# » math-mat

## Making and saying numbers:

Use a handful of dried beans, cheerios, beads, buttons or any other small objects to represent numbers in the mats. If you have Base 10 Blocks, that is the perfect manipulative to use alongside these mats but are not necessary.

## General Information before using the mats:

For grades 1-3 stick with whole numbers until your child has a strong grasp of them. Use as large of numbers as your child understands. Here are some guidelines to help you out: Grade 1 – up to 20 (may go larger) Grade 2 – up to 100, Grade 3 – up to 1000. Older students still need to practice this and can use the larger numbers to gain a deeper understanding of the place value system.

NOTE: There are couple of changes that you may notice from when you were in school:

1)  We don’t say ‘and’ unless we’re referring to a decimal so the number 234 is said; “two hundred thirty-four” (NOT “two hundred and thirty-four).

2) We don’t use commas to separate the parts of a number but rather just use spaces: 1 234 rather than 1, 234.

## Whole Number Identification and Comparisons:

### Whole Number Identification and Comparisons: – Idea #1:

• Create a number on the mat and then say the numbers.
• For example, what you see below would represent 234 and we can say that this means there are 2 hundreds, 3 tens and 4 ones.

• Challenge Question: if you didn’t have ANY objects in the hundreds column, how could you represent 234?
• The idea here is to understand that 10 tens is also equal to 100.

If you have base 10 blocks, show the numbers with the blocks on the mat

### Whole Number Identification and Comparisons: – Idea #2:

• Say the number and then create it on your mat. Same idea as #1 but backwards. Challenge your child by giving numbers like 231 (two hundred thirty-one).
• Challenge Questions: ask them to create the same number without using any objects in the hundreds column.

If you also have base 10 blocks, show the numbers with the blocks on the mat

### Whole Number Identification and Comparisons:  – Idea #3:

• Build the same number in many different ways. For example: build 364 in as many different ways as possible. Record all the different ways and explain how they are equal to 364. For example, you could have 2 hundreds, 16 tens, 4 ones.

If you also have base 10 blocks, show the numbers with the blocks on the mat

### Whole Number Identification and Comparisons: – Idea #4:

• Create a number that is somewhere between 45 and 67, or 405 and 504, or 3078 and 3109 (choose any two numbers you want – if you leave a smaller gap, it becomes more challenging). They can also explore the smallest and largest numbers possible that fit within the range.

If you also have base 10 blocks, show the numbers with the blocks on the mat.

### Whole Number Identification and Comparisons: – Idea #5:

• Give students two numbers and ask which is larger and to prove how they know by using their mats and words to explain. For example: 48 vs 61, 102 vs 99, 180 vs 169, 700 vs 599, 1099 vs 1200, 3489 vs 3479. Use contexts to support this idea, for example, ‘Who has more toys, Joe with 102 toys or Ben with 99 toys?’

### Whole Number Identification and Comparisons: – Idea #6

• Give students a number and ask them to round to the nearest 10, 100 or 1000 by using counters (and/or base 10 blocks) by determining ‘which is it closer to?’ This way of rounding works for all bases of numbers and helps to understand what rounding means. Use contexts to help as well, for example, ‘If I have 236 stickers, is this closer to having 230 or 240 stickers? How do you know?’

## Whole Number Addition and Subtraction

### Whole Number Addition and Subtraction – Idea #1

• Give students two numbers (single or multi-digit depending on their current level of understanding) or a context involving adding two numbers. For example, ‘Sara has \$210 and she earns another \$17, how much money does Sara have now?’ Estimate the sum first and then ask them to show each of the numbers on the mat and finally, add them using their place values and regrouping where necessary. This way of approaching addition helps students to understand the place value system as it relates to addition.

If you also have base 10 blocks, show the numbers with the blocks on the mat

### Whole Number Addition and Subtraction – Idea #2

• Give students two numbers to subtract. Estimate the difference and solve using the mat in two ways: by taking away or by finding the difference between the two numbers. Use contexts for each.
1. Taking away example: Nikki has 41 Pokemon cards and gives away 18, how many does she have left?’ Students will need to regroup their tens to allow for enough ones to be taken away.
2. Difference example: Nikki has 41 Pokemon cards and John has 18 Pokemon cards, how many more cards does Nikki have? (or how many fewer cards does John have?)
• Many students find adding up the easiest way to subtract and so explore both!

