Good to Know
Good To Know is a digital video series for adults that introduces the methods, vocabulary, and processes their child learns at school. These short, clear and fun videos will help to explain math topics that are taught in Pre-Kindergarten, Kindergarten and Grades 1-4 Common Core curricula. The videos will help develop a conceptual understanding of how math practices build on previous knowledge and empower parents and caregivers to help their children learn foundational math skills!
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!
Your child sets the foundation for understanding multiplication and division in second grade. The first layer in building this foundation is a concrete understanding. He will use objects as counters to create equal groups.
Making equal groups, drawing pictures, and using repeated addition all build a strong foundation for third grade, where your child will dive right into multiplication and division!
When a whole is broken into equal parts each part is a fraction. Each part of this fraction is one-half. Your child will draw tape diagrams as a visual tool to help him break apart one whole. In third grade, your child will break one whole into two equal parts, three equal parts, four equal parts, six equal parts, and eight equal parts.
Let’s solve a third grade word problem: Braydon had pizza for lunch. He ate one-forth of it and left the rest in the box. Draw a tape diagram of Braydon’s pizza.
Your child will draw a picture like this to model the whole. He knows to break it into four equal parts. Each part is one-fourth of one whole. Then he will be asked to shade the part Braydon left in the box. Braydon ate one-fourth, so these three parts are left in the box.
Last, your child will be asked to draw a number bond that matches what you drew. At first, he will show his understanding like this. Later, he will understand this.
Practice drawing fractions as tape diagrams and number bonds and, viola! Understanding fractions will be a piece of… pizza!
And that is good to know.
A) Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
B) Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
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!
Your child’s introduction to multiplication is through repeated addition. He will draw an array to visualize, or see, five groups of four stars. He will count the stars and find the total.
As his understanding improves, he will skip count to find the total more efficiently. Your child will use a variety of visual models, to represent multiplication as he works toward developing multiplication fluency.
Fluency in third grade means knowing, from memory, all products of two one-digit numbers. This includes facts from zero times zero all the way up through nine times nine.
Then, your child will use these facts to develop the connection between multiplication and division. Knowing that five times four equals twenty is the first step in understanding that 20 stars, divided into five groups, equals four stars in each group. Or, twenty divided by five equals four.
Talk about the relationship between multiplication and division with your child. I know this… So I also know this! With lots of practice, your child will achieve fluency!
And that’s good to know.
Part of using base-ten numbers correctly is understanding how to express the same number in different forms. This video demonstrates how to express base-ten numerals written in standard form, unit form, expanded form, and number name.
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.
Becoming comfortable with two-digit and three-digit numbers is an important skill in second grade. Your child will master addition and subtraction problems within one-thousand. But, how your child learns to understand addition and subtraction is very important.
If you look closely, a place value chart is a helpful tool to use before your child uses the standard algorithm. The place value chart teaches your child why the standard algorithm works. How powerful!
This video addresses Common Core Grade 2 Standard Number & Operations in Base Ten: Use place value understanding and properties of operations to add and subtract.
Learning to assess the reasonableness of an answer is an important mathematical skill. It’s your child’s way of seeing if she’s on the right track when problem solving. Sometimes we use rounding to estimate a solution.
In third grade, your child will round whole numbers using a vertical number line and round to the nearest ten or to the nearest hundred.
Let’s round seven-hundred sixty-two to the nearest hundred. Your child knows seven-hundred sixty-two is made up of seven hundreds, six tens, and two ones. Seven hundreds is seven-hundred. So seven-hundred-sixty-two will fall somewhere above seven-hundred on the vertical number line.
How many hundreds come after seven hundreds? Five-hundred, six-hundred, seven-hundred, eight-hundred… Eight hundreds!
Next, your child will find the midpoint or halfway mark. What falls halfway between 700 and 800? This can be tricky, so your child may skip count by fifty. Six-hundred, six-hundred fifty, seven-hundred, seven-hundred fifty, eight-hundred… Seven-hundred fifty is the midpoint!
Ask your child: Where will you place seven-hundred sixty-two on this number line? Ummm… Here! Just a little above the midpoint.
Using a vertical number line is a very helpful model. Your child can clearly see that seven-hundred sixty-two is closer to eight-hundred than it is to seven-hundred, so it rounds up to eight-hundred.
Seven-hundred sixty-two rounded to the nearest hundred is eight-hundred. Or, seven-hundred sixty-two is approximately equal to eight-hundred.
Talk with your child about this special case: When a number falls exactly on the midpoint, you round up. Like this - twenty-five is the midpoint, and twenty-five rounded to the nearest ten is thirty because you round up. Twenty-five is approximately thirty.
Using a vertical number line gives your child a visual representation for rounding. With practice, she will always see when to round up and when to round down.
And that’s good to know.
In third grade, your child will solve two-step word problems using addition, subtraction, multiplication, and division. Let’s try one: There were ten adults and five children at the movies. Each adult ticket costs $8.00 and each child ticket costs $3.00. What is the total cost of all the tickets?
What is this question asking us to find?
Write an answer statement to stay on track. The total cost of the tickets is…. Let’s find out!
We know what to find, so your child will use a tape diagram to solve.
There are ten adults, so divide the tape diagram into ten equal parts. Each adult ticket is eight-dollars. Your child knows the total cost of adult tickets because he is fluent in multiplication. He knows that ten groups of eight is eighty. The adult tickets cost eighty dollars.
This tape diagram represents the five children, so divide it into five equal parts. Each child ticket costs $3.00. Now we find the total cost of child tickets. Five groups of three is fifteen. The child tickets cost fifteen dollars.
Check back with your answer statement. We’re not done yet! We need to add the costs together. Eighty dollars plus fifteen dollars equals...
Your child may use the break apart mental math strategy to make a ten. He will break apart fifteen into one ten and five ones, so he can easily add with a ten. Ninety plus five equals ninety-five.
Don’t forget to complete your answer statement! The total cost of the tickets is ninety-five dollars.
Your child used multiplication and addition to solve this two-step word problem. You can see how developing strong mental math strategies learned in younger grades makes a big difference when solving two-step problems!
Your students continue to use tape diagrams as a visual tool to solve word problems. Now, they solve for an unknown in any position.
This video demonstrates Common Core Grade 2 Standard Operations & Algebraic Thinking: Represent and solve problems involving addition and subtraction.
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.