About the Lessons
Thinking With Numbers is an online math education platform offering three unique and interactive sections of lessons. By joining us you gain access to hundreds of lessons from the following three "Making Sense of" sections:
Counting is an important skill that young children need to learn, but it is far more than a rote activity. There are common errors and misconceptions that children encounter while learning to count. The lessons are designed address each of these difficulties.
The lessons focus on helping children make sense and answer the following questions:
- What number comes next?
- Do these sets match one-to-one?
- What does the last number you count tell you?
- Does the order you count make a difference?
- If sets match, do they have the same number?
- How can you use matching to compare sets?
- Does moving the objects change the number?
- Does replacing objects change the number?
- Does adding or removing objects change the number?
- What number is one more? …two more?
- What number is one less? …two less?
The lessons provide the structure, imagery, and challenge for children to deeply understand and make sense of counting. Paper-and-pencil assessments provide feedback to help teachers or parents determine student achievement.
Learn more about the Counting And Comparing lessons by clicking on the View Sample Videos button to the left!
These lessons enable students to understand numbers and their partitions. Each of the lessons makes use of representations, such as the five-frame, ten-frame, and a part-part-whole diagram, to help students understand and solve the problems without counting.
The lessons provide experiences for students to successfully recognize the number of objects in a five-frame, a ten-frame, and objects arranged in common patterns, without counting. Students are challenged to figure out the number of objects under a cloud, after animations.
Four types of problems follow:
- Given part of a number, figuring out how many need to be added to make a given whole.
- Given the whole number and a part that is removed, figuring out how many are remain hidden.
- Given the whole number and a part that needs to remain, figuring out how many need to be taken away.
- Children are asked to figure out a hidden part when a number is separated into more than two parts.
Collectively these lessons help children put numbers together and take them apart. This contributes to the development of number sense. Paper-and-pencil assessments provide feedback to help teachers or parents determine student achievement.
Learn more about the Numbers And Paritions lessons by clicking on the View Sample Videos button to the left!
The first purpose of these lessons is to provide daily opportunities for students to explore and make sense of using addition and subtraction in everyday life. The second purpose is to help them develop reasoning strategies, which leads to confidence and fluency with basic facts.
Students solve word problems, create word problems, and figure out the number of objects hidden behind clouds after animations. These explore lessons include all of the different problem structures, as identified by Cognitively Guided Instruction, and lay a foundation for the reasoning strategies that follow.
Students make sense of and learn when to use counting on, counting back, counting up to subtract, using ten to add and subtract, using known facts to add and subtract, using nice numbers and changing the problem, then adjusting. Strategic choice, of these reasoning strategies, enables students to quickly and efficiently solve all basic facts and mental computation problems with two- and three-digit numbers.
Students estimate with two- and three-digit numbers using four different strategies. They also make sense of written computational procedures.
Paper-and-pencil assessments provide feedback to help teachers or parents determine student achievement. On-line assessment reports for each reasoning strategy provide feedback to demonstrate progress and to identify students who are not yet using a specific reasoning strategy.
Learn more about the Adding And Subtracting lessons by clicking on the View Sample Videos button to the left!
