Explain three different ways to solve the problem.

• Max had 46 comic books. For his birthday his father gave him 37 more comic books. How many does he have now?

• Kevin had 84 gumdrops. During the week he ate 29 gumdrops. How many gumdrops does he have left?

know basic factsTEKS Expectations

Addition Subtraction Multiplication Division

K Number sense using Number sense using modelsmodels

Number sense using Number sense using modelsmodels

PatternsPatterns

1st • Concrete and Concrete and pictorial models to 18pictorial models to 18• Strategies to solve Strategies to solve basic problemsbasic problems

•Concrete and Concrete and pictorial models to 18pictorial models to 18• Strategies to solve Strategies to solve basic problemsbasic problems

Skip counting by 2, 5, Skip counting by 2, 5, 1010

2nd • Strategies to Strategies to rememberremember• Recall and apply Recall and apply factsfacts

•Strategies to Strategies to rememberremember• Recall and apply Recall and apply factsfacts

Model, create and Model, create and describedescribe

Model, create and Model, create and describedescribe

3rd Review, reinforce, Review, reinforce, remediate/interveneremediate/intervene

remediate/interveneremediate/intervene

Review, reinforce, Review, reinforce,

• Learn and apply to 12 Learn and apply to 12 x 12x 12• Identify patternsIdentify patterns

•Identify patternsIdentify patterns• ModelsModels•

4th • Recall and applyRecall and apply• Patterns for 10 and Patterns for 10 and 100100• Strategies to Strategies to rememberremember

• Strategies to Strategies to rememberremember

5th Review, reinforce, Review, reinforce, remediate/interveneremediate/intervene

Review, reinforce, Review, reinforce, remediate/interveneremediate/intervene

Multiplication• Equal-Groups Problems When the number and size of groups are known, the problem is a

multiplication situation. When either the number of sets or the size of sets is unknown, division results.

• Comparison Problems In multiplicative comparison problems, there are really two different

sets, as there were with comparison situations for addition and subtraction. One set consists of multiple copies of the other.

• Combination Problems Combination problems involve counting the number of possible

pairing that can be made between two sets. The product consists of pairs of things, one member of each pair taken from each of the two given sets. The two factors in these problems each represent the size of a set, so that is no reason to distinguish between two division situations.

Equal Groups: Whole Unknown (Multiplication)Equal Groups: Whole Unknown (Multiplication)

Mark has 4 bags of apples. There are 6 apples in each bag. How man apples does Mark have altogether.

If apples cost 7 cents each, how much did Jill have too pay for 5 apples? (rate)

Peter walked for 3 hours at 4 miles per hour. How far did he walk? (rate)

Equal Groups: Size of Groups Unknown Equal Groups: Size of Groups Unknown (Partition Division)(Partition Division)

Mark has 24 apples. He wants to share them equally among his 4 friends. How many apples will each friend receive?

Jill paid 35 cents for 5 apples. What was the cost of 1 apple? (rate)

Peter walked 12 miles in 3 hours. How many miles per hour (how fast) did he walk? (rate)

4 x 6 = 24

5 x 7 = 35

3 x 4 = 12

24 ÷ 6 = 4

35 ÷ 7 = 5

12 ÷ 4 = 3

Combination: Product UnknownCombination: Product Unknown

Sam bought 4 pairs of pants and 3 jackets, and they all can be Sam bought 4 pairs of pants and 3 jackets, and they all can be worn together. How many different outfits consisting of a pair of worn together. How many different outfits consisting of a pair of pants and a jacket does Sam have?pants and a jacket does Sam have?

You want to make a set of attribute pieces that have 3 colors and You want to make a set of attribute pieces that have 3 colors and 6 different shapes. If you want your set to have exactly one 6 different shapes. If you want your set to have exactly one piece for every possible combination of shapes and colors, how piece for every possible combination of shapes and colors, how many pieces will you need?many pieces will you need?

Combinations: Size of a Set UnknownCombinations: Size of a Set Unknown

Sam bought some new pants and jackets. He has a total of 12 Sam bought some new pants and jackets. He has a total of 12 different outfits. If he bought 4 pairs of pants, how many jackets different outfits. If he bought 4 pairs of pants, how many jackets did Sam buy?did Sam buy?

Your set of attribute materials consists of 18 different pieces. Your set of attribute materials consists of 18 different pieces. There are 3 colors, and each color comes in different shapes. There are 3 colors, and each color comes in different shapes. How many different shapes are in the set?How many different shapes are in the set?

In the experiment of missing a coin and rolling a die, there are 12 In the experiment of missing a coin and rolling a die, there are 12 possible outcomes. Of course, the coin has two sides. How possible outcomes. Of course, the coin has two sides. How many sides does the die have?many sides does the die have?

3 x 4 = 12

3 x 6 = 18

12 ÷ 4 = 3

18 ÷ 3 = 6

12 ÷ 2 = 6

Word Problems

• Equal-Groups Problems• Comparison Problems• Combination Problems• Join• Separate• Part-Part-Whole• Compare

Strategies for Multiplication Facts

• Multiplication facts can also be mastered by relating new fact to existing knowledge.

Doubles Facts that have 2 as a factor are equivalent to the addition doubles and should already be known by students who know their addition facts. The major problem is to realize that not only is 2 x 7 double 7, bus so is 7 x 2. Try word problems where 2 is the number of sets. Later use problems where 2 is the size of the sets.

Five Facts

This group consists of all facts with 5 as the first or second factor as shown here. Practice counting by fives to at least 45. Connect counting by fives with rows of 5 dots. Point out that six rows is a model for 6 x 5, eight rows is 8 x 5, and so on.

Zeros and Ones Thirty-six facts have at least one factor that is either 0 or 1. These facts, though apparently easy, tend to get confused with “rules” that some children learned for addition. The fact 6 + 0 stays the same, but 6 x 0 is always zero. The 1 + 4 fact is one more idea, but 1 x 4 stays the same. The concepts behind that facts can be developed best through story problems. Above all else, avoid rules that sound arbitrary and without reason such as “any number multiplied by zero is zero.

Nifty NinesTwo patterns that are useful for mastering the nines are:1. The tens digit of the product is always one less that the “other” factor (the one other than 9), and 2. The sum of the two digits in the product is always.

These two ideas can be used together to get any nine fact quickly. For 7 x 9, 1 less than 7 is 6, 6 and 3 make 9, so the answer is 63.

Helping Facts The chart shows the remaining 25 multiplication facts. These 25 facts can be learned by relating each to an already known fact or helping fact. For example, 3 x 8 is connected to 2 x 8 (double 8 and 8 more). The 6 x 7 fact be related to either 5 x 7 (5 sevens and 7 more) or to 3 x 7 (double 3 x 7). The helping fact must be known and the ability to do the mental addition must also be there.

Division Facts and “Near Facts”• If we are trying to think of 36 ÷ 9, we tend to thing, “nine times

what is thirty-six?” For most, 42 ÷ 6 is not a separate fact but is closely tied to 6 x 7.

Pinczer, E. (1995). A remainder of one. Boston:

Houghton Mifflin.

http://nlvm.usu.edu/en/nav/grade_g_2.html

Base BlockBase Block AdditionBase Block SubtractionNumber Line ArithmeticNumber Line BarsNumber Line BounceRectangle DivisionRectangle Multiplication