# T4T Exploring Counting Patterns

Lesson Excerpt:

NC Mathematics Standards:

Extend and recognize patterns in the counting sequence.

1.NBT.1 Count to 150, starting at any number less than 150.

1.NBT.7 Read and write numerals, and represent a number of objects with a written numeral, to 100.

Understand place value.

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and     ones.

Use place value understanding and properties of operations.

1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Standards for Mathematical Practice:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Student Outcomes:

●     I can count to 150 starting at any number (within 80 first semester).

●     I can read and write numbers to 100 (within 80 first semester).

●     I can explain patterns in the digits of numbers on a number chart.

●     I can use number patterns to help me mentally find 10 more or less than a two-digit number.

Math Language:

Pattern

Row

Column

Digits

Tens Place

Ones Place

Materials:

●     A large class number chart, such as a number line or a hundred chart, is a useful classroom resource to support students with the Counting Around routine

●     Word problem on chart paper to use with the whole group

●     A class set of printed copies of the problem for students to glue in their math journals

●     A basket of tools including snap cubes, tens frame cards, and number lines

●     Number charts for each student.  This lesson suggests a 100 chart, but this may vary for differentiation and time of year (50 chart, 100 chart, 150 chart, and/or 101-200 chart)

●     10-20 transparent chips per person

●     Chart paper for anchor chart

●     A 101-200 number chart for pairs only filled in to 120 (for first semester, may use a 100 chart only filled in to the number 60 and focus on filling in the next two blank rows)

●     Gather materials listed above

●     Write word problem on chart paper

●     Copy and cut student copies of the word problem to glue in math journals

●     Select and prepare appropriate number charts for each student

●     Select and prepare appropriate number cards for partners to arrange in order

Directions:

1.      Counting Around Routine (5 minutes)

Counting Around may be used with the group seated in a circle.  The teacher gives a starting number and each child says the next number in the counting sequence until the teacher gives the stop signal.  Once students learn the routine, they may be asked to count on by ones, tens, twos, and fives, starting at various numbers.  Teachers may ask questions to encourage students to predict and test their ideas such as:

·         Let’s start with the number 20 and count by ones.  Who do you think will say 30?  How do you know?

·         Let’s start with the number 45 and count by tens.  Who do you think will say 95?

How do you know?

Note:  This routine may be used regularly throughout the school year and differentiated based on the students’ understanding of counting.  It may be used for practice counting forward or backward in whole and small group instruction.  The routine can be especially useful for extending rote counting by ones from 100-150 and counting by tens from any start number.  This routine may be encouraged as a partner activity in stations or as students wait in line throughout the day.

2.      Counting in a Problem Context (20 minutes)

Show students the following problem on chart paper, asking them to read aloud with you.  Read again.   (After midyear, a higher number, such as 84, could be used as a start number).

Tim was counting his race cars.  He stopped counting at 64 so he could eat lunch.  What will be the next numbers Tim says when he counts the rest of his 16 cars?  How do you know?

64, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___

Explain what you did using pictures, numbers, or words.

Ask students to restate the problem in their own words to partners and ask the whole group:

Students go to their work spaces to glue the problem into their journals.

Students solve the problem with partners using their tools and explain their work.

Teachers monitor student work and may ask questions such as:

·         How do you decide what numbers come next?

·         Do you notice a pattern in the numbers as you count?

·         What seems to be repeating?  What seems to stay the same?

·         What’s important to remember when you write larger numbers?

·         What tool(s) did you use?  How did that help?

·         Could you use a different tool to prove your answers?  Which way is quicker and easier?  Why?

*Any students who finish early may create a similar problem involving counting by adjusting the character and objects.

Bring students back together to share counting strategies.  Select at least one student who used the hundreds chart as a tool to share.  Use their explanation to transition to the next activity.

3.      Investigate Counting Patterns and Summarize Ideas on an Anchor Chart (15 minutes)

Give students 100 charts and transparent chips.  Students touch each number on their 100 chart tool as the class counts together from 1-100.  Ask:

·         Do you notice a pattern in the numbers as you count across any row on the chart?

·         Talk with your partner about the patterns you notice as you count across a row.

·         Does that happen in every row?  Why?

·         Try to use specific math language (students may reference an interactive word wall featuring words such as pattern, row, column, digits, tens place, and ones place).

On the anchor chart, record the patterns that students notice.

Next, students use transparent chips to keep track of numbers that they say as they start at 10 and count by tens.  Ask partners to discuss:

·         What do you notice about the numbers we covered with chips?

·         What do you notice about their digits?

·         What happens if you start at another number in the first row and count by tens? Try it!  (Test the idea a couple of times with different starting numbers 1-9)

·         Does that happen in every column? Why?

On the anchor chart, record the patterns that students notice.

4.      Extend the Counting Sequence (15 minutes)

Review the patterns students noticed on the hundred chart.

Ask:  Would the same patterns appear on a 101-200 chart?  Why?

Distribute 101-200 number charts to pairs that are only filled in to 120.  Starting at 101, point intentionally to the digits as you read the numbers from 101-120.  Invite students to join in with reading the numbers when they notice the pattern.

·         What do you notice?

·         Discuss with your partner how we could use these patterns to help us to continue counting to 150?

·         What might we say after 120? What might that look like?  Can you and your partner find the number card that shows that number?  Can you keep counting?

Allow partners to rote count from 121 to 150.

Ask partners to sequence the number cards to fill in the chart from 121-150.

Encourage them use counting to check their number placements.