Children enjoy playing games and games can be a great context for mathematics learning and discussion. Through games children can develop appropriate, efficient and flexible use of mathematical strategies. Family game time can provide fun, a good challenge, and enable children to develop their mathematical understanding. Games with dice and cards can help students develop their mathematics skills. There are many games specific to mathematics that can be played with dice or cards. One example is Multiplication Tetris. For this game dice or playing cards (2-9, with aces as a 1) are used with grid paper. Players take turns rolling two dice or picking two cards. The two numbers are then used for the width and length dimensions of a rectangle. The rectangle can be placed anywhere in the grid paper as long as it does not overlap with another rectangle. Play continues until one player does not have a place for their rectangle. The figure below shows the start of a game.

Another game that can be played is Small, Large, or Target. This game is played by having players try to get the smallest number, the largest number, or be closest to a target number. This is decided at the start of the game along with what operation will be used (addition, subtraction, multiplication, or division). The number of boxes used in this game can be varied with 2, 4, 6, or 8 boxes. Ten playing cards are needed (2-9 and Ace as 1 and Jack as 0). One player picks one of the ten cards while the cards are face down. After the card is selected each player decides what box to place the number in. Once a number is placed in a box it cannot be changed. Play continues until all boxes are filled with a numbers. Players then solve the problem and the winner is determined. The winner is based on what was selected at the start of the game; either trying for the smallest number, the largest number, or being closest to a target number. The figure below has a sample game with two sample game cards. For this game, the card with the sum of 159 is the winner. Games provide an ideal context for children to have a positive attitude towards mathematics, persevere in problem solving, discuss mathematics, and see that they can improve through effort and using their resources.

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Mathematics may viewed as a subject that always has one correct solution and one best solution strategy. In order for students to develop conceptual understanding for procedural fluency, building mathematical reasoning is essential through seeing multiple strategies for approaching problems. Open-ended questions can develop children’s number sense and help them be adaptable, problem-solvers, and good communicators. Open-ended problems encourage discussion and exploration. They show that mathematics can involve creativity and also demonstrate how mathematics is relevant and realistic.

For example, one open-ended question is how many ways can you represent 28? There are a number of ways to do this and below are just a few.

For example, one open-ended question is how many ways can you represent 28? There are a number of ways to do this and below are just a few.

Students can develop number sense, estimation, and mathematical reasoning through open-ended questions. They can also help students be curious about the world and learn how to problem solve, which is the basis of good mathematical thinking. Making estimations, predictions, and thinking about other ways that daily things can be done can help students do well in mathematics. The table below has examples of open-ended questions that parents could discuss with their child. Mathematics is not a spectator sport and children should get used to the idea of being an active learner for mathematics.

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The importance of reading for a child’s development is vital. Reading books and having books read to children makes a big difference. Reading books benefits a child’s mathematics development as well because reading comprehension and vocabulary is important for mathematics. Books with a focus on mathematics can bring more benefits. Children’s literature allows students to interact with mathematics in context, helping them draw meaningful connections between experiences in the classroom and life outside the classroom, which can motivate them in learning mathematics. Books that integrate mathematics can allow for interesting mathematical questions to be posed.

There have been many benefits that have been found with the integration of children’s literature and mathematics. This approach allows for mathematics and language skills to develop simultaneously as children learn to read, write, and talk about mathematics. Books can help students learn mathematics through multiple representations. Inclusion of literature enables students to see mathematics as real, relevant, and motivating. Mathematics achievement has also been found to be increased through the integration of children’s literature. In addition, the inclusion of children’s literature with mathematics has been recommended as a way to reach a diverse range of students.

I write children's books that integrate mathematics based on these benefits. One of my books is*Trick or Dog Treat**.* In this book Goldy is a curious golden retriever that sees math all around him. Children see what happens when Goldy gets to go Trick-or-Treating for the first time. Will Goldy get any treats in his pumpkin pail? The mathematical questions incorporated in the book allow children to work with numerical patterns and develop the transition from additive to multiplicative thinking. The picture below is one example picture that is included in the book. In the picture Goldy sees that there are four houses on each block and wonders how many houses would be on two, three, four or five blocks? Through my books that I have written, I seek to help students see mathematics in everyday life, to enjoy discussing mathematics, and also to have a positive attitude towards being able to learn mathematics.

