GTK: Fourth Grade
When first learning to multiply two two-digit numbers your child will use the area model.
To start, your child will use her knowledge of place value to decompose into tens and ones. To decompose means to break apart. Let’s decompose these numbers by the value of each digit.
The value of two tens is twenty. The value of three ones is three. Three tens is thirty. And five ones is five. Decomposing numbers allows your child to use the multiplication fluency she developed in third grade to multiply large numbers with mental math.
So, what is twenty-three times thirty-five?
Three tens times two tens equals sixty tens or six-hundred. Thirty tens times three equals nine tens or ninty. Twenty tens times five equals ten tens or one-hundred. And three times five equals fifteen.
Your child will then add these products together. Six-hundred plus ninety equals six-hundred ninety. One-hundred plus fifteen equal one-hundred fifteen. By fourth grade, your child will fluently add three-digit numbers, like this, using the standard algorithm.
Your child can clearly see why twenty-three times thirty-five equals eight-hundred-five. The area model gives your child a visual representation that decomposes the numbers she is multiplying. At this point in fourth grade, your child is developing a pictorial level of understanding, which will give her a strong foundation for using partial products and, later, using the standard algorithm to multiply.
To decompose means to break apart. Your child has already decomposed whole numbers with number bonds, tape diagrams, and place value charts. In fourth grade, he will decompose fractions.
Three-eighths is a fraction. We can decompose three-eighths into parts using a tape diagram as the visual model. One-eighth, plus one-eighth, plus one-eighth equals three-eighths.Your child will write this as an equation. These are called unit fractions.
He will also decompose three-eighths as two-eighths plus one-eighths. Decomposing fractions into different parts helps your child to understand that one whole can be expressed in more than one way.
Sometimes your child will work with improper fractions. Ten-fourths is an improper fractions because the numerator is greater than the denominator. Your child will decompose an improper fraction by considering the denominator and pulling out one whole. Four-fourths equals one whole. After pulling out four-fourths, six-fourths remain.
But wait! He can pull out another whole! Your child knows one whole equals one, so he can now see ten-fourths equals one plus one plus two-fourths.
Practice decomposing fractions with your child so he will be ready for mixed numbers and performing operations with fractions!
In fourth grade, your child will use the four operations to solve word problems involving money. In order to do this, she will first learn to decompose, or break apart, one dollar into smaller units. We call these units: quarters, dimes, nickels, and pennies.
Ask your child: How many quarters make up one dollar? How many quarters make up two dollars?
Think about nickels: How many nickels make one dollar? She knows one dollar is one-hundred cents, so she might skip count by five to one-hundred. There are twenty nickels in one-hundred cents!
When using money, it’s very important to consider the units. One dollar can be written like this or like this. Five cents can be this or this.
With practice, your child will understand all the ways we represent money and be comfortable using decimal notation. Find opportunities to talk about money with your child so she can problem solve with confidence!
When your child first learns to multiply two two-digit numbers, she will use the area model. This visual tool illustrates how to decompose numbers and find four different products. As her skills improve, she will move from this pictorial model into a concrete method called partial products.
Using partial products to solve forty-three times fifty-six, looks like this. She will start by multiplying tens times tens. Next, she will multiply tens times ones. Then, ones times tens and last, ones times ones.
These are called partial products. This is the product, or answer. Using partial products removes the pictorial step but places the same emphasis on the actual value of the numbers being multiplied.
By the end of fourth grade, your child will use the standard algorithm to multiply! This algorithm is used to develop an abstract level of understanding. If she jumps right to using the algorithm,
she will not develop the conceptual understanding of multiplying two-digit numbers.
The standard algorithm has fewer lines of work because your child has a greater understanding of what she’s multiplying! Your child knows the actual value of these products because she has a strong understanding of partial products.
And that’s good to know.
In fourth grade, your child will use the metric system to measure length, mass, and capacity. Length refers to the measurement of something from end to end. Long lengths are called distance.
Mass refers to the measure of the amount of matter in an object.
Capacity refers to the maximum amount that something can contain, commonly called volume. This cup has a maximum capacity that is much smaller than the capacity of this swimming pool.
Kilometer, meter, and centimeter are metric measurements of length. Kilogram and gram are used to measure mass. Liter and milliliter measure capacity.
Learning what unit is appropriate for each measurement can be challenging. Ask your child:
What unit is best to measure our trip to grandma’s house? Is it best to measure your mass in kilograms or grams? What unit is used to tell us the capacity of this juice bottle?
Talk about these units at home so your child will be confident when converting units of measure. That is, expressing a measurement in a different unit. He will recognize patterns of converting units on the place value chart. Just as one-thousand grams is equal to one kilogram, one-thousand ones is equal to one thousand.
Your child will practice this by completing conversion charts. He will convert between units using his place value knowledge. Talking about length, mass, and capacity will help your child become familiar and confident with all types of units!
Knowing which unit is larger or smaller is important as he converts from one unit to another unit within a system of measurement. Having a strong understanding of units is very helpful when your child begins to add, subtract, multiply, and divide with units of measure.