**High Achievement Math Program; Critical Thinking Activities**

When math students are engaged in critical thinking, they grow. Students expand their vocabulary, depths of understanding, math skills, frames of reference,, and overall interest in math.

The Critical Thinking Activities component of the High Achievement Math Program engages students through five powerful activities.

**1) Paired Learner Activities (P3CR)**

Paired Learner Activities are critical thinking activities that engage students in problem solving, collaboration, communication, connections, and mathematical reasoning (P3CR). Each activity connects with a foundational math strand (number sense, algebraic thinking, measurement, geometry, probability, statistics). Paired learners would work together to read the activity, develop a problem solving plan, implement the plan, and evaluate their solutions and work. Generally, each P3CR activity is contained on a single page, and takes students about 15-20 minutes to complete . A great way to build Paired Learner Activities into the class routine is to consistently implement one P3CR activity every Friday, or another day of the week. P3CR activities come with answer keys and student score-keeping forms. The P3CR activities are excellent math activities that will help all students grow.

**2) Mental Math Strings**

Mental Math Strings combine vocabulary, mental math, and fun. Each string consists of simple commands that teachers read and students follow. Here’s an example.

• Start with the number of quarts in two gallons

• Square your answer

• Round your answer to the nearest ten

• Add the number of minutes in one hour

• Add the digits of your answer together

• Cube your final result (Answer: 27)

Students execute each command mentally. No paper, pencils, or calculators are allowed. At the end of the challenge, a student who succeeds verbally works through the Mental Math String line by line so all students know how to arrive at the correct answer. Mental Math String challenges are great tickets-out-the-door activities.

**3) Computation Challenges**

Computation Challenges are ten-question, ten-minute, half-sheet problem sets that challenge students to skillfully calculate with whole numbers, fractions, decimals, and integers. Computation Challenges also engage students in place value, Order of Operations, simple equations, and more. Computation Challenges are best implemented one day each week, perhaps on a Friday, before the Paired Learner Activity. The challenge for each student is to solve as many problems correctly as he or she can. Progress charts are included so students can chart their week-to-week progress. The levels of difficulty of the weekly problems are held steady through the year. This allows students make and monitor meaningful gains from week to week.

**4) Math Breakdown Activities**

Math Breakdown Activities connect with the Four-Phase Problem Solving strategy. For each word problem,

• Students break the problem down and list all the facts that are provided, and the question being asked.

• Students devise a problem-solving plan, get their plan approved by the teacher, and solve the problem. The students and teacher work together to evaluate everybody’s work and answers. Students must correct any mistakes that were made.

• Students create a new problem that is similar to the one they just solved. Each student solves their own problem.

• Students work with a partner, swap problems, solve each other’s problem, and work together to evaluate each other’s work.

The Math Breakdown Activities provide word problems and Math-Breakdown templates for students to use.

**5) My Math Dictionary**

My Math Dictionary is a set of visual organizers that students can use to organize math vocabulary, and create and maintain their own math dictionaries. The visual organizers help students organize vocabulary into important categories like whole numbers, fractions, integers, algebra, measurement, plane geometry, 3-D geometry, probability, statistics, and more. As new math vocabulary appear in units and lessons, students enter those words into their dictionaries and construct their own definitions and examples.

**High Achievement Math Program; Critical Thinking Summary**

The High Achievement Math Program Critical Thinking Activities are sure to raise students’ levels of engagement, thinking, and achievement. These activities are a great supplement to any math program, and provide a huge bang for the buck. The program provides 40 Paired Learner Activities, 100 Mental Math Strings, 36 weekly Computation Challenges, and more. (**$19.00**)

## Item description

High Achievement Math Program; Critical Thinking ActivitiesWhen math students are engaged in critical thinking, they grow. Students expand their vocabulary, depths of understanding, math skills, frames of reference,, and overall interest in math.

The Critical Thinking Activities component of the High Achievement Math Program engages students through five powerful activities.

1) Paired Learner Activities (P3CR)Paired Learner Activities are critical thinking activities that engage students in problem solving, collaboration, communication, connections, and mathematical reasoning (P3CR). Each activity connects with a foundational math strand (number sense, algebraic thinking, measurement, geometry, probability, statistics). Paired learners would work together to read the activity, develop a problem solving plan, implement the plan, and evaluate their solutions and work. Generally, each P3CR activity is contained on a single page, and takes students about 15-20 minutes to complete . A great way to build Paired Learner Activities into the class routine is to consistently implement one P3CR activity every Friday, or another day of the week. P3CR activities come with answer keys and student score-keeping forms. The P3CR activities are excellent math activities that will help all students grow.

2) Mental Math StringsMental Math Strings combine vocabulary, mental math, and fun. Each string consists of simple commands that teachers read and students follow. Here’s an example.

• Start with the number of quarts in two gallons

• Square your answer

• Round your answer to the nearest ten

• Add the number of minutes in one hour

• Add the digits of your answer together

• Cube your final result (Answer: 27)

Students execute each command mentally. No paper, pencils, or calculators are allowed. At the end of the challenge, a student who succeeds verbally works through the Mental Math String line by line so all students know how to arrive at the correct answer. Mental Math String challenges are great tickets-out-the-door activities.

3) Computation ChallengesComputation Challenges are ten-question, ten-minute, half-sheet problem sets that challenge students to skillfully calculate with whole numbers, fractions, decimals, and integers. Computation Challenges also engage students in place value, Order of Operations, simple equations, and more. Computation Challenges are best implemented one day each week, perhaps on a Friday, before the Paired Learner Activity. The challenge for each student is to solve as many problems correctly as he or she can. Progress charts are included so students can chart their week-to-week progress. The levels of difficulty of the weekly problems are held steady through the year. This allows students make and monitor meaningful gains from week to week.

4) Math Breakdown ActivitiesMath Breakdown Activities connect with the Four-Phase Problem Solving strategy. For each word problem,

• Students break the problem down and list all the facts that are provided, and the question being asked.

• Students devise a problem-solving plan, get their plan approved by the teacher, and solve the problem. The students and teacher work together to evaluate everybody’s work and answers. Students must correct any mistakes that were made.

• Students create a new problem that is similar to the one they just solved. Each student solves their own problem.

• Students work with a partner, swap problems, solve each other’s problem, and work together to evaluate each other’s work.

The Math Breakdown Activities provide word problems and Math-Breakdown templates for students to use.

5) My Math DictionaryMy Math Dictionary is a set of visual organizers that students can use to organize math vocabulary, and create and maintain their own math dictionaries. The visual organizers help students organize vocabulary into important categories like whole numbers, fractions, integers, algebra, measurement, plane geometry, 3-D geometry, probability, statistics, and more. As new math vocabulary appear in units and lessons, students enter those words into their dictionaries and construct their own definitions and examples.

High Achievement Math Program; Critical Thinking SummaryThe High Achievement Math Program Critical Thinking Activities are sure to raise students’ levels of engagement, thinking, and achievement. These activities are a great supplement to any math program, and provide a huge bang for the buck. The program provides 40 Paired Learner Activities, 100 Mental Math Strings, 36 weekly Computation Challenges, and more. (

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