As another resource, The Everyday Mathematics K-6th grade curriculum literature and mathematics list is available at the following link. It has a list of books and related mathematics topics that can be discussed through the books. https://everydaymath.uchicago.edu/teachers/k/literature-list/

]]>There have been many benefits that have been found with the integration of children’s literature and mathematics. This approach allows for mathematics and language skills to develop simultaneously as children learn to read, write, and talk about mathematics. Books can help students learn mathematics through multiple representations. Inclusion of literature enables students to see mathematics as real, relevant, and motivating. Mathematics achievement has also been found to be increased through the integration of children’s literature. In addition, the inclusion of children’s literature with mathematics has been recommended as a way to reach a diverse range of students.

I write children's books that integrate mathematics based on these benefits. One of my books is

As another resource, The Everyday Mathematics K-6th grade curriculum literature and mathematics list is available at the following link. It has a list of books and related mathematics topics that can be discussed through the books. https://everydaymath.uchicago.edu/teachers/k/literature-list/

If mathematics is conveyed to be about memorization then less students are able to be successful. Concepts are less likely to be retained and students number sense to determine the reasonableness of answers is diminished with a focus on memorization. Mathematics is not about how quick problems can be done but efficiency with understanding is great! Reasoning should be emphasized over memorization. There are multiple strategies for solving mathematics problems. With a basis of conceptual understanding students can become skillful in using procedures and strategies flexibly.

One way that parents can encourage reasoning over memorization is by doing number talks with their child. Through number talks students can develop number sense and their math fact fluency. Number talks are becoming more prevalent in elementary grades mathematics classes and parents can also do them at home with their child. Number talks help students develop number sense and mental math abilities. In a number talk, a mathematical problem is posed and children are given time to think to solve the problem mentally. Next, all possible answers are shared for the problem without any statement about which is correct or incorrect. Children then defend an answer by sharing the strategy they used to solve the problem. Discussion occurs so that consensus can be reached on the correct answer and for students to hear the different ways the problem was solved. Number talks can involve one problem or a sequence of related problems. For example, a teacher may pose 28 x 5 and students may use the following strategies.

One way that parents can encourage reasoning over memorization is by doing number talks with their child. Through number talks students can develop number sense and their math fact fluency. Number talks are becoming more prevalent in elementary grades mathematics classes and parents can also do them at home with their child. Number talks help students develop number sense and mental math abilities. In a number talk, a mathematical problem is posed and children are given time to think to solve the problem mentally. Next, all possible answers are shared for the problem without any statement about which is correct or incorrect. Children then defend an answer by sharing the strategy they used to solve the problem. Discussion occurs so that consensus can be reached on the correct answer and for students to hear the different ways the problem was solved. Number talks can involve one problem or a sequence of related problems. For example, a teacher may pose 28 x 5 and students may use the following strategies.

A sequence of problems could involve 8 x 5, then 20 x 5, and then 28 x 5 for students to get see the strategy of partial products.

In a number talk, the goal is not to find the most complicated way to solve a problem, but to focus on strategies that build number sense, make use of related facts, and develop efficient, flexible strategies that can be used with accuracy. The table below has some strategies that parents can work on in discussing problems with their child. Having an idea of what answers make sense and how to separate and combine numbers flexibly can be developed with number talks. For example, solving 19 + 38 by taking one from the 38 and adding it to 19, making it 20 + 37, is an easier problem to solve.

]]>In a number talk, the goal is not to find the most complicated way to solve a problem, but to focus on strategies that build number sense, make use of related facts, and develop efficient, flexible strategies that can be used with accuracy. The table below has some strategies that parents can work on in discussing problems with their child. Having an idea of what answers make sense and how to separate and combine numbers flexibly can be developed with number talks. For example, solving 19 + 38 by taking one from the 38 and adding it to 19, making it 20 + 37, is an easier problem to solve.

Have a Positive Attitude Towards Mathematics

One of the most important things that parents can do is to demonstrate a positive attitude towards mathematics. One of the worst things that parents can say is, “I never got math.” When it is conveyed that mathematics is a subject that some students can do and others cannot, it can cause students to put forth less effort and accept that failing mathematics is okay. Parents can encourage their child that mathematics can be learned like any subject. They can also instill in their child the importance of mathematics to better understand the world and for decision making. When parents have a positive attitude towards mathematics and encourage their child they can do well in mathematics, it can make a big difference. The table below has phrases that parents and teachers should avoid as well as positive messages that can be communicated instead.

]]>This activity integrates children’s literature, engineering design, mathematics, and English language arts. The children’s book I wrote helps students learn more about engineering and biomedical engineering. Biomedical engineering is an interdisciplinary STEM field that combines biology and engineering to create solutions for medicine and healthcare. English language arts standards are incorporated through reading the children’s book and a class discussion about the book. After reading the book, students work on an engineering design challenge to design and build a prosthetic leg. Mathematics is incorporated through measurement.

