Lesson 1 was a problem-solving lesson on algebraic thinking designed to show teachers the implementation of anchor tasks. The anchor task for this lesson is taken from Primary Mathematics Grade 6 textbook for algebra but for the fifth graders, we did not move to formally writing expressions. The problem is to arrange five consecutive whole numbers in the arrangement seen in the photos such that the vertical sum and horizontal sum are equal. Students articulate the general pattern they saw using words. They saw several patterns. With little guidance, one student saw that "in a population, if there are more even numbers then the numbers in the middle are even". With some help a girl saw that one of the totals can be obtained by "times-ing 3".
Lesson 2 is the first lesson on finding 1/2 of 3/4. Students used paper folding to discuss the anchor task. Two main ideas emerged - halving the entire 3 fourths and halving each of the fourths.The focus today is to review a fraction of a whole number and using it to do say 1/2 of 6 eighths as 1/2 of 6 apples.
This open lesson is for teachers to study the three-part lesson format and differentiated instruction.
A student later articulated that what helped were (1) the paper and (2) the 'advice' which is essentially is instruction between desks or differentiated instruction - different kids got different advice based on their current level of understanding.