Activities to support Forward and backward number word sequences
Where are they now?
Students:
- fluently say the forwards number word sequence to 20
- fluently say the backwards number word sequence from 20
- confidently name the number before a given amount within the range of 0-30
- confidently name the number after a given amount within the range of 0-30
Where to next?
Students:
- identify one- and two-digit numerals
- say the forward number word sequence to 100, confidently across the decades
- say the backward number word sequence to 100, confidently across the decades
- say number word just before a given number word without dropping back to one
- say number word just after a given number word without dropping back to one
Outcomes
The following activities provide opportunities for students to demonstrate progress towards the following outcomes. A student:
MA1-1WM describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols
MA1-2WM uses objects, diagrams and technology to explore mathematical problems
MA1-3WM supports conclusions by explaining or demnstrating how answers were obtained
MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
How?
Bucket count-on-and-back
Drop a small collection of blocks one by one, into a bucket. Ask the students to count aloud as each block is added to the container. After dropping the blocks, show the students the contents of the bucket. Then hold the bucket above the eye level of the students. Ask the students to state how many blocks would be in the bucket if one more block was added. Repeat the question, changing the number of blocks to be added to two and three blocks. Encourage the students to count-on from the number of blocks already in the bucket to find the total. Ask students to record their thinking on mini whiteboards to enable the teacher to see what the students are thinking.
Variations
- Ask the students to pretend there are a nominated number of blocks in the bucket and label the bucket using a post-it note. Drop additional blocks into the bucket. Students count-on to find the total sum of the blocks in the bucket
- Start with a nominated amount inside the bucket and count back as each block is removed
- Increase the number range, or, count forwards and backwards in composite units e.g. by 2s
The counting game
Students select a target number, for example, 34. The goal is to be the student who says that number. Students can count on by saying the next 1, 2 or 3 number words in the sequence. Students collect a counter if they say the target number. A new target number is chosen and students play again.
E.g. Target number 11
Student A: 1, 2, 3...
Student B: 4, 5...
Student A: 6, 7, 8...
Student B: 9, 10, 11... I won!
Variations
Start from a given number and count back, trying to be the person who says zero Students count within a range, for example, starting at 81 and count down to 50 Vary the amount of number words that can be said other than 1, 2 or 3 number words
Why?
These activities encourage and support fluency in counting sequences. An understanding of, and fluency with, number word sequences support students in developing more sophisticated strategies such as counting-on-and-back.
Hundred chart patterns
Display a large hundred chart and provide students with their own, as well as a pile of counters or whiteboard markers, etc. Discuss any number patterns that can be seen on the hundred chart.
Through discussion and investigations, teachers should draw out patterns such as:
- There are ten numbers in each row and ten numbers in each column
- There are 10 columns and 10 rows
- Alternate columns are all odd numbers
- Alternate columns are all even numbers
- As you go down the hundred chart, each number increases by ten
- As you go up the hundred chart, each number decrease by ten
- As you go left to right across the rows, each number goes up by one
- As you go right to left across the rows, each number goes down by one
Teaching Point
Teachers should take time to investigate patterns by using rich questioning in discussions to challenge student thinking and support deep learning. Making connections between the patterns on a hundred chart and a vertical hundred number line would be useful in showing students a range of representations. Investigating patterns in a 0-99 chart and comparing them to a 1-100 chart, a 1-120 chart and number line would also be beneficial.
Variations
- Cut the hundred chart into strips and make a 1-100 number line. Ask students questions such as: Place a marker (or peg, for example) on 7. “What number is ten more than 7? Do we have to count or can we use our knowledge of the hundred chart to help us work out a solution?”
- Cut the hundred charts into puzzle pieces. Have the students use the patterns within the hundred chart to restore the chart
- Provide incomplete sections of the hundred chart (see example below). Have the students use the patterns within the hundred chart to complete the section provided
- Provide students with a blank 10 by 10 grid to represent a hundred chart and fifteen numbered counters (each displaying a different numeral in the range of one to one hundred). Students place the counters onto the grid in the correct numerical position. Explain choices to a partner who checks by counting
- Play the hundreds chart game by using two specially made dice, a counter each and a hundred chart each. Students start off with their counter on 50 and take turns to roll both dice. Students predict what square they will land on, their partner records their prediction. They then move according to the dice they rolled and their partner records their move. The first student to reach 100 wins.
