Skills tested

Addition and subtraction facts.

Materials needed

A whiteboard and marker for you to use.

One set of completed true-or-false cards.  You can find a pdf of complete cards here: t-or-f cards .

Manipulatives such as renkenreks, blocks, or chips.

Optionally, a set of blank cards.

Directions

Goal:  Have students decide as a group whether equations with simple additions and subtractions are true or false.

1.  To introduce the activity, the tutor writes on the whiteboard:

True or false?

2 + 3 = 5 +1

Read the equation, and give the students time to think.  When they are ready, ask if any students think it is true.  If some do, ask for their reasoning.  If the students seem stuck, ask them what the equals sign means.  Resist the idea of telling students that the equation is false.  Instead, ask questions that help students develop convincing arguments or demonstrations, such as using blocks to show the difference between 2+ 3 and 5 + 1.

2.  Give each pair or group of students a set of complete cards.

3.  Instruct the students to divide the cards into two piles – one true and one false. 

4.  The students need to be able to justify their decisions to each other, using manipulatives or verbal arguments.

5.  If the students can’t agree on the status of a card, they should bring it to the tutor for discussion.

6.  When the students have finished sorting, the tutor will review the two groups of cards and, if necessary, discuss the reasoning.

What to look for

This game often uncovers the misconception that the equals sign means “make.”  Students might look at the opening statement and read it as a sentence, as in 2 + 3 makes 5, which is true, and then we add 1.  If this happens, ask the students to think about the value of each side of the equation and to compare those values. 

*Adapted from Mindset Mathematics Grade 1  by Jo Boaler, Jen Munson, and Cathy Williams.

Skills Tested: Addition, Subtraction

Materials Needed: A deck of cards with the face cards removed. There are numbered cards at reading team as well.

Directions:

1. Set a timer to 5 minutes.

2. Give the first student two cards from the top of the deck to add. If they can get it correctly, you can give the next pair of cards to the next person.

3. The game ends when the timer runs out. You should try and make it so that it ends on yourself, but the person who has the timer run out on them is the loser.

4. Ask them to reflect on what allowed them to add numbers faster (e.g. not counting on their fingers, etc.)

Variations:

1. Do this with subtraction!

Skills Tested: Addition

Materials Needed: Deck of cards with the face cards removed

Directions:

1. Pass each player two cards.

2. Each player should be asked to add what they have but to not share what the result is.

3. If they would like another card, they can ask you for one, but if they go over 21 they lose. 

4. The person closest to 21 without going over 21 wins.

Skills Targeted: Recognizing Numerals

Materials Needed: Any number of objects so long as they have a different color on each side.

Follow these instructions:

1. Have a fixed number of beans in your hands.

2. Toss them out in front of the students.

3. Have the students say the total number of beans, number of one color, and number of the other color.

4. Gather the beans and toss the same amount again. Hopefully they get that the total remains the same but that there are different numbers of the two colors each time.

Skills Tested: Counting

Materials Needed: 20 small counters, 10 in each of 2 colors for each group, 1 die per team, 1 cup per team, and the game board.

Directions:

1. Decide which team goes first. The other team chooses the color of counters for each team.

2. Each team begins with ten counters of the same color.

3. On each turn, roll the die and choose a counter to move. Count forward the number of spaces shown on the die. As one team member moves the counter, the other says the numbers on the spaces aloud. If there is another counter of either color on the number at which you finish, put that counter into your cup and leave your counter in that space.

4. If your move ends in 10, put your counter into your coup. If your counter gets to 20, put it into your cup.

5. The game ends when one of the teams does not have any counters to move.

6. The team with the most counters in its cup wins.

Skills Tested: Basic addition and subtraction

Materials Tested: The following worksheet if you don't have the time to make a picture yourself.

Directions: Print out the worksheet corresponding to addition or subtraction, depending on what works best for you. Have students fill in the empty spaces by completing the addition or subtraction task, matching the number to the color on the guide.

Skills Tested: Counting forward, addition, subtraction

Materials Needed: Any of the following worksheets

Directions: Print out any number of the worksheets and hand them to the students to work on.

Skills Tested: Counting, recognizing numerals

Materials Needed: This board, something to mark positions on the board (a coin, beans, or anything), and a dice. Please also download this sheet (with instructions).

Directions:

1. Each of the two players chooses one of the sides: either the red or the green.

2. Place the marker on the number 5. 

3. At every player's turn, roll the die. The player can then move the marker in his/her direction and then pass the dice. The following player will have to rolle the dice again and move towards his/her direction, but now starting at the previous tile (not necessarily 5).

