Put Together, Take Apart - Lake Washington School District

Putting Together, Taking Apart

Addition and Subtraction

Mathematical Emphasis
Investigation 1—Combining and Separating

Developing models of addition and subtraction situations
Solving problems using numerical reasoning
Recording solution strategies clearly
Recording solution strategies clearly

Investigation 2—Working with 100

Becoming familiar with the structure and patterns of the number system from 1 to 100
Using coins as a model for adding and subtracting multiples of 5 and 10
Using the 100 chart as a tool for combining and comparing numbers
Developing strategies for addition and subtraction
Comparing numbers to 100

Investigation 3—Finding the Missing Part

Developing ways to approach different sorts of addition and subtraction situations
Recognizing and solving problem structures with a variety of givens and unknowns
Solving problems using numerical reasoning
Recording solution strategies clearly
Creating situations for equations
Comparing solution strategies

Investigation 4—Add Up to 100

Working with 100 and combinations of numbers that equal 100
Adding strings of numbers by “chunking” or grouping numbers that go together
Writing a story that reflects an addition equation

Investigation 5—Addition and Subtraction Strategies

Developing strategies for comparing two quantities
Calculating the distance between two numbers using the 100 chart
Developing ways to approach different types of addition and subtraction situations
Recognizing and solving problem structures with a variety of givens and unknowns
Solving problems using numerical reasoning
Recording and comparing solution strategies

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?
What have you already tried? What steps did you take?
What do you need to do next?
Can you show it in a different way?
How did you get your answer?

Helping At Home

Encourage your child to use his or her own strategies for addition and subtraction.
For homework, your child will be writing various types of story problems. Ask your child to tell you about strategies he or she uses to solve these problems. Encourage your child to use words, pictures and numbers in explanations.
Your child will be bringing home some of the games being played in math class. Take some time to play these games with your child.
Children will be working with problems involving money. Use some change to investigate ways to make $1 or $2 with your child.
Look for addition and subtraction situations at home and share them with your child. For example, if you bake a batch of cookies and you set some aside for school lunches, how many cookies will be left for the family to eat?
Keep in mind that numbers under 100 are about the right size for most second graders.

Vocabulary Terms

Combining: Addition
Equation: A mathematical statement containing an equal sign, showing two math expressions are equal
Multiple: A mathematical operation where a number is added to itself a number of times
Number Strings: Mathematics problems with more than two numbers being added
Separating: Subtraction
Skip Counting: Counting forward or backward by multiples of a given number
Strategy: Method used for solving a problem

Mathematics Vocabulary Web site

Mathematics Strategy—How Students Learn to Add and Subtract

This unit helps students develop the number sense necessary to be able to solve numerical problems in whatever context they appear. There are many algorithms that, while both efficient and accurate, also keep more visible the connections between the numbers and the problems. In this unit, students develop such procedures, which are connected closely to the meaning of the operations and are based on number relationships they know.

There are several goals for students as they develop procedures to solve addition and subtraction problems. The most important goal is that procedures are based on sound number sense and an understanding of the problem. Speed should not be a criterion for solving any kind of mathematics problem. Rather, efficiency in use is the critical criterion for students’ mastery of computation with whole numbers. Solving problems in a way that is based on sound number sense and knowledge of the base ten number system, as well as being efficient and accurate, will equip children to be strong mathematical thinkers.

Source: Investigations in Number, Data, and Space: Putting Together, Taking Apart. Dale Seymour, 1998. (Pages 15-16)

Mathematics Strategy—Moving from 1’s to Groups

Some students may solve addition or subtraction problems by counting all the objects or by counting on from one of the numbers, while other students break numbers into parts or groups. Many students use a combination of these strategies. Here are some strategies students have used to solve 37 + ___ = 63

Count all by 1’s (Count out 63, count out and remove a group of 37, count the leftovers)
Count on by 1’s (38, 39, 40, 41, …. 63)
Count on by 1’s and 10’s (47, 57, 58, 59, 60, 61, 62, 63)
Count by chunks (3 more to 40, 23 more to 63)

Students refine their strategies as their understanding of number and number relationships develops. Moving from counting by 1’s to counting by groups and making use of 10’s is important mathematical work in second grade.

Source: Investigations in Number, Data, and Space: Putting Together, Taking Apart. Dale Seymour, 1998. (Page 94)

Mathematics Game—Win 5

Materials

100 Chart

Deck of Add and Subtract Cards (ones and tens)

Markers

Game piece for each player

Paper

Playing the Game

Object of the game is to win five of the markers from the 100 chart.

Place 12 markers on the 100 chart, each on a different number. Each player is dealt five of the Add and Subtract Cards; unused cards are placed face down in a pile. Players choose an unmarked number somewhere on the 100 chart as their starting place and put their playing piece on that space.

For each turn, a player tries to move to a number with a marker by using any amount of the Add and Subtract cards in his/her hand.

If a player is able to land on a marker, he/she wins that marker and takes it off the board. (A player can only win one marker on a turn and it must be the last number square of the turn.)

Moves are written down on the record sheet as a math equation. If you start on 33 and use the cards +3, +3, +10, -1, you would write: 33 + 3 + 3 + 10 – 1 = 48.

Put the used Add and Subtract cards in a discard pile and draw new cards from the deck to replace them. Players should always have five cards in their hands. If cards in the deck are used up, shuffle the discard pile and place face down as the new deck.