Mathematical Emphasis
Investigation 1—Finding Factors

• Understanding the relationship between skip counting and grouping
• Becoming familiar with the relationships among commonly encountered factors and multiples
• Increase fluency in counting by single-digit numbers (2’s, 3’s, 4’s, 6’s, 8’s) as well as by useful two-digit numbers (10’s, 20’s, 25’s)
• Developing familiarity with the factors of 100 through work with cubes, coins, and 100 charts

Investigation 2—Using Landmarks to Solve Problems

• Using knowledge about factors of 100 to understand the structure of multiples of 100 (if there are four 25’s in 100, there are twelve 25’s in 300)
• Developing strategies to solve problems in multiplication and division situations by using knowledge of factors and multiples
• Estimating real quantities that are close to 200, 300, and 400
• Reading and using standard multiplication and division notation to record problems and answers

Investigation 3—Constructing a 1000 Chart

• Using factors of 100 to understand the structure of 1000
• Estimating quantities up to 1000
• Using landmarks to calculate distances within 1000 (How far is it from 650 to 950?)

Tips For Helping At Home
Questions To Ask:

• What is the problem about? Tell me in your own words.
• What did you do in class to get started?
• Can you make a drawing (model) to help you figure out the problem?
• Can you solve a simpler version of the problem?
• What have you already tried? What steps did you take?
• Does your answer make sense?
• How do you know your answer is correct?
• Did you show all of your work?

Activities at Home

• Skip counting (counting up by a number like 5, 10, 15, 20…) is an excellent way to learn multiples and factors. Any home activities that use skip counting will give your child practice.
• When your child is working on a problem at home, you can help by asking your child to tell you how he or she got an answer. There are many ways of doing these problems—and no single “right” way. What’s important for your child to know is how his or her own way works.
• Any time you need to estimate or deal with large numbers, please involve your child. Whether buying food or deciding how many floor tiles to purchase, your child will benefit from discussing it.

Vocabulary Terms

Coins

Students will be using pennies, nickels, dimes, and quarters in this unit with an emphasis on dividing up a dollar

Factor

A number you can count by to land exactly on another number; a whole number that can be divided evenly into another number

Landmark Number

Numbers that are familiar and can be used to solve other unfamiliar problems (10, 25, 50, 100)

Multiple

A mathematical operation where a number is added to itself a number of times

Skip Counting

Counting up by a number (3, 6, 9, 12…)

Mathematics Vocabulary Web site

Mathematics Strategy—The Importance of Skip Counting
Skip Counting is counting up by multiples of a number. Children start at a number and count up consistently by a fixed amount. Often children start at a number and count up by that same amount (example; 4, 8, 12, 16, 20…) although it is possible to start at any number and count up by multiples (example: start at 17 and count up by 2’s).

Skip counting builds a foundation for many important mathematical concepts. Important mathematics skills and concepts are developed. Among these are:

• Understanding properties of numbers,
• Understanding relationships among numbers,
• Recognizing order and making predictions,
• Learning factors and multiples of numbers,
• Using logical reasoning.

Source: Investigations in Number, Data, and Space: Mathematical Thinking at Grade 3. Dale Seymour, 1998. (Page 27)

Mathematics Activity—How to Practice with Flashcards

Which are easy? Which are hard?
Give your child addition cards. Have them sort the cards into two piles: “Combinations I Know” and “Combinations I am Working on.” Cards to into the known pile if they are at a recall level (students know the answer and can tell you in less than 3 seconds).

Have your child choose one or two problems from the “working on” pile and analyze the problem. Come up with a hint to help remember that combination. Hints should be combinations they already know that can help them remember the correct answer.

After practicing with that hint for a week, have your child go through the pile again and see if more combinations are remembered.

Learning Difficult Combinations
Choose one combination that is not known and focus on it for a week. Every day have your child figure out a different way to remember the answer (7+6 could be remembered as 6+6+1 or 7+7-1 using doubles. 7+6 could be 7+3+3 or 6+4+3 breaking one number apart and making a ten). After a week of focus, have your child go through the whole pack of combinations again.

If a child knows the hint: 7 + 7, she can use it to find 7+8.

If a child knows the hint: 7+3=10, he can use it to find 7+(3+5).

Mathematics Activity—Using Triangle Flashcards

Three corner flashcards help students

• Develop number sense
• Recognize patterns
• Build fact strategies
• Boost problem solving skills
• Relate subtraction to addition/LI>

Use three corner flashcards to practice addition and subtraction combinations.

• For addition, you cover the top number (largest of the three numbers) and add the bottom two corners or numbers. The answer is the top numeral.
• For subtraction, you cover one of the bottom corners. Subtract the bottom number that still shows from the top number. The covered numeral is the answer.

Cut out the triangle flashcards and mount on tagboard. These cards are excellent for home practice.

Get to Flash Cards With Hints (for printing)

Get to Triangle Flashcards (for printing)