GTK: Third Grade
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.
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.
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!