then 3 and 2 cannot be a combination of 6. For example, after making various arrangements with toothpicks, students learn that only a certain number of sub-parts exist within the number 4:

Then, after numerous opportunities to explore, represent and discuss “4”, a student becomes able to fluently answer problems such as, “One bird was on the tree. Three more birds came. How many are on the tree now?” and “There was one bird on the tree. Some more came. There are now 4 birds on the tree. How many birds came?” Traditional flash cards or timed tests have not been proven as effective instructional strategies for developing fluency. Rather, numerous experiences with breaking apart actual sets of objects help children internalize parts of number.

Suggested task for teaching this standard: What the Heck is a Rekenrek?

Teacher Look-Fors (Formative Assessment):

• Are students able to model a given number within 5 on the Rekenrek?
• Are students able to model a given number in more than one way on the Rekenrek?
• Are students able to construct a viable argument as to how they correctly modeled the given number?
• Are students able to draw a pictorial representation on the recording sheet?

Assessing the Standard:

 Emergent The student is unable to successfully add and subtract within 5. Progression Student is able to successfully add and subtract within 5 but through the use of manipulatives.The student is able to successfully add and subtract within 5 but does so beyond 3 seconds. Meets Student is able to fluently recall facts within 5 from memory.* Exceeds Student is able to fluently recall facts through 10 from memory.*

* Memorization: The rapid recall of arithmetic facts or mathematical procedures. Memorization is often confused with fluency. Fluency implies a much richer kind of mathematical knowledge and experience. When students learn their facts from memory it is built through a learned experience which is then automatized which result in the ability to fluently recall the acquired strategy. From memory and memorization should not be evaluated as equal. (Taken from kindergarten grade level overview)

Assessment Resource: Bears in the Cave