Whole Number Spreadsheet Workshop
Spreadsheets are powerful and useful tools for generating and presenting a variety of number related activities for primary aged children. These activities can provide interesting opportunities for children to practice skills, to develop or reinforce key concepts, to explore patterns and relationships, and to solve problems.
In this workshop you will explore some possible activities and make use of spreadsheets to complete some sample tasks. The spreadsheets are not difficult to use or to construct. You may learn things you didn't know about how to work in a spreadsheet environment. Hopefully, you will be inspired to use spreadsheets in your teaching of mathematics and for children's learning of mathematics. You might even consider creating your own for these purposes.
To open these spreadsheets:
Right click (PC) or click and hold (Mac) on this link for the Maths 1 SSheets. (DON'T just click once as you would a normal link - you will end up with a page of gibberish. If this happens, use your browser's BACK button to return).
Choose save this link as... (Mac users - if given the choice, save as 'text' not 'source')
Save the file in a sensible location - the desktop (Macs), or your briefcase (PCs) might be a good place.
Run Microsoft Excel. From the file menu, choose open, find the file where you saved it, highlight the filename and click Open.
Num Sentences (skill practice, concept development or reinforcement, problem solving)
For the spreadsheet Num Sentences children "recalculate" the spreadsheet to generate four single digit numbers and operations within three given number sentences. They use the numbers to complete the number sentences based on conditions set by the teacher. The children work individually or in pairs, and independently of the teacher. Nothing is entered into the spreadsheet by the children. They do all needed computations mentally or by written methods on paper, and record their answers as number sentences on paper.
Open the Excel Workbook titled Maths 1 SSheets (see instructions baove) and select the sheet Num Sentences. You will see something like that below (the numbers and operations may be different.)
Use the Num sentence spreadsheet to complete these tasks:
(a) Hold down the command-key (the •(apple)-key for a Macintosh) and press the = key to "recalculate" the sheet. Some numbers and operations will probably change.
Use each number once in each number sentence (A, B, and C) to give the largest possible number. Record the number sentences and number named in each case. Would you get the same answer for C without the brackets? Why?
(b) Recalculate the sheet again. Use each number once in each number sentence A, B, and C to give the smallest possible number. Record the number sentences and number named in each case. Would you get the same answer for C without the brackets? Why?
Four 4's (skill practice, concept reinforcement, problem solving)
The Four 4's spreadsheet presents children with the task of creating number sentences for numbers from 1 to 10 using any combination of operations and brackets and only four 4's. Away from the spreadsheet children work out, using mental or written computation methods, a number sentence they believe gives the desired goal number. They enter the number sentence as text in the cell in column C which is in the same row as the desired number. When a number sentence has been entered for each goal number (more than one sentence is required for some goal numbers), the text answers are "copied and pasted" into column E. The child then goes to each cell in this column in turn and places an = sign in front of the text. With the = sign preceding the text, the sheet recognises this as a formula and performs the indicated calculation. In this way the child checks if the number sentence does give the desired number. Useful discussion about the order of operations and the use of brackets can arise from this activity.
Select the sheet Four 4's and you should see something like this:
Use the Four 4's spreadsheet in the manner described above to write a number sentence for each goal number. To get you started a number sentence for the number 1 has been given. Remember that when a goal number appears more than once a different number sentence needs to be given each time it appears.
More or less (concept reinforcement, patterns and relationships, problem solving)
For the spreadsheet More or less children enter a number and then enter a "formula" into the sheet for the number which is three less than the number and a formula for the number which is five more than a number. When they enter a different number, the sheet gives the number that is three less and the number which is five more than the one entered. Children are asked to complete tasks related to these numbers.
Select the sheet More or less and you should see something like this:
Select cell D3 by clicking on it. Type the number 12 and press enter. The number 12 should now be in cell D3. Into cell B3 enter a formula for the number which is 3 less than the number in D3 in this way: select cell B3, press the = key, click on cell D3, press the &endash; key and then 3 on the numeric key pad, press enter. The number 9 should now be in cell B3. In a similar way, enter a formula into cell F3 for the number which is 5 more than the number in cell D3.
