# Mathematical goals. Starting points. Materials required. Time needed

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1 Level N of challenge: B N Mathematical goals Starting points Materials required Time needed Ordering fractions and decimals To help learners to: interpret decimals and fractions using scales and areas; find equivalent fractions; relate fractions and decimals; order fractions and decimals; and to reflect on and discuss these processes. Learners will have met these concepts before. Many, however, may still have misconceptions and difficulties. Typically, these include: confusing decimal and fraction notation (e.g. is confused with 4.4 or 0.4); believing that the magnitude of a decimal depends on the number of digits it contains (e.g > 0. because 62 >, or 0.4 < 0.32 because 0.4 is in tenths and 0.32 is in hundredths); ignoring numerators when comparing fractions (e.g. 4 > 3 5 because quarters are greater than fifths). During the session, learners will confront and discuss such misconceptions. Also, many learners associate fractions with part/whole areas and decimals with number lines. This activity aims to build a more connected understanding of all these ideas. For each learner you will need: mini-whiteboard. For each small group of learners you will need: Card set A Decimals; Card set B Fractions; Card set C Areas; Card set D Scales. For learners who struggle, keep in reserve Card set E Areas and Card set F Scales. These goals may be adapted for learners aiming at lower level qualifications. For example, you may decide to focus just on interpreting and ordering decimals. For learners aiming at lower levels, use Card sets E (instead of C) and F (instead of D). Each card set includes one blank for learners to use when creating their own cards. Between 30 minutes and hour, though this will vary depending on the learners involved. Level of challenge: B N

4 Level of challenge: B BLANK PAGE FOR NOTES N 4

5 N Card set A Decimals N 5

6 N Card set B Fractions N 6

7 N Card set C Areas C C2 C3 C4 C5 C6 C7 C N 7

8 N Card set D Scales N

9 N Card set E Areas E E2 E3 E4 E5 E6 E7 E N 9

10 N Card set F Scales N 0

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