Colour it in
Provide students with 2 different coloured markers, questions, 2 x 0-9-sided dice and a 1-120 chart. One student (student A) rolls the dice to form a 2-digit number. The student reads the number to their partner (student B) who records it on the hundred chart using their marker. Student B asks student A one of the following questions:
- What is the number before ___?
- What is the number after____?
- What is the number that comes 2 before __ ? • What number comes 2 after ___?
- What number is 10 before ___?
- What number is 10 after ____?
- What number is 20 before ____?
- What number is 20 after ____?
Students should be encouraged to visualise the hundred chart to help them solve their problem. If student A answers correctly, the corresponding number is coloured in. Student B asks an additional question, marking it on the chart if their partner is correct. Students swap turns after the second question, or, if the first student was incorrect. The student with the most coloured in spaces is the winner.
Teaching Point
It is important to expose students to counting numbers beyond 100. As with teen numbers, the numbers between 100 and 120 are often more difficult for students to read.
Before and after: figurative
Prepare “before and after” charts for each pair of students (see example below) with written numerals in the chart. These numerals should be within an appropriate range for the students. Provide the students with numeral cards to sort and place on the chart in either the “number before” or “number after” spaces to form number sequences.
Teaching Point
To scaffold this activity, use charts where the students have to identify only one number before and one number after the given number.
Variations
- Add more cards than needed in order to encourage critical thinking and conversation between students. Ask students to prove how they knew where to place each of the numeral cards
- Use a range of cards with number words, numerals and images to place in the “before and after” charts
- Ask students to place the numeral card that is two before or two after the given number
- Add an additional number to the initial chart, or, set it up to support counting by tens
Number line take-over
Provide students with 2 dice, a mini whiteboard and 2 different coloured markers. Have
the first student roll both dice and form a 2-digit number, drawing an empty number line
and recording their number. The second student rolls the dice and forms a 2-digit number, recording it on the same number line. Students continue taking turns to roll the dice and record a number on the number line, aiming to have the most numbers written in order on the number line uninterrupted by their partner’s. For example:
Bingo: The number before or after - figurative
Construct bingo cards for each student (BLM - Bingo). The teacher or students write numbers between 1 - 100 on their bingo card. Hold up a numeral card so that all students can see it (or flash a numeral using the interactive whiteboard). Have students check their bingo card, and if it contains a numeral which is one before the numeral displayed, tell them to cover the numeral with a counter. The winner is the first student to cover all of the numerals on his or her bingo card.
Variations
- Say the number words and have students identify the numeral before or after
- Extend the range of numbers
- Instead of numeral cards, show students numerals represented as MAB pictures on cards, concealed numbers on a hundred chart, or ask for the number before, after, two before, two after, etc
Bundling
For students who are learning to count in composite units (groups of 10, for example), present the students with large collections of popsticks. Have the students bundle the popsticks into groups of ten and place any remaining popsticks to the right of the bundles. Students should label the groups of ten as “one group of 10”. Encourage the students to count by tens to find the total and add on any remaining popsticks. Students should then label the collection using numeral cards. Interlocking blocks, such as Multi-link, Unifix or Centicubes, could also be used.
This could be used to explore counting by tens forwards and backwards. To support students, provide a template such as the one used in Fences (see emergent section). Students should make piles of 10 pop sticks to form 1 ten. Have the students match the numerals written on the baseboard (10, 20, 30, 40, etc.) as students sequence the pop sticks along the fence.
Zap: figurative
Arrange the students so that they are standing in a circle. Instruct them to count backwards from one hundred down to 83 (for example). Have each student call out one number in the sequence. When the target number (in this case, 83) is reached, the student calls out “zap!” and the person next in the sequence sits down. Continue the activity with the students commencing the backward count again. This process continues until one student remains standing.
Variations
- The students count in a forward number word sequence within a given range
- Students who are out remain in the circle and continue to say “zapped” whenever it is their turn. The following student continues the count from the number after the number that would have been said instead of “zapped”
- Have students record the number words spoken on mini whiteboards once they have been zapped
- Count backwards by 10s from 100
- Count forwards by 10s to 100
Why?
Students need to know the correct forward and backward number word sequences in order to state the number before or after a given number. Fluency in understanding and recalling the forward and backward sequences is necessary for students to eventually progress to counting-on-and-back.
Using calculators to count
Provide the students with at least one calculator for each pair of students.
Instruct students to:
- Enter a given number on the calculator
- Use the constant function on a calculator to add on or back from a given number, by ones or by tens
Provide the students with a hundred chart on which they can record the number patterns.