After readings students the book,*The Little Engineer That Could, *the teacher then leads a class discussion using the following questions. Alternatively, these can be used as individual writing prompts. Describe Cadence and her feelings throughout the story. What was her motivation for helping Danny? How did her actions contribute to the sequence of events in the story. How did Cadence respond to challenges that arose?

To begin the design challenge students watch the following video about the Invictus Games. The Invictus Games is an international sporting event for wounded, injured and sick Servicemen and women. The Games strive to use the power of sports to inspire recovery, support rehabilitation and generate a wider understanding and respect of all those who serve their country.

After readings students the book,

To begin the design challenge students watch the following video about the Invictus Games. The Invictus Games is an international sporting event for wounded, injured and sick Servicemen and women. The Games strive to use the power of sports to inspire recovery, support rehabilitation and generate a wider understanding and respect of all those who serve their country.

After watching the video, students answer the following questions.

1. Why do you think the Invictus Games are held?

2. Do you know anyone who has been injured, sick, or hurt?

3. Why is important to help and encourage others?

4. Have you ever done something that was difficult? Why is it important to keep putting forth effort and to not give up?

Challenge

Sergeant Danny Mendez is participating in the Invictus Games. He wants your team to develop a comfortable leg for walking around the games when he is not competing. As a first step you will design and build the leg for one person in your group to test your prototype.

Criteria and Constraints

There are three criteria for the design. 1) The leg should be comfortable. 2) The leg should be sturdy and stable. The person in your group must be able to walk 10 feet with the prosthetic leg. 3) The prosthetic leg should be aesthetically pleasing (look good).

Rubric for criteria 1)

1 point- leg is not comfortable and causes pain.

2 points- leg is mildly comfortable with little discomfort or pain.

3 points- leg is comfortable with little discomfort and no pain

Rubric for criteria 3)

1 point-leg is not aesthetically pleasing

2 points- leg is somewhat aesthetically pleasing

3 points- leg is aesthetically pleasing

The constraints are that you can only use the provided materials and that you have 60 minutes to design and build the prosthetic leg.

Materials

Your group will have scissors, measuring tape, and a ruler.

-Duct tape

-cardboard tube

-pvc plastic pipe

-large rubber bands

-toliet plunger (unused)

-wood board

-sponge

-bubble wrap

-cardboard

-string

-rope

]]>1. Why do you think the Invictus Games are held?

2. Do you know anyone who has been injured, sick, or hurt?

3. Why is important to help and encourage others?

4. Have you ever done something that was difficult? Why is it important to keep putting forth effort and to not give up?

Challenge

Sergeant Danny Mendez is participating in the Invictus Games. He wants your team to develop a comfortable leg for walking around the games when he is not competing. As a first step you will design and build the leg for one person in your group to test your prototype.

Criteria and Constraints

There are three criteria for the design. 1) The leg should be comfortable. 2) The leg should be sturdy and stable. The person in your group must be able to walk 10 feet with the prosthetic leg. 3) The prosthetic leg should be aesthetically pleasing (look good).

Rubric for criteria 1)

1 point- leg is not comfortable and causes pain.

2 points- leg is mildly comfortable with little discomfort or pain.

3 points- leg is comfortable with little discomfort and no pain

Rubric for criteria 3)

1 point-leg is not aesthetically pleasing

2 points- leg is somewhat aesthetically pleasing

3 points- leg is aesthetically pleasing

The constraints are that you can only use the provided materials and that you have 60 minutes to design and build the prosthetic leg.

Materials

Your group will have scissors, measuring tape, and a ruler.

-Duct tape

-cardboard tube

-pvc plastic pipe

-large rubber bands

-toliet plunger (unused)

-wood board

-sponge

-bubble wrap

-cardboard

-string

-rope

*anticipating*likely student response to challenging mathematical tasks;*monitoring*students’ actual responses to the tasks (while students work on the tasks in pairs or small groups);*selecting*particular students to present their mathematical work during the whole-class discussion;*sequencing*the student responses that will be displayed in a specific order;*connecting*different students’ responses and connecting the responses to key mathematical ideas. (Smith & Stein, 2011)

-What did I learn today?

-What good ideas did I have today?

-What did I struggle with today?

-Where could I use the knowledge I learned today?

-What questions do I have about today's work?

-What new ideas do I have that this lesson made me think about?

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