## Decimal Number Identification and Comparison

Students in Grades 4 & 5 learn numbers beyond the chart on the mat (10 000 and 1 000 000) and decimals (hundredths for grade 4 and thousandths for grade 5). In grades 6 and above students are doing more complex operations with decimals so it is really important that they understand what decimals mean. Ideally, students have base 10 blocks along with their decimal place value mat to really understand sizes of decimals. You can use any other items to represent the amount of tenths, or hundredths, but this will be far more abstract than using base 10 blocks.

NOTE: We want our students to use proper place value language so that they understand the size of the numbers. We used to say; ‘two point three’ but now say ‘two and three tenths’. Saying the value is what we do with whole numbers, for example we say fifty-two, rather than five two when we read this number: 52 and so we want to do the same with decimal numbers.

### Decimal Number Identification and Comparison- Idea #1

• Create a number on the mat and then say the numbers.
• For example, what you see below would represent 1.76 and we can say that this means there is 1 whole, 7 tenths and 6 hundredths. We call this; “one and seventy-six hundredths” because 7 tenths and 6 hundredths is the same as 76 hundredths.
• Challenge Question: if you didn’t have ANY objects in the tenths column, how could you represent 1.76?

If you have base 10 blocks, show the numbers with the blocks on the mat.

### Decimal Number Identification and Comparison- Ideal #2

• Say a number and then create it on your mat. Same idea as #1 but backwards. Challenge your child by giving numbers like 5.02 (five and two hundredths) and 5.2 (five and two tenths)
• Challenge Questions: ask them to create the same number without using any objects in the tenths column.

If you also have base 10 blocks, show the numbers with the blocks on the mat.

### Decimal Number Identification and Comparison – Idea #3:

• Build the same number in many different ways. For example: build 2.34 (or 0.234) in as many different ways as possible. Record all the different ways and explain how they are equal to 2.34. For example, you could have 1 whole, 13 tenths, 4 hundredths.

If you also have base 10 blocks, show the numbers with the blocks on the mat.

### Decimal Number Identification and Comparison – Idea #4:

• Create a number that is somewhere between 0.45 and 0.67, or 4.05 and 5.04, or 3.078 and 3.109 (choose any two numbers you want – if you leave a smaller gap, it becomes more challenging). They can also explore the smallest and largest numbers possible that fit within the range.

If you also have base 10 blocks, show the numbers with the blocks on the mat.

### Decimal Number Identification and Comparison – Idea #5:

• Give students two numbers and ask which is larger and to prove how they know by using their mats and words to explain. For example: 0.48 vs 0.7, 1.02 vs 0.99, 0.108 vs 0.2, 0.8 vs 0.599, 1.099 vs 1.2. Many children use whole number rules for all types of numbers, for example, they think 0.48 is larger than 0.7 because it has more digits.

If you also have base 10 blocks, show the numbers with the blocks on the mat as way to prove how much larger tenths are than hundredths, for example.

### Decimal Number Identification and Comparison – Idea #6

• Give students a number and ask them to round to the nearest whole, tenth, or hundredth by using counters (and/or base 10 blocks) by determining ‘which is it closer to?’ This way of rounding works for all bases of numbers and helps to understand what rounding means. Use contexts to help as well, for example, ‘If I have \$2.36, is this closer to having \$2.30 or \$2.40? How do you know?’

## Decimal Number Addition and Subtraction

### Decimal Number Addition and Subtraction – Idea #1

• Give students two numbers or a context involving adding two numbers. For example, ‘Sara has \$2.10 and she earns another \$1.70, how much money does Sara have now?’ Estimate the sum first and then ask them to show each of the numbers on the mat and finally, add them using their place values and regrouping where necessary. This way of approaching addition helps students to understand the place value system as it relates to addition.

If you also have base 10 blocks, show the numbers with the blocks on the mat.

### Decimal Number Addition and Subtraction – Idea #2

• Give students two numbers to subtract. Estimate the difference and solve using the mat in two ways: by taking away or by finding the difference between the two numbers. Use contexts for each.
1. Taking away example: Nikki has \$4.10 and spends \$1.80, how much money does she have left?’ Students will need to regroup their wholes to allow for enough tenths to be taken away.
2. Difference example: Nikki has \$4.10 and John has \$1.80, how much more money does Nikki have? (or how much less money does John have?)
• Many students find adding up the easiest way to subtract and so explore both!