Activities to support learning in forward and backward number word sequences
Where are they now?
Students:
- say the forward number word sequence to 100 or beyond
- say the backward number word sequence from 100 or beyond
- say the number word just after a given number word without dropping back to one
- say the number word just before a given number word without dropping back to one
- count forwards by 10s to 100
- count backwards by 10s from 100
Where to next?
Students:
- count beyond 100
- counts backwards from any number
- counts forwards by 10s and 5s, on and off the decade
- counts backwards from 1000 by 100s
- counts forwards by 100s to 1000
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 demonstrating how answers were obtained
MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
MA1-5NA uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers
How?
Bucket count-on-and-back
Drop MAB blocks, one by one, into a bucket. Ask the students to count aloud as each block is added to the container, swapping between ones, tens and hundreds. After dropping the blocks, show the students the contents of the bucket and label it. Hold the bucket above the eye level of the students. Ask the students to record on their mini whiteboards the next 10 number words we would say if we started counting from our number by 10s. Students share their thinking. Check by counting.
Repeat the question, changing the direction of count (forwards and backwards) a number of times to count by a given amount (ones, tens and hundreds) as well as counting by fives.
Variation
- Start with a nominated amount inside the bucket and count back as each MAB block is removed
Before and after: counting-on-and-back
Prepare “before and after” charts for each pair of students (see examples below). Provide the students with four 0-9 dice and a marker. The first student rolls 4 dice, choosing 2 dice to form a 2-digit number. He or she then writes their number in a square on the chart. The second student then rolls all 4 dice, using them to form a 2-digit number that fits within the chart, writing it in the appropriate space. If a student cannot form a number that fits the chart, they miss a turn.
Students take turns. The student who fills in the most spaces in the chart is declared the winner.
Encourage students to use their understanding of the hundred chart to work out the number that is 10 more or less, for example.
Variation
- Have students make 3-digit numbers
Why?
This activity provides practice in recognising and sequencing numbers up to 100.
Grocery line
Display a collection of grocery items of varying mass up to 1000 grams (1 kilogram). Allow the students to compare the mass of each item according to the number of grams indicated on each package. Have the students order the items according to their mass, from heaviest to lightest. Have the students record the weight of their items on an empty number line.
Discuss with students questions such as:
- How many items weigh less than 500 grams?
- What are the masses of the items that are more than 300 grams?
Variation
- Collect from catalogues pictures of items costing less than $1000 . Ensure the price of each item is in whole dollars and is clearly indicated. Present the catalogue items to the students and ask them to sequence the items in terms of cost, e.g. book club catalogues
Skip counting
Lead the students in oral counting by tens, up to 120 (for example), and then backwards from 120. Support the oral counting by pointing to the location of these numbers on a 120 chart. Cover the multiples of ten on the hundred chart and have a student point to the position of each number as the class counts forwards or backwards by ten. Vary the activity by using other counting patterns, such as counting by fives, or counting off the decade.
Why?
These activities provide opportunities for students to further develop their understanding of the number word sequences. Teachers should use the opportunity to investigate
and discuss the relative size and position of numbers. Knowing number patterns and counting sequences for multiples will assist students in solving problems.
Ten strips and hundred charts
A ten strip is a line of ten boxes with a dot in each box (BLM - Ten Strips).
Display a strip of four dots. Ask the students: “How many dots are there altogether?” Place a ten strip below the four dots and repeat the question. After the students determine the answer, indicate the corresponding number on the hundred chart. Continue counting-on by 10s, adding one ten strip at a time and locating the total on the hundred chart. Use this to support students in counting backwards by 10s as well as counting off the decade by providing a small selection of counters (such as 3) before showing each ten strip.
Variations
- Ask the students to estimate how many number words we might say if, for example, we count backwards by 10s starting at 112. Discuss estimations that would be unreasonable and those that would be reasonable
- Substitute a ten frame (BLM - Ten Frames) for the dot strip
- Use groups of 10 ten frames and count forward and backwards by hundreds, on and off the decade
Straw javelin
Place masking tape on the floor to indicate a starting point. Organise the students into a line behind the starting point. Have the students take turns to throw a straw as far as they can. Provide the students with Unifix blocks so they can measure “how many blocks” they threw the javelin. The students measure the distance the straw travelled by placing the Unifix blocks along the floor from the starting point to the straw.
Ask students to work out the best way to organise their blocks so that it is easy to count how far their javelin travelled (for example, using groups of tens, using a marker to indicate groups of twenty, etc.).
Discuss with students questions such as:
- Which is the most efficient way to count the blocks? Why?
- How far did the furthest javelin travel?
- How far did the nearest javelin travel?
Variations
- Change the activity from throwing a straw to other actions, such as taking a giant step from the starting point and then measuring the distance of the step
- Organise the students into pairs. Provide each pair of students with lengths of string and ask them to use the string to measure their arm span and their height. After the students have completed measuring with the string, they place the string on the floor. Have the students use towers of ten Unifix blocks to record the length of the string
Teaching point
This activity is a good example of how a task can be designed to support learning in a range of areas, linking concepts and ideas.
Why?
This activity should be used to draw upon the idea that ten, made up of ten ones, can be used as a countable unit. As such, when students are counting, teachers should encourage the students to count by 10s, on and off the decade, to work out how many blocks were needed.
Zap counting-on-and-back
Arrange the students so that they are standing in a circle. Instruct them to count backwards from 523 down to 493 (for example). Have each student call out one number in the sequence. When the target number (in this case, 493) 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 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
- Have students record the number words spoken on mini whiteboards once they have been zapped
- Count backwards and forwards by 10s, off the decade
- Count backwards and forwards by 5s
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 recalling the forward and backward sequences is necessary for students to progress towards using more sophisticated strategies.
Using calculators to count: Counting-on-and-back
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 count-on or count-back from a given number, by tens, fives or hundreds
Provide the students with a mini whiteboard to record the number words they say.