As an example, say Bob chooses green, while Alice chooses red. On Bob's turn, he rolls the dice and gets a 4. He then moves from 5 to 9 (towards the green). On Alice's turn, she gets a 6. She then moves from 9 towards 3 (towards the red). Then, it proceeds like this. If a player ends on his/her side, they win!

This is a multi-week task as the students will likely make their own "rekenrek" first and then you can play various activities in the subsequent weeks. Please see this google document for ideas and specifics. 

Skills Tested: Addition

Materials Needed: Two die and this sheet.

Directions:

1. Have the students roll two dice.

2. The students should then add the numbers they roll.

3. Once they add the two numbers, they should mark down the number in the appropriate column on the sheet.

4. The game ends once a column is entirely filled.

Skills Tested: Place values, addition, types of facts

Materials Needed: Unifix cubes (example shown on the left). Boxes of these are available at Reading Team.

Directions: There are multiple games that can be played with this, all explained in this google document.

Skills Tested: Addition, Currency

Materials Needed: Coins, which can be taken from a money board game available at Reading Team

Directions: First, hand out one of each coin and let them discuss what they know and don't know about coins. Discuss their size, weight, color, etc.

1. Give each pair of kids a cup of coins containing pennies, nickels, and dimes.

2. Have them roll a dice and take that many coins.

3. Take turns until they get greater than or equal to 25 cents.

4. Have them explain their thinking aloud.

5. See if kids will regroup the pennies to larger coins by giving them less than 25 pennies.

Skills Tested: Addition

Materials Needed: Cards with numbers

Directions:

1. Break up the group into 2-4 groups.

2. Within each group, divide the children into two teams.

3. A child from each team draws 2 cards out of many and flips them over to reveal the number on each card and proceed to add the two numbers.

4. The child with the bigger sum wins.

5. You can also say that the child with the smaller number wins.

Skills Tested: Doubling

Materials Needed: Any set of bingo boards (easily generated online) and a die.

Directions:

1. Roll a die.

2. Ask the students to double the number.

3. Mark an x over the spot on the bingo board corresponding to that number if it exists on the board.

4. Continue until someone fills in a whole row or column.

Skills Tested: Subtraction

Materials Needed: This worksheet.

Directions: Hand students copies of this worksheet for them to work on.

Skills Tested: Addition

Materials Needed: A deck of cards with 1-10 and multiples of 10 up to 90. A recording sheet.

Directions: The goal is to earn the greater amount of points by collecting numbers to make sets with totals less than or equal to one hundred.

1. Put the cards face down between the teams. Spread them out and mix them up to shuffle them. Leave them spread out for the game.

2. Take turns.

3. Begin each turn by turning over two cards. Add the numbers. If you choose to turn over another card, you must also add that number to your total.

4. Decide when to stop turning over a card and adding the number to your total.

5. If your total is less than one hundred when you stop, you get 1 point for each card you used. If it is equal to one hundred, you get 1 point for each card and a 10 point bonus. If it is greater than 100, you get 0 points.

6. Record a number sentence for this turn, the points it was worth, and your total points.

7. Put the cards back face down and mix them all up again before the other team takes its turn.

8. The team with the greater total score after six rounds wins.

Variations:

1. Add cards with multiples of one hundred and have students play Yahoo! 1,000

2. Don't have players mix the cards up after a turn; rather, have them put the cards facedown, with both teams able to see where they have been placed. This change will make memory more important and allow for more strategic moves.

3. Include a few wild cards that may represent any other card in the deck to encourage students to think about how they might, if possible, make a sum of one hundred from their current total.

Adapted from "Well Played" by Dacey et. al

Skills Tested: Generating mathematical expressions, addition

Materials Needed: 1 deck of Equal Values cards per group. 1 Equal Values recording sheet per team. Number scale available at reading team.

Directions: The goal is to get the most pairs of cards that have equal values.

1. Give each team a card with the equal sign.

2. Shuffle the remaining cards. Deal each team four cards faceup for all to see. Put the other cards facedown in a pile.

3. Decide which team goes first.

4. On each turn, you can do one of three things:

   • Find two of your cards that have an equal value. Set this pair beside you. Replace them with two cards from the top of the pile.

   • Trade one of your cards with one of the other team's cards when that lets you make a pair. Set this pair beside you. Replace your card with a card from the top of the pile.

   • Draw a card from the top of the deck and add it to your cards.

5. When a team makes a pair, both teams must agree that the sums are equal and then the team that made the pair must record the expressions on its recording sheet.

