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MATH STRATEGIES:

### What's Awesome and What's Less Than Awesome

Listed below are best practices for teaching mathematics as listed in the publication

__Best Practice, Today's Standards for__

__Teaching and Learning in America's Schools__by Steven Zemelman, Harvey Daniels, Arthur Hyde.

**WHAT'S AWESOME**

**WHAT'S LESS THAN AWESOME**

TEACHING PRACTICES TEACHING PRACTICES

*Use of manipulative materials *Rote practice

*Cooperative group work *Rote memorization of rules and formulas

*Discussion of mathematics *Teaching by telling (lecture)

*Justification of thinking *Single answers and single methods to find

answers

*Writing about mathematics *Stressing memorization instead of

understanding

*Problem-solving approach to instruction *Repetitive written practice

*Content integration *Use of drill worksheets

*Use of calculators and computers *Teaching computation out of context

*Being a facilitator of learning *Reliance on paper and pencil calculations

*Assessing learning as an integral part of instruction *Being the dispenser of knowledge

PROBLEM SOLVING PROBLEM SOLVING

*Word problems with a variety of structures and *Use of cue words to determine operation to solution paths be used

*Everyday problems and applications

*Problem-solving strategies (especially *Practicing problems categorized by types

representational strategies)

*Open-ended problems and extended *Practicing routine, one-step problems

problem-solving projects

*Investigating and formulating questions from

problem situations

CREATING REPRESENTATIONS CREATING REPRESENTATIONS

*Creating one's own representations that make *Copying conventional representations

sense without understanding *Creating multiple representations of the same *Reliance on a few representations

problem or situation

*Translating between representations of the same *Premature introduction of highly abstract

problem or situation representations

*Representations using electronic technology

*Using representations to make the abstract ideas *Forms of representations as an end product more concrete

*Using representations to build understanding of

concepts through reflection

*Sharing representations to communicate ideas

COMMUNICATING MATH IDEAS COMMUNICATING MATH IDEAS

*Discussing mathematics *Doing fill-in-the-blank worksheets

*Reading mathematics * Answering questions that need only yes

or no answers

*Writing mathematics * Answering questions that need only

numerical answers

*Listening to mathematical ideas

REASONING AND PROOF REASONING AND PROOF

*Drawing logical conclusions *Relying on authorities (teacher or answer

key)

*Justifying answers and solution processes

*Reasoning inductively and deductively

MAKING CONNECTIONS MAKING CONNECTIONS

*Connecting mathematics to other subjects and *Learning isolated topics

to the real world

*Connecting topics within mathematics *Developing skills out of context

*Applying mathematics

NUMBERS/OPERATIONS/COMPUTATION NUMBERS/OPERATIONS/COMPUTATION

*Developing number and operation sense *Early use of symbolic notation

*Understanding the meaning of key concepts such

as place value, fractions, decimals, ratios, *Memorizing rules and procedures without

proportions, and percents understanding

*Various estimation strategies *Complex and tedious paper and pencil

computations

*Thinking strategies for basic facts

*Using calculators for complex calculations

GEOMETRY/MEASUREMENT GEOMETRY/MEASUREMENT

*Developing spatial sense *Memorizing facts and relationships

*Actual measuring and exploring the concepts *Memorizing equivalencies between units of

related to units of measure measure

*Memorizing geometric formulas

*Using geometry in problem solving

STATISTICS/PROBABILITY STATISTICS/PROBABILITY

*Collecting and organizing data *Memorizing formulas

*Using statistical methods to describe analyze

evaluate, and make decisions

ALGEBRA ALGEBRA

*Recognizing and describing patterns *Manipulating symbols

*Identifying and using functional relationships

*Developing and using tables, graphs, and rules *Memorizing procedures

to describe situations

*Using variables to express relationships

ASSESSMENT ASSESSMENT

*Making assessment an integral part of teaching *Having assessment be simply counting

correct answers on test for the sole

*Focusing on a broad range of mathematical tasks purpose of assigning grades

and taking a holistic view of mathematics *Focusing on a large number of specific and

isolated skills

*Developing problem situations that require *Using exercises or word problems requiring

applications of a number of mathematical ideas only one or two skills

*Using multiple assessment techniques including *Using only written tests

written, oral, and demonstration formats

website link

This week in math we are working on sequencing numbers. Students are given a collection of 16 various numbers and they must put them in order. We will also be learning games to practice addition facts.

Second Grade

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Everyday Math

Family Math Games

All you need is a deck of cards or a pair of dice. Concentration (add, sub, multiplication, division)

The object of the game is to find pairs of matching cards among an array of face down cards. Help your child write addition, subtraction, multiplication, or division facts on one set of index cards, and the answers on another set. Shuffle the cards and lay them out face down. The first player turns over two cards. If they match, theplayer keeps the two cards and takes another turn. The next player continues by trying to find two matching cards. When all cards have been collected, the player with the most pairs wins.

