Counting by 10, 5, 2, and 25

Counting by 10

How to use:

  • Have students count while watching. What do you notice? What do you wonder?
  • Questions and big ideas:
    • What is the pattern when we count by 10s? The number gets bigger by 10 each time we count. I see 1, 2, 3… inside of 10, 20, 30. It is showing 1 ten, 2 tens, 3 tens, etc.
    • (Pause at any point) What number will come next in the pattern? How do you know? (if stopped at 60) I think 70 will come next because when I count by 1s I say 5, 6, 7, so if I’m counting by 10s I should say 50, 60, 70 because after 6 tens comes 7 tens.
    • Which is more efficient, counting by 10s or 1s? (the best answer depends on the context, here are a few potential answers)
      • It is more efficient to count by 10s because we have so many _____ (objects/items) to count. Counting by 1s would take much longer.
      • It is more efficient to count by 1s because the ______ (objects/items) aren’t in groups of 10 and it would take longer to put them into groups of 10 than to just count them by 1s.
    • What are some things that are easy to count by 10? Number of fingers/toes a person has, 10 dollar bills, dimes, the sides of decagons (note: contact Christopher Danielson immediately if your student brings this up on their own)
    • What does it sound like to count by 10 after 100? How is it similar to counting by 10 from 0? 

 

How to use:

  • Have students count while watching. What do you notice? What do you wonder?
  • Questions and big ideas:
    • (Pause at any point during the counting) What do you notice about the tens frames and the number we’re on now? (if stopped at 40) There are 4 tens frames filled up, and that makes the number 40. 4 tens is the same as 40.
    • Why is it called skip counting? Every time we count, we are adding 10, so we are skipping all the numbers we would say if we counted by 1s.
    • How is counting by 10s the same and different than counting by 1s? Counting by 10s and 1s is similar because both are like adding: the numbers are getting bigger each time we count. They are also similar because you can see the pattern of “1, 2, 3…” (like counting by 1s) in the tens place when you count by 10s. They are different because counting by 10 is faster than counting by 1 because you are adding 10 at a time instead of 1 at a time.
    • Pause point #1: What is the pattern when we count by 10? In the ones place, the numbers are always 0. The tens place increases each time, with the pattern 1 ten, 2 tens, 3 tens, etc, similar to counting by 1s (1, 2, 3…).
    • Pause point #2: (Read Graham Fletcher’s post about the “upside down” hundreds chart used in this video hereWhat does counting by 10 look like on the hundreds chart? 
    • What are some things that are easy to count by 10s? Number of fingers/toes a person has, 10 dollar bills, dimes, the sides of decagons (note: contact Christopher Danielson immediately if your student brings this up on their own)

 

Counting by 5

How to use:

  • Have students count while watching. What do you notice? What do you wonder?
  • Questions and big ideas:
    • (Pause at any point during the counting) What do you notice about the tens frames and the number we’re on now? (if stopped at 35) There are 3 tens frames filled up, and that makes the number 30, which I see in the number bond next to the number line. There are also 5 extra ones, which I can also see in the number bond. The tens frames show 35 – 3 tens and 5 ones.
    • Why is it called skip counting? Every time we count, we are adding 5, so we are skipping all the numbers we would say if we counted by 1s.
    • How is counting by 5s the same and different than counting by 1s? Counting by 5s and 1s is similar because both are like adding, the numbers are getting bigger each time we count. They are different because counting by 5 is faster than counting by 1 because you are adding 5 at a time instead of 1 at a time.
    • Pause point #1, 2, 3: What is the pattern when we count by 5? In the ones place, the numbers are always 5 or 0. The tens place increases, but only every other time we count. The tens frame fills up every two times we count (since 5 and 5 make 10). On the hundreds chart, counting by 5s creates a line down the middle of the chart (the numbers that have a 5 in the ones place) and the right side of the chart (the numbers that have a 0 in the ones place).
    • Pause point #4: How is counting by 5 similar to counting by 10? When we count by 5 we say some of the same numbers as when we count by 10 (like 10, 20, 30, etc). They are both faster ways of counting than counting by 1.Counting by 10 is faster than counting by 5. The pattern of counting by 10 is less complex than counting by 5, since it looks similar to counting by 1 (10, 20, 30 is similar to 1, 2, 3).
    • Pause point #5: (Read Graham Fletcher’s post about the “upside down” hundreds chart used in this video hereWhat does counting by 5 look like on the hundreds chart? 
    • What are some things that are easy to count by 5s? Fingers on hands, toes on the feet, nickels, 5 dollar bills, pentagon sides, time (especially on the clock), etc.

