A foamed sheet containing a polymer composition including a polymer formed by polymerizing a mixture including 40% to 90% of styrenic monomers; 5% to 45% of maleate-type monomers; 0.1% to 25% by weight of elastomeric polymers with Mn greater than 6,000; and 0.1% to 10% by weight of low molecular weight polymers that include one or more monomers according to the formula CH.sub.2.dbd.CR.sup.3R.sup.2, where R.sup.3 is H or a C.sub.1-C.sub.3 alkyl group and R.sup.2 is a C.sub.1-C.sub.22 linear, branched or cyclic alkyl or alkenyl groups. The low molecular weight polymer has Mn of from 400 to 6,000 and can optionally include functional groups. The foamed sheet is made by injecting blowing agents into the polymer melt composition; mixing the blowing agent with the polymer composition; and extruding the mixture to provide a foamed sheet. The foamed sheets can be thermoformed into containers suitable for use in microwave heating of food.