The number chart is an excellent tool for helping students learn about place value. It provides students with immediate feedback on their work and highlights patterns and relationships within numbers.
Bobby Kim, also known as The Hundreds, is a Los Angeles streetwear designer, author, photographer and Web3 creator. He recently signed with UTA for representation in fashion, speaking and film/television.
Counting
If you ask a young child to count to 100, they will often lose their place or skip over numbers. This is where a hundreds chart becomes a valuable tool, as it helps children build their fluency with numbers to 100 and develop counting skills. It also helps them understand the patterns of numbers and their numerals as they shade in the hundreds square.
Once children have a good grasp on counting to 100, it’s time to start looking at other numbers. Numbers greater than one thousand (1,00) have three whole digits and have a hundreds place, tens place, and ones place. This is where commas (,) become useful, as they make it easier to read the numbers.
Using base ten blocks, let’s work out what the value of each digit in these larger numbers is. For example, 7 falls under the hundreds place, 4 under tens and 3 under ones. We would represent this by placing these base ten blocks in the correct columns of the hundreds grid. We can then express this number in its written form, for example: 7 hundred and forty three balls.
Place Value
The place value system defines how much a single digit in a number is worth. Each digit has its own place or value, depending on its position within the number (ones, tens, hundreds, and so on). For example, if a digit is in the ones place, it’s worth one unit. If it’s in the tens place, it’s worth ten units. And if it’s in the hundreds place, it’s worth ten hundred units. Place value helps us express large numbers in a meaningful way.
Place value also relates to decimals because decimal numbers have places just like whole numbers, ones, tens, hundreds, and so forth. However, the values of the digits in a decimal are different than in a whole number because they start with tenths rather than ones.
A place value chart is a helpful tool to help students understand this concept. It shows how each digit is valued in a number, with each column representing a different place: ones, tens, hundreds, thousands, and so on. It also includes a place for zero, which is always valued at nothing.
In addition to a chart, the lesson plan contains other resources that can be used in class, such as an activity worksheet and practice sheet. It also contains a classroom procedure page, which lists a step-by-step guide for the teacher to follow when teaching this lesson. It includes a list of supplies that will be needed for the lesson and indicates when to hand out each worksheet.
This lesson plan also introduces students to the idea of tens and ones using base ten blocks. They can use these to represent a number, such as by placing one small block in the ones place, ten line-shaped blocks in the tens place, and one large square block in the hundreds place. They can then apply this understanding to solve problems, such as 100 + 40.
Throughout the year, students will continue to build upon their place value skills. For example, they will apply these concepts when working with decimals in measurement activities, such as converting metric measurements. They will also use their place value knowledge when solving multiplication and division problems with decimals. This will include knowing how to cross-multiply to find a remainder and when to convert between decimal and fractional numbers.
Multiplication
Multiplication is one of the four basic arithmetic operations, along with addition, subtraction and division. The ability to multiply figures is essential for calculating things such as area, volume and time, but it’s also important in everyday life, for example when ordering food at a restaurant or paying for items at the grocery store.
The first step in learning multiplication is memorizing tables; this allows children to quickly find the answers to simple multiplication problems without having to calculate. After children have memorized their tables, they can start to think more about the process of multiplication by combining what they know about place value and number sense. For example, if they know that 2 x 9 is 18, they can use the commutative property to figure out that 9 x 6 is 18.
Another way to understand multiplication is to look at how the number changes as it multiplies by 10. Multiplying by 10 moves each digit in a number one place to the left on a place value chart; multiplying by 100 moves two places, and multiplying by 1000 moves three places. This nested structure of numbers helps students to develop a clear understanding of the relationship between place value and multiplication.
Once students have understood the nested structure of numbers, they can apply their knowledge of multiplication to find hundreds using a strategy known as the “lattice method.” This involves adding together all of the partial products of the numbers and shifting each of the digits in the result by the number of places they move on the place value chart. For example, to find the product of 15 x 5, you would add up each of the three parts of the product: 5 + 2 + 1 = 12. Then, you shift the digits in the result by the numbers of moves they make on the place value chart: 10 + 2 + 3 = 15.
Finally, you would write down the final answer to the problem, which in this case is 24. This method of multiplication helps students to develop a deep understanding of how the parts of a number relate to each other and gives them confidence in solving problems of this type in the future.
Division
Division is the inverse of multiplication and is the process of breaking down a larger number into equal-sized groups. It is important to teach students that division can be used in everyday life as a tool for sharing things equally between two or more people. This can include sharing costs (like a $174 bill between four people), distance between destinations, weight of items (such as a 2lb bag of apples shared three ways) or anything else that needs to be divided.
To divide a number, you must first find the divisor. Then, multiply the divisor by the dividend to get the quotient. Then, subtract the remainder from the digits in the divisor to get the final answer. For example, dividing the number 136 by 3 is as follows: write 5 above the division bar, then multiply it by 3, and then add the remainder (5 – 1) to the first digit of the dividend (13).
When teaching the basics of division, it can help to introduce students to a tape diagram. Tape diagrams are useful because they allow students to visualize how a number is broken into hundreds, tens and ones. It also allows students to see the place value of each digit and how it changes when you break down larger numbers into smaller ones.
For beginners, a simpler way to teach division is to use a quotative model of division. A quotative model of division is a number divided into equal-sized groups based on the size of its divisor. For example, 3906 can be split into one group at the thousands level, three groups in the hundreds level, zero groups in the tens level and two groups at the ones level.
Using the division symbol, write the divisor outside the division bar and the dividend inside the division bar. For example, 65 / 5. Then, multiply the divisor by the division bar to get the answer, then write it above the dividend. For example, 5 x 6 = 1. Finally, subtract the remainder from the digits of the divisor to get the final answer.
