Arrow Card Activities for developing basic numeracy skills.
Introductory activities
Begin by drawing the students’ attention to the arrows on the right ends of the cards. These arrows must always be on top of each other when you are making a number.
- Students sort cards into groups of ones, tens, hundreds and thousands. (May need to demonstrate). “The ones, the Tens, the hundreds and the thousands”.
2. When the students have sorted the cards
begin by asking them to
show the following numbers.
Students can take turns in their pairs
showing the numbers. The
frequency of numbers can be reduced if
the students are successful.
When they show the number you can say
for example “how many tens in
30 to reinforce the idea of counting
different referents.
“Show me 1, 2, 5, 7, 9”.
“Show me 10, 20, 50, 70, 90”.
“Show me 100, 300, 500, 900”.
“Show me 1000, 3000, 5000, 7000”.
At this point the students should know the different components of the arrow cards and how to use them. Some students may still be trying to place a 3 next to a 5 to Build 35. When this happens remind them that the arrows need to go on top of each other when numbers are being built.
Developmental
Activities
Numeracy
The triangle of numeration also applies to the development of students concepts of place value and base ten in the same way that it is first developed with single digit cardinality.
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Base Ten/Place value Triangle of meaningThe three languages of
math
(Base ten model)
24 “Twenty-four” (Arrow cards) (Oral language) This triangle can be used to develop the association between: a) the number of objects b) the numeral or graphic symbol, and c) the spoken word for that number The arrows show that each representation can be a stimulus for responses in the other two. Students do not automatically learn all six relationships. Show a……. Ask “How many?”. Say “Show me the number for this many” Show b,,,,,,,Ask “What number is this?”. Say “Show me this many”. For c…….. Say “Show me five cubes”. Say “ Show me the number five”. |
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As the students build the numbers they will Build many observations and connections. They should be encouraged to share these observations with the class.
For example, some students will notice that building the numbers is the same as adding the numbers. The idea of expanded notation can then be developed by the teacher on the board by adding each number together as in 368 = 300 + 60 + 8. Some students may be concerned that the equation is the opposite way round from what they are used to. This can lead to a discussion of the purpose and value of the = symbol (it is a sign of equality so it doesn’t really matter which way round the equation goes).
3. “Show me 11, 12, 15, 19”
You may
need to demonstrate how to put the cards together
by matching the arrows.
Children in their pairs may work out that
one of them can find the
‘ten’ card and one can find the ‘one’ card.
They can take it in turns to
show the number they have built.
4. “Show me 34, 46, 57, 89”
Develop
the language that another name for 30 is three tens. You
may need to remind the
students that the 30 is still there. For
example the 0 is still there
behind the 4. Taking away the 4 will
reveal the 0 of the 30.
If students
are showing difficulty grasping the idea that 30 is the
same as 3 tens it might be
appropriate to introduce the use of place
value manipulatives such as Base
Ten blocks, Digi-blocks or bundles of
tens.
5. “Show me 29 and 92”
One student
can build one number and the other student in the pair
can build the other. Both
numbers should be placed in front of the
student so they can discuss the difference
between the value of the
9 in 29 and the 9 in 92.
Again, the ‘one’ digit can be removed to
reveal the value of the 9 in
92.
6. “Show me 100, 402, 125”
The development of the idea
of 0 in the middle of the number can be
introduced/reinforced here.
Students can be asked to provide the
numbers for the class to
build.
7. “Show me 1,000, 1,046, 6,893.
It might
be appropriate with some classes to introduce the date,
2005 at this point. This is
where the matching of the arrows on top
of each other becomes
really important. Some students may only
see the importance of
placing the arrows on top of each other when
they come to do this
activity.
8. “Show me 2,468, and 8642“.
Each
student in the pair can build one of the numbers. Students
attention can be drawn to the
fact that the numerals in different
places have different values.
The next activities can be used to develop the ideas of pattern in place value as well as simple mental addition and subtraction ideas. A model for base ten such as Digi-blocks or Base ten blocks can be used with students having conceptual difficulty.