6. If no cards are left in the pile, you can still have a turn, but you can't take a card from the pile. 

7. The game ends when no team can make another pair.

8. The team with more pairs wins.

Variations:

1. Have students only use the cards on page A-35, with sums to five, and deal only two cards to each team. Or, have students use the cards on pages A-36 and A-37, and deal three cards to each team.

2. Create cards with two- or three-digit numbers. To support mental math strategies, emphasize the commutative property, for example, 42 + 36 and 36 + 42. Also include expressions that encourage students to think about relationships among the numbers, such as 89 + 45 and 90 + 44.

3. Have students play with subtraction expressions and then with both addition and subtraction expressions, allowing students to note inverse relationships, such as 3 + 4 = 7 and 7 - 4 = 3.

Adapted from "Well Played" by Dacey et. al

Skills Tested: Finding differences from totals to nineteen

Materials Needed:

• 1 set of Take the Numbers Board Number Cards per group

• 1 deck of playing cards, without the face cards (aces stand for 1), per group

• 1 Take the Numbers Recording Sheet per group (page A-54)

Directions: The goal is collect the greater number of playing cards.

1. Put the nine board numbers faceup in a row so everyone can see them.

2. Mix up the playing cards. Put them facedown in a deck.

3. Deal four playing cards to each team faceup for all to see.

4. Take turns. On each turn, you place one of your playing cards below one of the board numbers. You can put your playing card below a board number that already has a playing card there or below one that does not. Then, look at the recording sheet for that number.

5. If you put the first card below a number, subtract the value of your playing card from the board number you chose. Cross out the board number on the recording sheet and write the difference you found in that column. Then, take a new playing card from the deck to add to your hand.

6. When there is already a card below the board number you chose, check the recording sheet. If your card is less than that last number in the column on the recroding sheet for the board number you chose, subtract your card from that number. Cross out the last number in that column and record the new difference.

7. If your card is equal to the last number in the column, subtract and record the zero difference. Turn over that game board number, as it is no longer in play, and take all of its playing cards. Put them facedown near your team. Take a card from the deck to put in your hand. Your turn is over.

8. If you can't place a number that gives a difference greater than or equal to zero, you lose your turn.

9. The game ends when neither team can place a card. The team that has collected the greater number of playing cards wins.

Variations:

1. Change the rules so that if a team gets a difference of zero, the other team gets those playing cards.

2. The students in one class suggested that teams place their initials next to a zero difference when their card resulted in that difference. Then the team with the greater number of initialed zeros would win.

3. Have students play without using the recording sheet to see how they determine the difference that remains when more than one card has been placed beneath a number on the game board.

Adapted from "Well Played" by Dacey et. al

Skills tested

Using groups to count

Materials needed

1 or 2 collections of objects such as coins, cubes, or crayons, with at least 21 objects in each collection

Cups or containers for organizing the objects

Directions

Goal:  Have students explore the connections between counting, grouping, and place value by working with collections of objects.

1.  To introduce the activity, the teacher shows a collection of objects such as coins, cubes, or crayons.  There should be at least 21 objects in the collection (and preferably the number will not be an even multiple of 10). Ask, how can we organize the objects so that we can see how many there are?  Ask for ideas.  Tell them that their job is to create a way to organize and count the objects. 

2.    Give pairs of students a collection and a set of cups or containers.  Help them think about using groups of (of 2s or 5s, for example) to make the counting easier.  For example, if they put 5 items in each container, does that make the collection easy to count?   If they put 6 in each container, does that make the collection easier to count?

3.    Once they have finished, the students should report back on their count and their reasons for choosing their groupings.  Ask, did their methods make it easy for them to agree that their count was correct?  If the students didn’t use groups of 10, ask whether grouping by 10 would have made it easier to get the correct answer. 

What to look for

Typically in this activity, students will have to count the grouped objects by 2s, 5s, 10s (or some other number) and then count by 1s.  Do students struggle with this transition?

*Adapted from Mindset mathematics GRADE 1 by Jo Boaler et al.

Skills tested

Addition facts, including those about doubling and friendly numbers

Materials needed

Sets of completed do-it-yourself triangle fact cards.  These are cards on isosceles triangles with numbers on each vertex.  One number is the sum of the other two.  The sum should be highlighted by a circle or the use of a different color.  You can find a pdf of complete cards here: Triangle cards complete 

A board to write down the different relationships between the three numbers.

Optionally, you can also use some incomplete cards (available here:  Incomplete cards) and markers, and have the students complete them.

Directions

Goal:  Have students use addition facts to solve simple problems.

