We are a small but mighty group this week. As introduced in last week’s blog, math work starts with the concrete and leads naturally to the abstract. We had lots of progress in math this week. Many students are working with fractions. They are learning to add and subtract fractions with different denominators and to multiply whole numbers by fractions. All fraction work begins with students using cut pieces of circles, called fraction insets. In their addition and subtraction work, they manipulate the pieces to figure out what the common denominator is. After doing several problems, we look to see if they recognize a pattern in what they are doing. As they work, students notice that:
- To add or subtract fractions with different denominators, all fractions must be reduced to the same denominator.
- To change the terms of a fraction, they either multiply or divide both terms by the same number.
- If they multiply or divide the terms of a fraction by the same number, the value of the fraction doesn’t change.
In their work with the multiplication of whole numbers by fractions, they start by taking the whole circle insets and changing them into the number of fraction pieces they need in order to multiply. Students begin to notice that, as the denominator of the multiplier is increased, the total product is decreased. They then begin to notice the pattern, they simply have to multiply the whole number by the numerator to get their new numerator and the denominator stays the same. All students working with fractions are also learning to reduce their answers to the lowest terms.
We also have students working with decimal numbers, multiplying binomials, and squaring trinomials. I look forward to sharing more details about those lessons with you in the next few weeks.
Wishing you a beautiful weekend,
Karen and Angie