9. Build a number that is 10 more than 25.
Students may have difficulty with this idea at first even though they may be able to count by tens. Most learning to count by tens occurs on the decade names so the idea of counting by tens from 24 might be very difficult for some students. Holding a sequenced stack of ‘ten’ cards and peeling them away as the students say them helps. The same idea can then be used by holding a ‘one’ in the ones place and having the students count by tens as you peel each ‘ten’ away leaving the ‘one’ card in place.
10. Build a number that is 100 more than 163.
Students find counting by 100s easier than by tens because there is not a change in the vocabulary.
11. Build a number that is 1000 more than 4724.
Students remove the 4000 card and replace it with the 5000 card. They can then continue counting in 1000s and making the new numbers without changing any of the other place values.
12. Build a number that is 10 less than 76.
This activity can develop the idea of counting back by 10s.
13. Build a number that is 100 less than 453
Counting back by 100s
14. Build a number that is 1000 less than 5612.
Counting back by 1000s
15. Build a number that is 20 more than 25.
Developing the additive concept procedurally. Develop the idea of adding numbers in the tens place without having to do anything to the ones. This is an extension of the counting by tens idea and is very effectively when done in conjunction with the use of the Digiblocks or base ten blocks.
16. Build a number that is 300 more than 265
17. Build a number that is 2,000 more than 5,357
18. Build a number that is 30 less than 56
19. Build a number that is 500 less than 892.
20. Build a number that is 4,000 less than 6,291.
Supplemental
Activities
21. Build the number of the year we are in
22. Build the largest number you can build.
23. Build a number that has all the same numerals
24. Build a number that reads the same both ways.
251. Build a number in which all the digits add up to 15.
26. Build a number where all the numerals add up to your age.
27. Build a number that is easy to remember.
28. Build a number that is difficult to remember.
29. Build a number between 239 and 287.
30. Build a number larger than 1,384 but smaller than 1,388.
31. Build a number that rhymes with the word “fine”.
32. Build a 2-digit number that rhymes with ‘late’
33. Build a 3-digit number that rhymes with “you”
34. Build a 4-digit number that rhymes with “line”
35. How many different numbers can you make with two one cards, two
ten cards and two hundred cards?
Using Arrow cards with Base Ten models
Arrow cards help children develop their understanding of the procedural knowledge of number; the conventions we use to record number using the base ten system. To develop relational understanding of this procedural knowledge through the development of the conceptual knowledge of number we need to use the arrow cards initially in association with a base ten model. Many such models exist including teacher made materials such as bundles of popsicle sticks, tens of unifix cubes, and ten strips. Commercial materials such as base ten blocks and Digi-blocks are also available,
When the arrow cards are use in conjunction with a base ten model care should be taken to ensure that the student verbalizes the numbers as well as constructing them with the arrow cards. At each step, the triangle of numeracy should be referred to make sure the student is developing understanding between all three manifestations of number.
The Base 10 system we use is built upon the idea of place value. The essence of place value is the idea of groups of groups of ten. Within each place, the numerals 0 – 9 are used to count numbers of that referent. At this point the numeral 1 takes on the value of a ten when a 0 is placed next to it to the right. The 0 denotes that there are no ones
Base Ten Blocks activity resources
http://www.arcytech.org/java/b10blocks/description.html
Digiblocks activities
http://www.digi-block.com/dbls/packit/db.cfm
Part Five - Projects that use Arrow Cards
The following projects are nationally funded projects that support the participation of teachers as part of national incentives to improve student math skills at an early age.
Primary National Strategy – Wave 3 Mathematics Pilot
http://www.wave3.org.uk/pages/downloads/wave3_TS2.pdf
A nationally funded and supported project that utilizes Arrow cards in a variety of activities and contexts.
New Zealand Math Numeracy Project
http://www.nzmaths.co.nz/numeracy/project_material.htm
Reference
Wright, Robert J., Martland, Jim,