How to use:

  • Have students count while watching. What do you notice? What do you wonder?
  • Questions and big ideas:
    • What is the pattern when we count by 5? In the ones place, the numbers are always 5 or 0. The tens place increases, but only every other time we count. The tens frame fills up every two times we count (since 5 and 5 make 10). On the hundreds chart, counting by 5s creates a line down the middle of the chart (the numbers that have a 5 in the ones place) and the right side of the chart (the numbers that have a 0 in the ones place).
    • How are counting by 5 and 10 similar? When we count by 5 we say some of the same numbers as when we count by 10 (like 10, 20, 30, etc). They are both faster ways of counting than counting by 1.
    • How are counting by 5 and 10 different? Counting by 10 is faster than counting by 5. The pattern of counting by 10 is less complex than counting by 5, since it looks similar to counting by 1 (10, 20, 30 is similar to 1, 2, 3).
    • What are some things that are easy to count by 5s? Fingers on hands, toes on the feet, nickels, 5 dollar bills, pentagon sides, time (especially on the clock), etc.

Comparing Counting by 1, 5, and 10

Counting by 2

How to use:

  • (Read Graham Fletcher’s post about the “upside down” hundreds chart used in the first video here)
  • Have students count while watching. What do you notice? What do you wonder?
  • Questions and big ideas:
    • What is the pattern when we count by 2? Each time we count, we are adding 2 to our number. It sounds like we are skipping a number each time, (1) 2, (3) 4, (5) 6. The numbers 2, 4, 6, 8, and 0 are a pattern in the ones place. When we count by 2s on the hundreds chart the numbers we say line up to create columns: the column where all the numbers have 2 in the ones place, the column where all the numbers have 4 in the ones place, etc.
    • How is counting by 2 the same as counting by 1? How is it different? It is the same because each time we count our total is getting bigger. It is different because counting by 2 is faster than counting by 1.  It might be harder to count by 2 if the thing you are counting isn’t in groups of 2.
    • What are some things that you can count by 2? Arms, legs, eyes, ears, hands, feet, shoes, wheels on bicycles, etc.

 

 Counting by 25

How to use:

  • Have students count while watching. What do you notice? What do you wonder?

 

Counting by 10 starting at 4

How to use:

  • (Read Graham Fletcher’s post about the “upside down” hundreds chart used in this video here)
  • Have students count while watching. What do you notice? What do you wonder?
  • Questions and big ideas:
    • What is the pattern when we start at 4 and count by 10? The number is getting bigger by 10. The ones place in every number we say is 4, and the number in the tens place is getting bigger each time by one ten: 14 has one ten, 24 has two tens, 34 has 3 tens, etc.  On the hundreds chart it looks like we are going up the column in a straight line.
    • How does the color of the circles help us to see the pattern? The red circles are staying the same, just like there is a red 4 in the ones place of each number we say, and the black circles show us the number of tens. 54 has 5 tens and 4 ones, just like the circles have 5 groups of ten.
    • What does it sound like to start at ____ and count by 10? How can the hundreds chart help you visualize counting by 10?

 

Thank you to all of the collaborators on Twitter and email who shared ideas and feedback for these visuals.

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