With the formulas entered into the sheet More or less enter different numbers into cell D3 to complete these tasks:
(a) What is the number when 38 is five more than the number?
(b) What is the number when 62 is three less than the number?
(c) What is the number three less than the number when the number five more is 57?
(d) What is the number five more than the number when the number three less is 123?
(e) What is the number when the sum of the numbers three less and five more is 72?
(f) What is the number when the sum of the numbers three less and five more is 238?
(g) Describe how to find the number when you know the sum of the number three less and the number five more. To help you do this make cell D5 give the sum: select cell D5, press =, click on cell B3, click on cell F3. Now enter different numbers in cell D3 and look for a pattern.
Mult grids (concept development or reinforcement, problem solving)
For the spreadsheet Mult grids children enter formulas in cells of different size grids to give the product of row number(s) and column number(s), and a formula in the "tail" of the grid that gives the sum of these numbers. The row number and the column numbers are changed and children look for relationships and patterns in the results and link ideas about written methods for multiplying numbers.
Select the sheet Mult grids spreadsheet and you should see something like this:
For the 1 x 2 mult grid:
Enter this formula in cell C3: = B3*C2.
Enter this formula in cell D3: = B3*D2.
Enter this formula in cell E4: = C3 + D3.
Enter different numbers in the row of the grid and the
columns of the grid and note what is given in the "tail" of
the grid, cell E4.
Now do these tasks:
(a) With a row number of 6, give three different combinations of column numbers that make the sum of the grid numbers be 54.
(b) With a row number of 24, give three different combinations for the column numbers that make the sum of the grid numbers be 360.
(c) Find a row number and column numbers that make sum of the grid numbers be 630? Now find a different row number and column numbers that make the sum of the grid numbers be 630? Can you choose any number as the row number? What must be true about the row number in relation the sum of the grid numbers?
Enter appropriate formula to complete the 2 x 2 mult grid.
Now do these tasks:
(a) Make the row numbers be 4 and 9. Find three combinations of column numbers that make the sum of the grid numbers be 312.
(b) Make the row numbers be 20 and 8. Find three combinations of column numbers that make the sum of the grid numbers be 1204.
(c) Experiment to find how the grid relates to the standard "algorithm for multiplication".
Find a factor (concept development, concept reinforcement)
For the spreadsheet Find a factor children enter a number under the heading "Number" and a second number under the heading "This number a factor?". If the second number is a factor of the other, a number sentence showing this relationship is produced. If the second number is not a factor, no number sentence is produced. The sheet is a tool to be used by the children. They choose the input numbers and interpret what the output tells them about the "is a factor of" relationship for these numbers. The children use the sheet to help them complete number related tasks constructed by the teacher for the purposes of concept development or reinforcement.
Select the sheet Find a factor and you should see something like this:
Use the Find a factor spreadsheet to complete these tasks:
(a) Confirm that the number 91 is not a prime number. Give a number sentence that shows why it is not prime
(b) Confirm that the number 97 is a prime number. How did you use the information gained from the spreadsheet to confirm this?
(c) Determine whether the number 5287 is a prime number.
(d) Find all the factors of the number 5082.
(f) Construct a "factor tree" leading to the prime factorisation of 5460.
Place Value (concept reinforcement)
For the spreadsheet Place Value children enter a number less than ten-thousand (up to four digits). The spreadsheet gives information about the number based on ideas of place value. This sheet can be used by children independently of the teacher to check work done with materials like MAB in building a number by trading up from ones to tens, then from tens to hundreds, etc. It can help to reinforce children's understanding of different ways in which a number can be viewed in terms of its place value.
Select the sheet Place Value and you should see something like this:
Use the Place Value spreadsheet to complete these tasks:
(a) Enter the number 2397 in cell B5. What is the ones digit? tens? hundreds? thousands?
(b) Enter the number 346 in cell B5. How many ones in this number? Tens? Hundreds?
(c) 4368 MAB mini's are placed on the floor. Enter the number 4368 in cell B5 and use the results to copy and complete the following:
Mini's not grouped.
Have 4368 ones.
4368 = 4368Mini's grouped in tens once.
Have ________tens + _______ ones
4368 =Mini's are grouped in tens two times.