1.  To introduce the activity, the teacher shows a card.

2. Ask the students, what do you see?  Then ask, how are these three numbers connected?  Some students might say that 4 + 10 = 14.  You might also get 10 + 4 = 14 and 14 – 4 = 10.  Write down the responses on the board.  Ask if everybody understands every fact about addition can be turned into a fact about subtraction.  Point out that the sum is circled and the other two numbers are not circled.

3. Explain that now you will show them other cards, with one corner covered up.  They have to guess what the covered-up number is.  First show them cards with the sums covered.

4. Show them cards with one of the other numbers covered up.  See if they understand that they need to subtract the other number from the sum.

5.   Optionally, give the student unfinished cards with 1 or 2 numbers missing, and ask them to complete the cards.  Discuss the results with the students. 

Other ways of obtaining cards

You can make cards by trimming off a piece of 8.5” by 11” inch paper, so that it is square.  Fold it diagonally twice and then write numbers, using the addition facts (e.g., doubles facts and friendly numbers) you want to emphasize.  For first grade, we’ll want to keep the sums less than or equal to 20. Then cut the paper into triangles. 

You can also do a Google search for “Triangle fact cards pdf,” but you will have to pay to get a printable document.

Skills tested

Estimation; understanding of place value.

Materials needed

Bag or container of beans or large beads.  You’ll want to have at least 20 beans or beads in the container.

Place value sheet (Click here).

One slip of paper and a writing instrument for each student.

Cups or containers.

Directions

Hold up the bag or container.  Ask the children to estimate how many beans or beads are in the container. Have them write their estimates on a slip of paper. Then collect the estimates and write them on board – or put them in a chart. 

The count, as a group, the beans or beads, placing 10 in each container.  Place a full container on the side of the paper labelled “10s.”   Leave the remainder on the other side of the board.

Then count the cups by 10:  “Ten, twenty, thirty.”  And then add the 1s.  For example, “thirty one, thirty two, thirty three.”

Do this several times over a few weeks.  You should see improvements in students’ ability to estimate.

Tip

Barrata-Lorton talks about using peanuts for this exercise.  But some children might have allergic reactions to peanuts.  You can also use pieces of pasta. 

*Adapted from Mathematics Their Way  Mary Baratta-Lorton, pp. 308-09.

Skills Tested: Subtraction, Collaboration, Math Logic

Materials Needed: 

1. A set of Name That Number cards for each group (Easy, Medium, Hard)

2. Whiteboards and markers available at the Reading Team

Directions: The goal is to use the clues to find the mystery number.

1. Work as a team of three puzzle solvers.

2. Place the clues facedown. Each solver randomly takes two of the clues.

3. Decide how to share the clues.

4. Work together, read the clues as many times as necessary, and talk about what you know. Try to find the number that fits all the clues.

5. When you think you have the solution, read the clues again to check.

Variations:

1. Have solvers show their clues one at a time, without talking or gesturing. After all the clues have been shown, each solver may rearrange the order of one of the clues. Through eye contact, rather than talking, solvers communicate that they think they have a solution. Solvers may then talk to check the clues.

2. If you choose to make your own Name That Number cards, you could create examples that would result in two or four numbers that met all criteria and change the question to What are the numbers?

3. Have groups record their thinking of how they used their clues to figure out the puzzle. They may use number lines to record their steps, for example.

Adapted from "Well Played" by Dacey et al.

Skills Tested: Estimation and Subtraction

Materials Needed:

1. A sufficient number of copies of the tic-tac-toe game board. I recommend bringing at least 2 for each student (easy, medium, hard)

2. Whiteboards and markers to work on

3. Optional: Hundreds tables or number lines

Directions: The goal is to have students use estimation skills to choose pairs of numbers to subtract in order to mark three differences in a row, column, or diagonal on the answer board.

1. Decide which team will be X and which team will be O. Take turns.

2. On each turn, the team picks a number from Sign A and one from Sign B. Then, both teams subtract the number on Sign B from the number on Sign A. Once both teams agree on the difference, the team whose turn it is finds it on the answer board and writes its X or O on the number.

3. If the team gets a difference that is already marked with an X or O, it loses its turn.

4. The first team to write X or in three touching differences in a row, column, or diagonal is the winner.

Variations:

1. Add a game rule: If a team find an incorrect difference, it loses its turn.

2. For game boards B or C, you can add more challenge by changing the goal to marking four differences in a row, column, or diagonal.

3. By changing the numbers on the signs and the game board, you can vary the difficulty level of the game.

4. You can also create a version of the game in which the players choose addends on signs to get sums on the answer board.

Adapted from "Well Played" by Dacey et al.