“In today’s lesson we are going to look and listen for patterns as we count from 1 to 100. [IS.3 - Struggling Learners and ELL Students] Let’s see how the numbers are organized.” [IS.4 - All Students]
Display the transparency of the Complete the Hundreds Chart on the overhead projector, covering all but the top two rows (see M-1-3-2_Complete the Hundreds Chart in the Resources folder).
“How many tens are showing?” Allow students to respond.
“Yes, two tens are showing in these two rows. What is another word for two tens?” Allow students to respond.
“That’s right, twenty is another name for two tens.” Expose another row.
“How many tens are now showing?” Allow students to respond.
“Yes, three tens. What is another name for three tens? That’s right, thirty.”
Continue in this manner sliding the mask up and down the rows. Ask if students hear any patterns in the words. They may respond, “Three sounds like the beginning of thirty.” “Sixty starts with a six.” “They all end with a –tee sound.”
Using the same array, show four full lines and ask, “How many?” Then expose one blank in the fifth row: “How many now?”
They will say, “Four tens and one more.” “Forty plus one more.” “Forty-one.”
“Right. We have 41 single units. Other names are 4 tens and 1 one or 4 groups of ten and 1 single.”
Uncover one more blank and elicit names for forty-two. Continue in this way, adding one more blank space each time, until the pattern is established. Repeat with other decades between twenty and ninety.
Next use the 1–100 number chart (see M-1-3-2_Hundreds Chart in the Resources folder). Cover all except the top three rows.
“How many tens are showing?” Allow students to respond.
“Yes, there are three tens. What is the other name for three tens? Yes, thirty. Notice the number for thirty. Where will we find the number thirty-one?”
Students may respond, “Under in the next row.” “In the next square under the twenty-one.”
Move the mask to show the numeral 31. Predict what the next few numbers will be. Move the mask down a few more rows, to the fifties, for example, and expose the numerals to 53.
“How many tens do we have?” (five) “What is another name for 5 tens?” (fifty). “How many more than fifty do you see?” (3 ones)
“What is another name for 5 tens and 3 ones?” (fifty-three)
Remove the mask and let students study the full hundreds chart.
“How is this chart like the one with the squares?”
They will likely say, “It has one hundred.” “There are 10 rows of ten on each.”
Discuss how the written numbers describe the number counted for the dots on the array.
“Do you see any patterns on the hundreds chart?” [IS.5 - All Students]
Students may say, “Each row has ten.” “You can count ten, twenty, thirty, forty, etc.” “The numbers in the middle get bigger by ten; 35, 45, 55…” or “The numbers on the right side get bigger by 10.”
Avoid incorrect language such as, “the numbers in the tens place go up by one,” by rephrasing to model correct thinking: “You have made great observations. The tens in the columns increase by 1 ten in each row. We can count the rows by tens. We can also see that 6 rows of ten, or 6 tens, is sixty. Forty has 4 tens, which is 1 ten more than thirty.” [IS.6 - All Students]
Display a 1–100 chart with some of the numbers removed or covered (start with six to eight). (This could be a poster, classroom pocket chart, a number line, or an overhead transparency.) Ask students to tell what numbers are missing and replace or uncover them.
“Which number should be in this space? (for example, 34) How do you know?” [IS.7 - All Students]
Students will offer answers like, “34 comes after 33 and before 35.” “The space above is 24 and another ten makes 34.” “Three tens and 4 more spaces/ones make 34.”
“Those are good strategies. Looking at the numbers that come before and after the missing number gives us clues to find the missing number. Counting how many tens and singles there are will help us. And looking at the number above the space that has one less ten is a good idea. Let’s try some more.”
Repeat the activity until all missing numbers are filled in.
To make this activity more challenging, remove or cover numbers in a sequence from three or four different rows.
After repeated practice over a few days, give students a “windows” page (see M-1-3-2_Number Puzzles in the Resources folder). They can use the patterns and strategies they used while working with the hundreds chart to fill in the missing numbers. (This could also be used as a transparency for whole group work.) For additional practice, have students work on a “fill in missing numbers” worksheet (see M-1-3-2_Fill in Missing Numbers in the Resources folder.) [IS.8 - Struggling Learners]
“Look at the first shape on your page. This shape fits in the hundreds chart we have been using. The numbers 54 and 65 are filled in for us. Can someone show us where this shape can be found on our hundreds chart?”
Have a student trace the shape with his/her finger on top of the corresponding numbers on the hundreds chart.
“We need to figure out which numbers are missing in the blank spaces, or windows. How can we do that?” Allow students to respond.
They will likely say, “We can start at 54 and count by ones in the top row.” “Sixty-five plus one more ten is 75, so that goes under the 65. Then you can write the numbers one less than 75 and one more than 75.” “I looked at the hundreds chart and found the numbers.”
“You are using good strategies. Who will share the missing numbers?” Allow a student to read the numbers.
Ask, “Did we use the numbers 64 or 66?” (no) “Why not?”
“There wasn’t a window for them.”
“That’s right. So we are only filling in the numbers missing in the windows.”
“Look at the next shapes on your page and use your strategies to fill in the missing numbers. Each window should have a number.”
When students have completed the windows page, let them check their work with a partner by comparing pages. Walk around and listen to their discussions. Ask questions such as, “How did you choose that number?” “If there were another window here, what number would go there?” “Did you have the same answers?”
Use the activities below to meet the needs of all students throughout the year.
Intervention: Give each student a hundreds chart (see M-1-3-2_Hundreds Chart in the Resources folder) and a pair of scissors. Direct students to cut the rows apart to create 10 groups of ten. Then explain how each piece represents ten. Use the rows of ten to create a number line from 1–100. Have students color the numbers 10, 20, 30 … for visual anchors. Practice counting across the number line by tens, tracing each line of ten with a finger.
Practice one more/one less by saying, “Find a number on the line (such as 37). Which number shows one more (38) or one less (36)?”
Guide practice based on observation of student skills.
“Today I am going to put my marker on the number 43. Jill, will you spin the spinner? What number did we spin? Look at the direction the arrow is pointing. Start on my number and move one space in the direction shown by the arrow. What number did you land on?”
Students should move one space in the direction the arrow is pointing. If it points diagonally up to the right, the student should move over one space to the right and up one number (or diagonally one square up to the right). From 43 the student would move to 34.
On following days, students could start at the same number and move in a different direction or start each day at a new number on the chart.
Expansion 1: Cut each of three colored hundreds chart into pieces. One should have only a few pieces, the second a few more, and the third should be the most challenging. Store the pieces in envelopes according to color or difficulty. Students choose a puzzle and reconstruct the hundreds chart.
An adaption for students with special needs may be to give students a hundreds chart in addition to the one that is cut apart. [IS.9 - Struggling Learners] This way students may use the whole hundreds chart as a “map” for the hundreds puzzle pieces. For example, the 30 piece would be put on top of the 30, the 21 piece would be put on top of the 21, etc. This requires less work than creating the hundreds chart from the pieces only.
Expansion 2: Have students work in pairs. Each student begins at 0 and spins the spinner (see M-1-3-2_Arrow Spinner or M-1-3-2_Arrow Spinner 2). After the first spin, each number s/he spins gets added to or subtracted from the number in the initial spin. The object is to be the first student to reach 100. If on the first spin a student spins a negative number, s/he stays at 0 until the next turn.
The focus of this lesson is to understand and recognize patterns on a hundreds chart. Students can determine that a number above or below a number on a hundreds chart is ten more or ten less than the given number. Students will establish relationships between numbers and strengthen their counting skills.