Dice Games (addition)

You will need 2, 3, or 4 dice and one score sheet. Tally to so many rolls or to a preset score such as 50 or 100 points. Vary it by adding the sums of the dice together, and the greatest or least score wins! Vary it again by rolling 3 colored dice and 1 white die. Subtract the number on the white die from the sum of the colored dice, and the greatest sum wins.Go Fish (addition)

Prepare flash cards from 0-10 (3 sets of each number). Play "Go Fish" to add numbers up to 10. (Ex: Sally has the number 4, so she asks her mother for the number 6 because 4+6=10.)Card Games (addition) War:

Divide the deck of cards evenly. Each player will put out two cards and add them together. Whoever has the highest total will take all cards. The object is to take the whole deck.Pig (addition)

Players take turns rolling two dice. A player may roll the dice as many times as he/she wants, mentally keeping a total of the sums that come up. When the player stops rolling, he/she records the total, and adds it to the scores from previous rounds. BUT if a one is rolled, the player scores a 0 for that round, and it's the next player'sturn.

Race for $1.00 (money addition)

You need 30 pennies, 10 nickels, 20 dimes, 1 quarter, a dollar, 2 dice, and a partner. Take turns. On your turn, roll the dice. The sum tells how many pennies to take. When you have 5 pennies, trade for a nickel. When you have 2 nickels, trade for a dime. When you have 2 dimes and one nickel, trade for a quarter. The first player to reach $1.00 is the winner.

Guess My Number (number logic)

You need: paper, pencil, partner. Player one picks a number from 0-99 and writes it down. Player two makes a guess and writes it down. Player one gives a clue: "Your guess is greater than my number" or "Your guess is less than my number". Continue playing until player two guesses player one's number. Switch jobs and play again.The 1 to 10 Game (addition)

You need: 2 dice, 1 deck of cards, and a partner. Use only the ace, 2, 3, 4, 5, 6, 7, 8, 9, and 10 cards. One of you takes the red cards, one of you takes the black cards. Take turns. On your turn, roll the dice and figure out the sum. Remove enough cards from your hand to add up to that sum. For example, if you roll a 5 and a 3, you can make 8 in many ways (5+3, 4+4, 4+2+2, 8, etc...). If you can't make the sum with the cards in your hand, roll again. If you can't make a sum after three rolls, you lose the game. You win if your partner can't make a number in three rolls or if you use up all of your cards.Number Family Rummy (fact families)

Use a deck of 40 cards: Four suits of ace through ten. The goal is to make families of three cards that are related by addition or subtraction. For example: 5, 5, and 10 are a family because 5+5=10, and 10-5=5. 6, 3, and 9 are a family because 6+3=9, 9-6=3, and 9-3=6. Shuffle the deck and deal 6 cards to each player. Place the remaining cards face down in a pile. If you have any families of cards, place them aside. If you don't have any families, you may draw one from the pile and discard one of your own. You may also discard the one that you picked up, if you don't want it. The first player to get rid of all 6 cards (2 fact families) is the winner. Remember that the ace equals one.Grab Bag Subtraction (subtraction)

Choose a number of things to work with, and put that many objects into a bag. You can use crayons, coins, beans, buttons, etc...) Grab a handful of the items and count them. Use subtraction to figure out how many items are now left in the bag. So if you put 100 items in the bag and pulled out 20, then you would write 100-20=80. Let your partner have a turn, and whoever leaves the least amount in the bag is the winner.Lineup (number order, multiples)

Prepare number cards from 0-50. If more than two players are going to play, you might want to prepare two decks. Shuffle the cards and deal 8 to each player. Players place their cards face up in a horizontal line in front of them in the same order in which they are received. Players may not move their cards around. The object of the game is to be first to have your cards in the right sequential order from smallest to largest. A player does this by taking a card on each turn from the top of the undealt deck, and using it to replace any of the cards in his lineup. He discards the card that is replaced. Whenever a player's lineup of numbers is in the correct order from smallest to largest, he calls out LINEUP and wins the game. You can vary this game by using multiples of numbers. You still have 8 cards, but are trying to get multiples in order from smallest to largest. So you can do multiples of 2 (2, 4, 6, 8, 10, 12, 14, 16) or multiples of 3 (3, 6, 9, 12, 15, 18, 21, 24). You can even have numbers such as 12, 16, 20, 24, 28, 32, 36, 40. Those are multiples of 4, but they don't necessarily have to start with the number 4. They are however, still in order from smallest to largest.Card Capture (addition, subtraction, multiplication, division)

Use a set of fact flashcards. Divide the cards equally between the two players. One player attacks, while the other player defends. The defending player shows his cards (problem side up) one at a time to the attacking player. If the attacking player says the right answer, he captures the card and adds it to his own. He can continue capturing cards until he answers incorrectly. When this happens, the defending player becomes the attacker, and gets his chance at capturing the cards. This continues with cards being captured back and forth until one player winds up with all of the cards, or has the most cards when time is called. You can even set the rules to the first player to capture 20 cards, or any number you'd like.Addition and Subtraction Turnover (addition and subtraction)

Each player is given 11 cards numbered 0-10. These are placed face up in a row. Players roll two dice on a turn and may choose to add or subtract the two numbers shows on the dice. If the resulting sum or difference equals one of the number cards face up, the player can turn that card face down. Next player then takes a turn. This continues until one of the players wins by turning all 11 of his cards face down.Subtraction Pig (subtraction)

Two or more players start out with 100 points each. Players in turn roll two dice andsubtract that number from their points. A player on a turn continues rolling the dice and subtracting the resulting number from his remaining points until a 1 appears on any dice rolled. That player's turn ends, and the next player takes a turn. When a player has lost all of his points, he is out of the game. The last player in the game, is the winner.