Have _____ hundreds + _____ tens + ____ ones
4368 =Mini's are grouped in tens three times.
Have ______ thousands + _____ hundreds + _____ tens + ____ ones
4368 =
SC-ones (concept reinforcement, patterns & relationships, problem solving)
For the spreadsheet SC-ones children enter a number from which to start counting and the number to count by. The sheet gives the numbers in the counting sequence, the ones digit of the number and draws a graph based on this data. The sheet is used by children to explore the patterns in the ones (or final) digit found in the numbers formed when counting.
Select the sheet SC-ones and you should see something like this:
Use the SC-ones spreadsheet to complete these tasks:
(a) Make the sheet count from three by fours. How many digits are needed before the ones digits begins to repeat itself. This is the cycle length of the ones digit pattern. List the ones digits in sequence as they appear for one cycle.
Now make the sheet count from zero by fours. Compare the ones digit pattern for this counting sequence with that above. How are they alike? How are they different?
(b) Make the sheet count from two by seven. What is the cycle length of the ones digit pattern. List the ones digits in sequence as they appear for one cycle.
Now make the sheet count from two by threes. Compare the ones digit pattern for this counting sequence with that above. How are they alike? How are they different?
(c) Based on your results from (b) predict and investigate two other counting sequences which you believe might be related in a way similar to those in (b).
SC-tens (concept reinforcement, patterns & relationships, problem solving)
For the spreadsheet SC-tens children enter a number to count by and a number to count from. The sheet gives the numbers in the counting sequence, the tens digit of the number and draws a graph based on this data. The sheet is used by children to explore the patterns in the tens digit found in the numbers formed when counting.
Select the sheet SC-tens and you should see something like this:
Use the SC-tens spreadsheet to complete these tasks:
(a) Make the sheet count from 0 by 1, 2, 3, 4, 5, 6, 7, 8, 9. How many digits are needed before the tens digit begins to repeat itself in each case?
(b) Make the sheet count from 0 by 5,15, 25, 35, 45, 55, 65, 75, 85, 95. What is the cycle length of the tens digit pattern in each case?
(c) Make the sheet count from 0 by 7,17, 27, 37, 47, 57, 67, 77, 87, 97. What is the cycle length of the tens digit pattern in each case?
(d) Explore to see if any of the above patterns in (c) are related to those produced when counting from 0 by 3,13, 23, 33, 43, 53, 63, 73, 83, 93? Describe any patterns that are related and tell how they are related.
Rem-chart (patterns & relationships, problem solving)
For the spreadsheet Rem-chart children enter a number from which to start a ten row by ten column chart formed by counting from this number by one. They enter a number by which to divide each number in the chart b (this is k) and a remainder must result when dividing by this number. The sheet produces the ten by ten chart and below gives only those numbers in the chart which have the designated remainder. The children use the sheet to explore number patterns arising from remainders when dividing one number by another.
Select the sheet Rem-chart and you should see something like this:
Use the Rem-chart spreadsheet to complete these tasks:
(a) Make the sheet show the numbers from 1-100 which have a remainder of 2 when divided by 4. Then make the sheet show the numbers from 201-300 which have a remainder of 2 when divided by 4. What changed and what remained the same in the pattern of numbers as you moved from 1-100 to 201-300?
(b) Make the sheet show the numbers from 1-100 which have a remainder of 1 when divided by 3. Then make the sheet show the numbers from 201-300 which have a remainder of 1 when divided by 3. What changed and what remained the same in the pattern of numbers as you moved from 1-100 to 201-300?
(c) Make the sheet show the numbers from 1-100 which have a remainder of 3 when divided by 9. Now make the sheet show the numbers from 1-100 which have a remainder of 0 when divided by 3. How are the two patterns of numbers related? How?
(d) A child says that if 2 is a factor of a number and 3 is a factor of a number then 6 is a factor of the number. Use the sheet to show that the child is correct.
A child says that if 4 is a factor of a number and 12 is a factor of a number then 48 is a factor of the number. Use the sheet to show that the child is incorrect.
Give another statement like that above which is correct and verify this using the sheet.
Give another statement like that above which is incorrect and verify this using the sheet.