Mathematics
Kindergarten
15 min
Count on ten frames - up to 3
Count on ten frames - up to 3
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1
Introduction & Learning Objectives
Learning Objectives
Explain the purpose and structure of a ten frame as a visual aid for number sense.
Accurately represent numbers on a ten frame to prepare for addition.
Demonstrate the 'counting on' strategy by adding 1, 2, or 3 using a ten frame.
Connect the visual process of counting on with ten frames to standard addition equations.
Articulate how ten frames enhance mental math strategies for small additions.
Apply ten frame visualization to solve simple addition problems involving counting on up to 3.
Ever wondered how visualizing numbers can make even complex math simpler? 🤔 Let's revisit a powerful tool that builds strong number sense!
In this lesson, we'll explore 'counting on' using ten frames, specifically adding up to 3. While see...
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Key Concepts & Vocabulary
TermDefinitionExample
Ten FrameA rectangular grid composed of two rows of five cells each, used to organize counters and visually represent numbers up to 10. It helps in understanding number relationships, especially with 5 and 10.A ten frame with 7 counters clearly shows '5 and 2 more', or '3 away from 10'.
Counting OnA mental math strategy for addition where you start with the larger number and count forward by the amount of the smaller number, rather than counting all items from one.To solve 6 + 2, you start at 6 and count '7, 8', arriving at 8, instead of counting 1, 2, 3, 4, 5, 6, then 7, 8.
AddendAny one of the numbers that are added together in an addition problem.In the equation 4 + 3 = 7, both 4 and 3 are addends.
SumThe result obtained when two or m...
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Core Formulas
The Counting On Principle
$$a + b = \text{start at } \max(a,b) \text{ and count forward by } \min(a,b)$$
This principle states that to efficiently add two numbers, you begin with the larger number and count forward the number of times indicated by the smaller number. This minimizes the counting steps and is particularly useful for mental math.
Ten Frame Structure for Visualization
$$\text{A standard ten frame consists of } 2 \text{ rows of } 5 \text{ cells each, totaling } 10 \text{ cells.}$$
This rule defines the consistent layout of a ten frame, which is crucial for uniform visual representation. The 5-group structure (top row) allows for quick recognition of numbers relative to 5 and 10, aiding in subitizing and number composition.
Sequential Filling Rule
$$\text{Fi...
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Challenging
For which of the following problems would the 'counting on with a ten frame' strategy be the LEAST efficient mental math strategy compared to an alternative like 'making ten'?
A.6 + 2
B.9 + 3
C.5 + 1
D.2 + 3
Challenging
Imagine a 'Twelve Frame' (2 rows of 6) is introduced. How would this new tool fundamentally alter the primary mental math benefit compared to a standard ten frame?
A.It would shift the mental 'anchor' from the base-10 system to a base-12 or base-6 system, making it less applicable for our standard number system.
B.It would make all addition problems easier to solve.
C.It would be impossible to use for 'counting on'.
D.It would be more effective for teaching subtraction but less effective for addition.
Challenging
A student claims, 'The ten frame is not a useful tool for 8 + 3 because the answer is greater than 10.' Evaluate this claim based on the principles of visualization and number sense.
A.The claim is correct; ten frames can only be used for sums up to 10.
B.The claim is correct because it is impossible to visualize numbers greater than 10.
C.The claim is incorrect; visualizing the problem on two ten frames (one full, one with the remainder) is a powerful way to understand 'making ten' and place value.
D.The claim is incorrect, but only because you can use a twenty frame instead.
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